The LTL Checker Plugins a (reference) manual

The LTL Checker Plugins
a (reference) manual
HT de Beer
H.T.d.Beer@student.tue.nl
Eindhoven, October 3, 2005
Contents
1 Introduction
2 Use
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
of the LTL Checker Plugins
Introduction . . . . . . . . . . . . . . . . .
Importing LTL Template Files . . . . . .
Using the stand alone LTL Parser . . . .
Starting the Default LTL Checker Plugin
Starting The LTL Checker Plugin . . . . .
Using the Template GUI . . . . . . . . . .
Viewing the Results . . . . . . . . . . . .
Exporting the Results . . . . . . . . . . .
Reusing the results . . . . . . . . . . . . .
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3 LTL Language
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
3.2 The Environment in which the Language operates
3.2.1 A running Example . . . . . . . . . . . . .
3.3 Definitions and Comments . . . . . . . . . . . . . .
3.3.1 Comments . . . . . . . . . . . . . . . . . . .
3.3.2 Attribute Definitions . . . . . . . . . . . . .
3.3.3 Renaming of defined Attributes . . . . . . .
3.3.4 Formula Definitions . . . . . . . . . . . . .
3.4 Formula calls . . . . . . . . . . . . . . . . . . . . .
3.5 Comparisons . . . . . . . . . . . . . . . . . . . . .
3.5.1 Standard comparisons . . . . . . . . . . . .
3.5.2 The string type operators and literals . . .
3.5.3 The set type operators and literals . . . . .
3.5.4 The date type literals . . . . . . . . . . . .
3.5.5 The number type literals and expressions .
3.5.6 Examples . . . . . . . . . . . . . . . . . . .
3.5.7 Parse errors . . . . . . . . . . . . . . . . . .
3.6 Propositional Logic . . . . . . . . . . . . . . . . . .
3.6.1 Not . . . . . . . . . . . . . . . . . . . . . .
3.6.2 And . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Or . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 Implication . . . . . . . . . . . . . . . . . .
3.6.5 Bi-implication . . . . . . . . . . . . . . . . .
3.6.6 Examples . . . . . . . . . . . . . . . . . . .
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3.7
3.8
3.6.7 Parse errors . . . . . .
Quantificational Logic . . . .
3.7.1 Universal Quantor . .
3.7.2 Existentional Quantor
3.7.3 Examples . . . . . . .
3.7.4 Parse errors . . . . . .
Linear Temporal Logic . . . .
3.8.1 Nexttime . . . . . . .
3.8.2 Eventually . . . . . .
3.8.3 Always . . . . . . . .
3.8.4 Until . . . . . . . . . .
3.8.5 Examples . . . . . . .
3.8.6 Parse errors . . . . . .
4 Grammar
4.1 Literals . .
4.2 Identifier . .
4.3 LTL File . .
4.4 Propositions
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2
Chapter 1
Introduction
This document is both a user manual for the LTL Checker plugins of the ProM
framework and a reference manual for the LTL Language. If you are only
interested in how to use the plugins, just read Chapter 2.
In that chapter, you will read about how to import your own LTL Template
files via the LTL Template Import plugin. Hereafter the most attention is on
how to start and use the Default LTL Checker plugin and the ’normal’ LTL
Checker plugin. At the end of the chapter, you will see that results obtained
from using the LTL Checker plugins can be used again in the ProM framework
as you can use every log.
On the other hand, if you are interested in how to specify your own LTL
properties, you will have to read chapter 3 too. That chapter explores all the
details of the LTL Language, from defining attributes to creating complex LTL
expressions. This chapter uses a simple running example to explain all the
language elements. This example is as LTL Template file and test log file added
to this manual, running.ltl and running.xml.
The last chapter contains the grammar of the LTL Language. It can be
used as a short summary of the chapter about the LTL Language, without any
explanation the structure of the language is presented.
3
Chapter 2
How to use the LTL
Checker Plugins
2.1
Introduction
This chapter is about how to use the LTL Checker plugins. There are three
different plugins which are all grouped under the name ”LTL Checker plugins”.
These plugins are an LTL Template Import plugin, a Default LTL Checker
plugin and the ”normal” LTL Checker plugin.
Figure 2.1: The ProM window after a first start.
The LTL Template Import plugin is a plugin to import LTL Template files.
LTL Template files are files containing the specification of properties written
in the special LTL Language ( Chapter 3 ). After importing such files, the
4
properties specified in it can be used to check workflow logs of processes: which
instances of the processes have the property?
The actual check is performed by one of the LTL Checker plugins. The Default LTL Checker plugin uses a standard LTL Template file with some common
ltl properties defined in it. By the ”normal” LTL Checker plugin there is no
standard LTL Template file, you can choose which LTL Template file you want
to use, just import that one.
Both the Default and the ”normal” LTL Checker plugins are analysis plugins.
These analysis plugins can be used on all mined logs given an appropriate input.
This means that if you will use the LTL Checker plugin, you should first mine a
log. Fortunately there is an empty mining plugin in the framework, using that
”mining algorithm” mining is reduced to just reading the log.
In the next sections of this chapter, all steps taken and windows encountered
while using one of the LTL Checker plugins are explained in full detail. The
first plugin to be explained is the LTL Template Import plugin.
2.2
Importing LTL Template Files
The window of the ProM framework will look like the window displayed in Figure
2.1. In this figure the window of ProM is displayed directly after starting ProM.
While using ProM, thus after mining, importing and analyzing, this window
may be filled with many internal windows. Because the goal of this chapter is
to teach you how to use the LTL Checker plugins, it is assumed that you start
ProM from scratch, just to keep things simple.
Figure 2.2: The import menu.
For importing an LTL Template File, you go to the File-menu, and then to
the sub menu Import. In this menu you can choose one of the items listed (
Figure 2.2 ), one of items is LTL template file. Click on this item and a new
open dialog is displayed.
5
Figure 2.3: The open dialog for importing LTL Template files.
In this dialog, you navigate to the directory containing the LTL Template
file you want to import, select this file, and click the Open button ( Figure
2.3 ). It is a good custom to give your LTL Template files the extension .ltl
because you will more easily recognize your ltl-files, and in the open dialog files
are initially filtered on this extension.
Figure 2.4: The contents of the imported LTL Template file are displayed.
Now the framework tries to open the LTL Template file. The file is parsed
by the LTL Parser and the contents of the file are putted in a read-only text
6
box. This window, you see it on Figure 2.4, has no functionality at all, but may
be, in some future it will become more elaborate.
Now the import has succeeded, as you can see in the message pane at the bottom of the ProM framework window: Parsing complete. /home/htdebeer/TestLTL/test11.ltl imported. Of course you will see the path and filename
of your imported file, but the message is clear.
If the import does not result in success, a message is also given in the message
pane: Importing of /home/htdebeer/TestLTL/test01.ltl aborted. In the
message pane under the tab error can you find the error message, which gives
the reason why or a hint how to solve the problem. For more information about
the parse error messages, have a look in the next chapter.
2.3
Using the stand alone LTL Parser
Happily the LTL Parser is also available as a stand alone program, so for debugging your own LTL Template files, you do not need to start ProM. The stand
alone LTL Parser can be started by typing the following on the command line,
assuming you are in the base directory of ProM:
java -classpath "lib/plugins/ltlchecker.jar" ←org.processmining.analysis.ltlchecker.parser.LTLParser ←file to parse . When you are using the DOS operating system, you have
to change the slashes into backslashes. The LTL Parser expects exactly one
filename.
If the parsing is successful, no message is send to standard out, the prompt
returns directly. If there is an error while parsing, a message is send to standard
out, consisting of the kind of error, and on the next line the message of the error.
There are three kinds of errors possible:
1. Error occurred during parsing: The file is opened, but the contents
are not parseble by the LTL Parser. The most likely reason is that you
have made an error by writing ltl expressions.
2. Error while reading filename. Check the file(name) and try again.
There are problems with opening and reading the file. Maybe the file does
not exist or it is already in use by another program.
3. Unknown error: All errors not of kind one or two are unknown, that is,
they are not expected by the parser but are thrown nonetheless. Most
likely it is then a bug, so send a bug report containing the error message,
and LTL Template file you try to import.
7
2.4
Starting the Default LTL Checker Plugin
Figure 2.5: A log is mined with the No mining action mining plugin.
How to start the Default LTL Checker plugin is explained in this section.
The Default LTL Checker Plugin can be started on every (mined) log, that is,
the active internal window of the ProM framework window should contain such
log. For now, we open just a log an mine it with the No mining action mining
algorithm ( Figure 2.5 ). This mining plugin does nothing but read the log and
displays the contents of it in a new window. If you want, you can visualize one
process instance.
Figure 2.6: The analyze menu to start the Default LTL Checker Plugin.
Now, with this new window ( or another log) activated so that it is the only
active internal window of the ProM framework window, you can run the Default
LTL Checker plugin via the menu Analyze, as is displayed in figure 2.6. After
8
clicking one of the Default LTL Checker Plugin menu items, a new window is
opened: the Template GUI ( Section 2.6 ).
The Default LTL Checker plugin can also be started as you can the LTL
Checker plugin, but that is explained later.
Internally the standard LTL Template file is parsed. This file, called standard.ltl
and can be found in the lib/plugins subdirectory of the ProM base directory.
You can change the contents of this file to your own needs. But, here again, it
is a good idea to try to parse a new standard ltl file before you use it ( Section
2.3 ). If the standard file can not be opened or parsed, a message box is shown
with the error message in it.
2.5
Starting The LTL Checker Plugin
While the Default LTL Checker Plugin does not need an imported LTL Template
file, the LTL Checker Plugin must have access to at least one such imported file.
Here too, as was the case for the default plugin, you should have an opened (
and mined) log to use this plugin.
Once you have both, log and LTL Template file, you can start the LTL
Checker Plugin by opening the Analysis window. This plugin can not be accessed through the Analyses menu because it needs two inputs: a log and an
LTL Template file, it is up to you to select the appropriate input.
Figure 2.7: The analyze window.
You can open the Analyze window by clicking on the binoculars button on
the toolbar ( or press ALT + A). This window is displayed in Figure 2.7. As you
can see, on the left hand side of the window you can select an analyze plugin.
In this case you will select the LTL Checker Plugin. But as said before you can
also select the Default LTL Checker plugin.
On the right hand side of the window you can select the log to check (the
first combo box) and the imported LTL Template file in which the property
9
to check can be found. Now the LTL Checker Plugin has enough information
to start, so click the Next button and a new internal window is displayed: the
Template GUI.
2.6
Using the Template GUI
Figure 2.8: Choosing a formula in the Template GUI.
The Template GUI is a window consisting of four parts and a check button.
The first part is a list of formula names from which you can choose a formula.
This selected formula is used to check on the log.
Initially the first formula of the list is selected. If no formulae are defined
the item no formulae is visible and selected. In the second part of the window,
the description pane, you will see the description, if any, of the selected formula
( Figure 2.8 ). If the imported LTL Template file is created with care, there
should be a description for every formula. If not, just guess what the meaning
is of the selected formula.
The third part of the window is the parameter table. If the selected formula
has any parameters these parameters are shown in this parameter table ( Figure
2.9 ).
10
Figure 2.9: Fill in some parameters in the Template GUI.
It is up to you to fill in the values you want for the different parameters.
Every row of the table exists of three columns: a name, a type and a value.
Initially every parameter has an initial value. For number attribute parameters
it is 0.0, for date it is the date of today formatted in the format specified by
the definition of the attribute, for both string and set attribute parameters the
initial value is type a string.
You can only fill in those values that are acceptable values for the different
kinds of attribute types. This means that every value, in case its type is number
or date, is parsed to a value of that type. If this parsing is successful, the new
value is placed into the table, if the parsing does not succeed the old value does
not change.
It is good to know that you can only fill in literals. That is, attribute names,
string lists and other formulae are not accepted as values, they are interpreted
as strings and, in cases of date and number attributes, they are parsed as dates
or numbers respectively.
Once you have set the values you want for the parameters, you can use the
next part of the Template GUI to set some check options. This part is right of
the list with formulae. There are three options you can choose from:
1. Check whole process Check all process instances in the log for the selected
formula.
2. Check till first failure Check all process instances in the log, but stop at
the first encountered process instance not having the property specified
by the selected formula.
3. Check till first success The reverse of the previous item. Check all process
instances in the log, but stop at the first encountered process instance
having the property.
11
Figure 2.10: The actual checking is going.
If you have set the check option you want and the parameters are valuated
as you wish, you can click the Check button to start the actual check ( Figure
2.10 ). You will find this Check button below the list with formulae, so in case
you select a formula without any parameters, you can then click directly the
Check button to start checking.
By the first check, the sets for the defined set attributes are created ( these
sets are reused by next checks ) and the check starts hereafter. While checking,
the progress of the check is displayed together with the name of the ’current’
instance ( On the figure, the names are just numbers, but it can be every string
). If you want to stop the checking, just click the Cancel button on the progress
window. After the check is done, a new window is displayed: the results window.
12
2.7
Viewing the Results
Figure 2.11: The window with the results: a tab with correct instances and one
with incorrect instances.
On the results window you see first the name of the checked formula. Below
this text, the window is divided into two tabs: one with the correct instances
and one with the incorrect instances. Both tabs have the same structure. In
the title of the tab, between parentheses the number of instances on that tab
is given. So you can easily see how much instances of the log are correct or
incorrect ( Figure 2.11).
On the tab itself you see two parts: the actual table with the instances on
the left and a visualization pane on the right. In this table, the process instances
are listed, the name of the instances exists of the process instance name and
between parentheses the rank of the instance in the log. Now you can easily see
how the correct and incorrect instances are distributed over the log.
The visualization pane on the right hand side of the log can be used to
visualize one of the instances listed in the table. Just select an instance and
click the Visualize selected button to create a visualization of the instance.
Both the lists of correct and incorrect instances can be exported or reused
as ordinary logs can be. Furthermore, a visualization can be exported too.
13
2.8
Exporting the Results
Figure 2.12: Exporting the results: logs and visualizations.
Exporting of the results, both the lists with instances and the visualizations,
is very easy. As in Figure 2.12 can be seen, just go to the File menu, sub menu
Export and click on the desired export. A save dialog is displayed then, in which
you can give a name and a place to save the export to.
2.9
Reusing the results
Figure 2.13: On the results the LTL Checker analysis can be done again with
the Default LTL Checker plugin.
It is possible to use the results of a check again in the ProM framework, for
example as input to the LTL Checker plugins. Both the Default LTL Checker
plugin ( Figure 2.13 ) and the ”normal” LTL Checker Plugin ( Figure 2.14 ) can
be applied on a result log, either the list with the correct instances or the list
with the incorrect instances.
14
Figure 2.14: On the results the LTL Checker analysis can be done again, also
the using the LTL Checker plugin.
So it is possible to refine logs as far as you want, till the point you are
satisfied. For example, you can filter first all instances with property P, and then
on those instances check for property Q. Of course, you can create a formula R
equivalent to P ∧ Q, which gives the same results, but then, you should know
beforehand you want to check both P and Q. Furthermore, how smaller the log,
how faster the check.
15
Figure 2.15: On the results the LTL Checker you can also run a mining algorithm.
Not only the LTL Checker plugins can be used on the result logs, other
plugins can be used too. For example the mining algorithms. In Figure 2.15
you see the Mine menu containing all the possible combinations of result log
and mining algorithm, just choose the desired item to start the mining.
16
Chapter 3
The Language to specify
LTL Properties: a reference
3.1
Introduction
Using the Default LTL Checker plugin or the LTL Checker plugin with LTL
Template files created by others is easy as you have read in the previous chapter.
Writing your own LTL Template files is another matter. This chapter tries to
give a full and complete overview of the LTL Language, so that you can specify
your own LTL properties.
Before the language itself is explained, the environment the language operates in is given.
3.2
The Environment in which the Language operates
The LTL Language specifies properties of workflow logs of processes. A process
can be seen as a list of N process instances. Every process instance itself is a
list of M ordered audit trail entries ( Figure 3.1). Actual M can be different
for any process instance. Both audit trail entries and process instances can
have data fields. About audit trail entries we know that there are always a
WorkflowModelElement and an EventType data field, other fields are permitted
too.
17
Figure 3.1: A log
In the language those date fields can be accessed by defining ( Subsection
3.3.2) attributes of the appropriate type ( number, set, string or date ) for
the data fields. Later these attributes can be used in logical expressions via
comparisons ( Section 3.5).
The value of these attributes depends on the ”current” audit trail entry while
checking the log. A log is checked one process instance a time. Every process
instance is checked by inspecting the audit trail entries one for one from the
last till the first. The current audit trail entry is that audit trail entry which is
currently inspected by the checking algorithm.
The value of an attribute is computed by getting the value of the corresponding data field of the current audit trail entry. If needed, this string value
is parsed to the appropriate type, thus in case the attribute is defined of type
number or type date it is parsed.
In the language you can use different sorts of logical expressions. First of
all, the ”normal” propositional logic. This logic is about truth values only,
that is, an expression is true if the operator applied on the operands results in
true, otherwise it results false. The context of a propositional logic expression
is determined by the temporal operators. If no temporal operators are used, a
logical expression is about the first audit trail entry of a process instance only.
Another sort of logic is the quantificational logic which you can use to specify
properties over all members of a set. Here again, the context of a quantificational
expression is determined by temporal operators.
The last kind of logical expressions are linear temporal logic expressions.
With these LTL operators you can specify properties about the current audit
trail entry, the next current trail entry given the current audit trail entry, any
audit trail entry given the current or all audit trail entries given the current
audit trail entry. The current audit trail entry is initial the first, so by not using
temporal operators, all logical expressions are about this first current initial
audit trail entry.
The temporal operators are the operators which gives you the possibility to
specify properties about a whole process instance, about all audit trail entries
of a process instance. You can specify temporal relations between audit trail
entries and so you change the context of the normal logical expressions.
18
3.2.1
A running Example
In this chapter a running example of a log existing of process instances of persons
doing different tasks is used. Every process instance has two data fields: a
name and a case number. For every audit trail entry minimal three data fields
are available: WorkflowModelElement, here called task ; Originator, here called
person and Timestamp, here not used. Furthermore, all audit trail entries do
have a EventType data field, but the value is always complete so this field is
not mentioned any more.
Figure 3.2: An example process instance
Besides those standard data fields, audit trail entries can have extra data
fields depending on the task. In Figure 3.2 you see a visualization of one of such
process instances of the example log. On the figure you see the current process
instance, that is the process instance for which a property is computed. The
current audit trail entry is the one with the red circle ( or the grey circle) called
D.
When new language elements are introduced they are explained by using this
figure. To be complete, for this running example there are two files added to the
manual: running.ltl and running.xml. The first file contains the ltl properties
specified this chapter and the second file contains a log to test the properties
specified in this chapter.
3.3
Definitions and Comments
An LTL Template file can consist of four different items: comments, attribute
definitions, renamings of those defined attributes and formula definitions. Those
items can be mixed in any order, but a definition can only be used if it is already
defined. Now the different items are described.
3.3.1
Comments
Comments are the most simple elements of the language. A comment starts
with a # and the rest of the line after the #, including the # is skipped by the
parser as comment.
It is a good practice to use comments in your LTL Template files to document
your files in such a manner that you and others can understand and adapt the
file later on, also after some time. It is very easy to create formulae, but to
19
understand them can be more difficult if the formulae becomes more complex,
then comments can be of great help.
Examples
We start our running example by creating some comment lines with some information about the file:
#######################################
# version : 0.0
# date
: 01122004
# author
: HT de Beer
##
Of course comments at the start of a file only is not that useful. It is also
possible to use comments in definitions of formula, after attribute definitions,
the line before renamings, and so on. Later on in this chapter, you will see
examples of this.
Parse errors
No errors specified.
3.3.2
Attribute Definitions
Definitions of an attribute are more complex than writing comments, but it is
easy enough. An attribute definition starts with a keyword denoting the type
of the attribute. There are four types and thus four keywords: number, set,
string and date.
After the type you give the name of the attribute. This name must be unique
and exists of two parts: a scope prefix and the name of the corresponding data
element in the workflow log. The scope prefix is either ”ate.” or ”pi.” and
denotes if the data element is an element of an audit trail entry (ate.) or if
the data element is an element of a process instance (pi). So if a data element
exists as well as a process instance element and as an audit trail entry element,
you can define both as an apart attribute because the scope prefix results in
two different names.
If you are not defining a date attribute, you are ready after putting a semicolon. For a date attribute you should give the := keyword followed by a date
pattern, and finally a semicolon too. Hereafter the different types are described:
• number
The first type of attribute you can define is the number attribute. A number attribute can contain values that can be parsed as integers or floating
point numbers. internally both integers and floating point numbers are
parsed to floating point numbers only. Examples are: 12, 12.34, 12.34e5,
9E-23 and -123444.
You define a number attribute for data element data-element as follows:
number pi.data-element; or number ate.data-element;, depending
on the scope of the data element.
20
• string
Attributes of type string are attributes which contain string values. Because in the log itself all data elements are strings, string attributes can
be used for all data elements. No extra parsing is needed from the data
element to an attribute. But when you want to use special properties of
dates, numbers or sets, it is a good idea to define data elements of the respectively type. For the string type, a special regular expression operator
is available ( Subsection 3.5.2 ).
You define a string attribute for data element data-element as follows:
string pi.data-element; or string ate.data-element;, depending
on the scope of the data element.
• set
The set type is used for quantification, because quantification can only be
used on set type attributes. For every set attribute a real set containing
all the unique values of this data element of all process instances and all
audit trail entries is created. An extra set operator is the in operator (
Subsection 3.5.3 ).
You define a set attribute for data element data-element as follows: set
pi.data-element; or set ate.data-element;, depending on the scope
of the data element.
• date
The last type is the date type. It can be used to access data elements
containing date strings. Because there are many forms in which a date
can be described, a special string, the date pattern is added to the date
type attribute definition. The date pattern is afterwards used to create a SimpleDateFormat object of the Java programming language. The
format of date patterns allowed is described at http://java.sun.com/j2se/1.4.2/docs/api/java/text/SimpleDateFormat.html, a web page containing
information about the SimpleDateFormat class.
For now we give a short description on how to create a date pattern, for
a full explanation, read the web page mentioned earlier. In short, a date
pattern exists of characters with special meaning. If you want to put
characters themselves in a data pattern, use a ”’” to enclose them. Now
a table with some date characters are given. This list is not complete,
therefor again, have a look at the web site mentioned earlier.
y
M
w
W
D
d
E
H
k
m
s
S
year
month in year
week in year
week in month
day in year
day in month
day in week
hour in day (0-23)
hour in day (1-23)
minute in hour
second in minute
millisecond
21
With these date characters, you now can build date patterns, like:
– yyyy-MM-dd : thus strings of the form 2006-12-09.
– ’date=’ddMMyy : strings like date=230907.
– HH:mm : strings denoting time like 12:45.
You define a date attribute for data element data-element and date pattern
”date-pattern” as follows: date pi.data-element := "data-pattern";
or date ate.data-element := "date-pattern";, depending on the scope
of the data element.
An attribute can only be defined and used if there is a corresponding data
element. All data elements you want to query about should be defined as an
attribute, also the standard data fields like WorkflowModelElement, EventType,
Timestamp and Originator. That these elements are treated separate from the
other data elements in the logs, does not mean they are treated special in
the LTL Checker and LTL Language. In fact, in the LTL Language all data
elements, the standard ones too, are treated the same.
Examples
Back to our running example of figure 3.2. As you can see in this figure a number
of attributes are available in the log. In this example we define all the attributes:
ate.WorkflowModelElement, ate.Originator, ate.dob, ate.distance, ate.question,
ate.answer, pi.name and pi.case.
#######################################
# version : 0.1
# date
: 01122004
# author
: HT de Beer
##
##
# Defining attributes:
##
set ate.WorkflowModelElement;
set ate.Originator;
date ate.dob := "yyyy-MM-dd"; # Date of birth: dates have the format ’year-month-day’.
number ate.distance;
string ate.question;
string ate.answer;
string pi.name;
number pi.case;
Parse errors
• Identifier is already defined
Occurs when you tries to define an attribute with the same name as another earlier defined attribute.
22
3.3.3
Renaming of defined Attributes
A renaming is exactly what it says: a renaming. In this case you can rename
a defined attribute, which must be the name of the data element prefixed with
either ”pi.” or ”ate.”, to a shorter, more readable or understandable alternative.
In fact, you can define as many alternatives as you want, as long as every
alternative has an unique name.
Of course, as is usual in programming languages, a name can not be equal
to one of the keywords. Thus as, ate, date, exists, forall, formula, in,
number, pi, rename, set, string, subformula are not permitted as names for
renamings and formulae. Furthermore, a name starts with a letter and can
consists of letters, digits, -, and .
A renaming can be created by the keyword rename followed by the attribute
name, the keyword as, the new name and finally the semicolon, as is the case
for all definitions. Thus for attribute name old-name and new name new-name
you write a renaming as follows: rename old-name as new-name;.
Examples
We now adapt our running example so that the defined attributes are named as
in figure 3.2. So ate.WorkflowModelElement is renamed as task, ate.Originator
as person and ate.dob as bdate. For the other attributes we rename them to a
new name without the scope prefix.
#######################################
# version : 0.2
# date : 01122004
# author : HT de Beer
##
##
# Defining attributes:
##
set ate.WorkflowModelElement;
set ate.Originator;
date ate.dob := "yyyy-MM-dd"; # dates have the format ’year-month-day’.
number ate.distance;
string ate.question;
string ate.answer;
string pi.name;
number pi.case;
##
# Renamings
##
rename ate.WorkflowModelElement as task;
rename ate.Originator as person;
rename ate.dob as bdate;
rename ate.distance as distance;
rename ate.question as question;
rename ate.answer as answer;
23
rename pi.name as name;
rename pi.case as case;
Parse errors
• Identifier is already defined.
The new name is already in use as another renaming or formula name.
• Identifier is not a defined attribute.
You try to rename a formula or a renaming, but that is not possible. You
can only rename attributes.
3.3.4
Formula Definitions
Now you can define attributes and rename them to something more writable, you
can use those definitions to define formulae. There are two kinds of formulae:
formulae and sub formulae. Both are defined exactly the same but the first
keyword, respectively formula and subformula, is different. The distinction is
that sub formulae are not visible in the Template GUI ( Section 2.6 ), that is,
they can not be called by the user of the GUI. Formulae are the visible formulae,
the formulae which the user can select and check.
A formula or subformula is defined as follows: the keyword formula or
subformula followed by an unique name, a list of parameters between parentheses (the list may be empty), the keyword :=, a description, the actual formula and finally the well known semicolon. Thus: formula A formula name (
arg1: attr1, arg2: attr2 ) := { A description } actual formula doing
something with the arguments ;.
The different elements of a formula definition are now explained.
The list of arguments of a formula
The list of arguments is a comma separated list of so called local renamings,
that is a new unique name in the local context followed by a colon and the
attribute the new name is a local renaming for. The name of the local renaming
can not be the same as a name of an attribute, renaming or formula, but it can
be the same as an argument of another formula.
Furthermore the attribute, comparable with types in programming languages, is an already defined attribute ( or a renaming of an attribute ). Such
a pair argument name : attribute name denotes that the name of the argument must be interpreted as a local renaming of the attribute. In expressions
later on in the formula definition, this name can be used as such ( but only on
the right hand side of an comparison, see Section 3.5 ).
The list, as said before, may be empty, but the parenthesis are obligatory in
all cases, also if the list is empty.
The description of a formula
A description of a formula is the part of the formula definition in which you
can inform the user of your defined formulae what the meaning and the use
of the formula is. In the Template GUI ( see section 2.6 ) the contents of the
24
description are displayed in the description pane. Because the description pane
renders its content as HTML 3.2, you can use those HTML 3.2 tags to create a
more elaborate description for the user.
In fact, it is recommend to use HTML 3.2 code in your description. But
only the contents of the body tag should be used because the rest of the HTML
code is supplied by the plugin itself. Furthermore it is advisable to create
your descriptions along the guidelines given below, just to create a consistent
view for the user. On the other hand, it is all up to you to do so or not.
I know programmers are lazy, so empty descriptions shall be used much. In
principle, there is nothing wrong with that, as long as you are writing the
formula definitions for your own. But once you write your formulae for an
(unknown) audience, use the description wisely.
A description is made out of braces where in between the contents of the
description are placed. The guidelines for writing a description:
1. Start with the title, or name of the formula in between h2 tags.
2. Divide your description into paragraphs using the p tags.
3. In the first paragraph you give a short description of the meaning of the
formula in terms of the arguments.
4. in the next paragraph, or, in case of a simple formula in the first, you
list the arguments using an unordered list( using the ul tag. Every item
in the list (create a list item with the li tag) starts with the name of
the argument in bold (b tag), followed by the meaning of the argument.
Give then the attribute in italics (i tag ) and the type of the attribute (
eventually in italics too). Then a recommendation of the value the user
should give. For example a range or the pattern of the date pattern in
case of a date attribute.
5. Write now a more detailed description and or other remarks if needed.
The actual formula
The actual formula is given in terms of propositional logic (section 3.6), quantification (section 3.7), linear temporal logic ( Section 3.8 ), comparisons ( Section
3.5 ) or (sub)formula calls ( Section 3.4 ). That is, the actual formula consists
of correct expressions ( in this language ) combined to bigger expressions by the
operators in this language.
Examples
For the running example we define now one formula, in which you see all elements of a formula definition. Because till now you have not learned how to
write the actual formula, a very simple formula is defined. The description as is
given here is the only full description according to the guidelines you will read
in this manual, because the goal is to learn to write ltl formulae, not to write
good descriptions.
25
#######################################
# version : 0.3
# ...
# This part of the file is as in example version 0.2
# ...
##
# Formulae
##
formula eventually_task_A_is_done_by_person_P( A : task, P: person ):=
{
<h2>Does eventually P task A?</h2>
<p>Is there a audit trail entry in a process instance in which person P
does task A?</p>
<p>
<ul>
<li><b>A</b> is a task, of attribute <i>ate.WorkflowModelElement</i>.
For this argument fill in the task you want to check for.</li>
<li><b>P</b> is a person, of attribute <i>ate.Originator</i>. Fill in
the person you want to know if he or she perform task A.</li>
</ul>
</p>
}
<>( ( task == A /\ person == P ) );
Parse errors
• Identifier already defined.
The name if this formula is already a defined identifier, either of an attribute, a renaming or another (sub)formula.
• Identifier is already defined or used.
The identifier used as argument name is already used as argument name
or as a global identifier, that is of an attribute, a renaming or a formulae.
• Identifier is not a defined attribute or renaming.
The identifier used as ’type’ of an argument is not a defined attribute or
a renaming, so it can not fulfill the role of an argument type.
3.4
Formula calls
A defined formula can be called in the actual formula part of a definition of
another formula. Important by calling a formulae is that the formula you want
to call must already be defined, you apply the right number of arguments, and,
of course, of the right type. That is, an argument of type A must be applied
with a value of type A, either an attribute itself ( the same, modulo renaming)
or a literal of the same type as the attribute.
26
You call a formula by entering the name followed by a parameter list surrounded by parenthesis, this list may be empty, according to the definition of
the formula to call.
The value of an argument in a call is bound at that place. With this feature,
you get the value of a data element of an attribute of the audit trail entry that is
current at the place the argument is used. If in the formula a nexttime operator
is used, the current audit trail entry becomes the next one, but the value of the
argument supplied to this formula stays the of the current one.
This ”early” binding can be useful when using the nexttime operator ( Subsection 3.8.1 ), because then the current audit trail entry becomes the next one
( if there is a next one of course ). With a formula call, you can supply such
nexttime operator with a value of a attribute before the then current. So you
can apply recursion of a sort. But you will read more on this subject in the
subsection about the nexttime operator.
Examples
Because our running example has only one formula defined yet, we call it here
in a new defined formula.
#######################################
# version : 0.4
# ...
# This part of the file is as in example version 0.2
# ...
##
# Formulae
##
formula eventually_task_A_is_done_by_person_P( A : task, P: person ):=
{
<h2>Does eventually P task A?</h2>
<p>Is there a audit trail entry in a process instance in which person P
does task A?</p>
<p>
<ul>
<li><b>A</b> is a task, of attribute <i>ate.WorkflowModelElement</i>.
For this argument fill in the task you want to check for.</li>
<li><b>P</b> is a person, of attribute <i>ate.Originator</i>. Fill in
the person you want to know if he or she perform task A.</li>
</ul>
</p>
}
<>( ( task == A /\ person == P ) );
formula does_John_drive() :=
{ Does John drive in a process instance? }
eventually_task_A_is_done_by_person_P( "driving", "John" );
27
Parse errors
• Identifier is not a defined formula.
You try to use a identifier of a attribute or renaming as a formula, and of
course, you can not call such a identifier as a formula.
• Defined number of parameters not equal the number of arguments applied
here.
You try to call a formula with not enough parameters, or with to much
parameters. Of course, this would not work, so assure that the number of
used parameters equals the number of defined arguments.
• Identifier has not the right type.
You try to use a identifier of an attribute or renaming or a local one with
a different type ( attribute) than defined in the formula definition. If at
place x in the argument list a argument of type A is defined, use a value
of type A on place x in the parameter list of the formula call.
• Identifier is not a local parameter in this context.
You try to call the formula with a identifier that is unknown in the local
context, so it is not known as a defined attribute or renaming, and not as
a argument to the formula in which the call is written down.
• Unable to parse this as a date given definition xyz
You fill in a date string as parameter, but this string can not be parsed
according to the definition of the used attribute in the argument list of
the formula definition.
• Type mismatch.
You try to use a string value on an argument of attribute with type number.
• Not expecting a integer.
A integer is applied where no number is expected.
• Not expected a floating point number.
A floating point number is applied where no number is expected.
3.5
Comparisons
The basis of formula definitions are the comparisons, that is the comparisons
of attributes, and thus data elements of process instances of audit trail entries,
with other values, which may be attributes too, but literals are also possible. All
attribute types have a number of ”standard” comparisons common, and some
have their own extra comparisons. First are the standard ones explained, then
per type the literals and special comparison operators are described. But before
that, the common form of a comparison is given.
28
Figure 3.3: Again the example process instance
A comparison exists of a left hand side attribute, thus no local argument,
with an operator and a right hand value. This right hand value is either a literal,
an attribute ( or renaming, or local argument) or a more complex expression in
case of number attributes.
A comparison results always false if in the current audit trail entry the left
hand side attribute ( and thus a eventually right hand side attribute too) does
not exist. In the running example a comparison of the form answer == "..."
results in false because the current audit trail entry, D, has no answer data
element.
So if you use a data element which does not exist for all audit trail entries,
be aware of the strange or unexpected results formulae may result.
3.5.1
Standard comparisons
==
The first standard comparison is the well known equivalence or ”is equal” operator ==. It compares the left hand side with the right hand side. Of course it
is true when both sides results in the same value given the current audit trail
entry ( and process instance).
In the example situation of Figure 3.3 where the audit trail entry labeled ’D’
is the current audit trail entry, a comparison like task == "driving" would
result in true, because task, referring to the ate.WorkflowModelElement and
corresponding data element has in the log the value ”driving”.
If the comparison was task == "asking" it would result in false, because
the data element WorkflowModelElement of the current audit trail entry has
value ”driving”.
!=
The ”is not equal” operator A != B is equal to !( A == B ) ( Subsubsection
3.6.1 ), and is the reverse of the == operator. So in the running example where
D is the current audit trail entry, task != "asking" is now true and task
!= "driving" false.
<=
The ”lesser than or equal” operator is denoted as <= and does just what you
expect that it does. Especially for date and number attributes this operator
29
and the counterparts >=, < and > are useful. For string and set attributes you
can use them for properties about the alfa numerical ordering of strings.
In the example distance <= 200 results in true in the current audit trail
entry there the distance is equal to 103.54.
>=
The bigger than or equal operator is denoted as >= and does just what you
expect, as all the standard operators do.
<
The lesser than operator is denoted as <.
>
The bigger than is denoted as >.
3.5.2
The string type operators and literals
A string literal looks like most string literals in most programming languages:
two quotes in which between the contents of the string is written down. In
principle every character can be in the string, only quotes themselves are not
permitted because they close the literals. For example "Hello world!" or
"980u908009ud0f098s0d8uf0u8sd0ff8us09d" are both correct strings.
For strings there is an extra operator: the regular expression operator ~=.
This operator has as string literal a string which is interpreted as a regular
expression pattern. Internally the matches method of the Java String class
is used, so if you want to know all the details of the patterns have a look at
http://java.sun.com/j2se/1.4.2/docs/api/java/util/regex/Pattern.html#sum.
Now follows a short introduction of regular expressions. With regular expressions you can specify patterns of characters, using special regular expression
operators.
Operator Meaning
Example
.
A arbritrary character
ma. : like may, mad, man, mau, ...
ˆ
The start of a line
$
The end of a line
regexp?
Zero or one time regexp
ma? : , ma
regexp+
One or more times regexp
ma+ : ma, mama, mamama, ...
regexp*
Zero or more times regexp
ma* : , ma, mama, mamama, ...
regexpx,y Between x and y times regexp ma1,2 : ma, mama
re1 | re2
re1 or re2
ma | pa : pa or ma
re1re2
re1 followed by re2
mapa : mapa, mamapa, mamamapa, ...
(re1)
Group re1
ma(pa)?ma : mama, mapama
[x-y]
Element of x...y
[1-9][0-9]+ : a number like 9, 83, 3859, ...
[abc]
Element of a b c
[dmy][1-9] : d3, y5, m5, m3, ...
With the building blocks given in this table you can construct more elaborate regular expressions, and more operators are available. To conclude this
very short introduction on regular expressions, some examples:
30
• .*word.* Search for strings with ’word’ in it, like this sentence.
• ID[0-9]{5,5} Search for strings starting with ID and followed by five digits.
ID98324, ID12347, etc.
• a*b* Search for sequences of n a’s, followed by m b’s, like aabb, abbbbbbbb,
aaaaaaaabbbb, etc.
• yes|Yes|y|Y Search for different ways to express yes.
3.5.3
The set type operators and literals
The set literals are exactly the same as string literals. That is easy explained:
the sets exists of just strings. Furthermore, the standard operators can be seen
as a cast to strings before using them, so you can test an individual value of
the set to another value. Sets are used for quantification, and therefor it is an
apart type.
Nevertheless a special set operator is defined: the in operator. It tests if the
left hand side attribute is in a by the user given set. It is of the form attribute,
the in keyword, and a list of strings, separated by comma’s between ”[” and
”]”. Because the language does not enforce the list to test for duplicates in the
set, it can be a multiset or bag too. In fact, internally it is transformed to a set,
but for you as user of the in operator, it is a bag. In the running example a
expression could be person in [ "John", "Mary", "Angilbert"], that is,
test whether the person of the current audit trail entry is either ”John”, ”Mary”,
or ”Angilbert”. In this case, it results true because in the current audit trail
entry ’D’ the person is ”John”.
3.5.4
The date type literals
The type date has no extra operators, but the literals themselves are more
powerful. In principle they are string literals too, but are interpreted with
the by the date attribute on the left hand side of the operator associated date
pattern. Those date patterns are explained before ( Subsection 3.3.2 ).
3.5.5
The number type literals and expressions
On the type number there are no extra comparison operators defined, but more
complex numerical expressions are possible. Number literals are either integers
or floating point numbers. That is, just digits, or digits with a period and
eventually an exponent ( for example 123, 0.4500988 or 314.9067E234 ).
The numerical operators are the well known ones: -, +, * and /. The unary
operator - is used as - value and the binary ones as ( value op value ).
The placing of parenthesis are a little bit strange and strict, but they are strict
too by the logical operators. Values can be either numerical expressions, number
attributes ( or renamings or arguments ) or number literals.
3.5.6
Examples
To the running example some helping formulae are defined with using some
comparison operators and literals. Because those comparisons are combined to
31
larger expressions with logical operators ( Section 3.6 ), those logical operators
are used although the meaning may not be completely clear yet.
#######################################
# version : 0.5
# ...
# This part of the file is as in example version 0.4
# ...
subformula has_Answer() := {
If the task is asking, then there is a answer not equal to the empty string.
This formula results in true for all task other than asking and for those
task equal to asking with a non empty answer.
}
( task == "asking" -> answer != "");
subformula distance_between( lbound: distance, ubound: distance ) := {
The distance of the current audit trail entry lies between the lower bound
and the upper bound. }
( distance >= lbound / distance <= ubound );
subformula reasonable_distance() := {
If the task is cycling, the distance must be between 0 and 65, if the task
is driving is must be between 0 and 300, if the task is flying, the distance
must be between 150 and 1340. }
(
( task == "cycling" -> distance_between( 0, 65 )
) /\
( ( task == "driving" -> distance_between( 0, 300 )
) /\
( task == "flying" -> distance_between( 150, 1340 ) )
)
);
subformula permitted_to_drive() := {
A person is permitted to drive if he or she is born before 2004-6-01. }
bdate < "2004-06-01";
subformula a_important_case() := {
Case is important if the word ’important’ is used in the name. }
name ~= ".*important.*";
3.5.7
Parse errors
• Identifier is not of type string.
This error is shown if you try to use the regular expression operator ~= on
attributes not of type string.
• Identifier is not of type set.
This error is shown if you try the in operator with attributes not of type
set.
• Expected value of type number.
32
You have used the special numerical operators with values or attributes (
which are more or less values too) not of type number.
• Unable to parse this as a date given definition . . . . .
Shown when you specify a date literal which is not parseble with the
pattern specified by the associated left hand side date attribute.
• Expected a string.
You use a left hand side attribute of type string, but the value you specified
can not be parsed as such.
• Identifier not defined.
You try to use an attribute or renaming as a value which is not defined
before use, hence this error.
• Type mismatch
The left hand side attribute and right hand side value does not match
types.
3.6
Propositional Logic
Now the comparisons and literals are explained, the basis for the propositional
logic is laid because the atoms of the propositional logic in the LTL language
are those comparisons. Furthermore, properly defined formulae exists of atoms
too, so they can be seen themselves as behaving like atoms, that is, resulting in
true or false. Let A and B correct atoms or formulae. They are used to combine
them with logical operators to larger expressions.
Figure 3.4: Again the example process instance
The explanation of the logical operators is done with the use of the running
example where the current audit trail entry is as it was before: D ( Figure 3.4
).
3.6.1
Not
The proposition !( A ) is true if and only if A itself is false. In a table:
A !( A )
0
1
1
0
33
As an example let A be answer == "Eindhoven". Now A is false, because
there is no answer data element in the current audit trail entry D, so !( answer
== "Eindhoven") is true. But the reverse holds too: let A be distance <
1000, with the distance equal to 103.54, you will see easily that the expression
!( distance < 1000 ) results in false.
3.6.2
And
The proposition ( A /\B ) is true if and only if A and B are together true. In
a table:
A B ( A /\B)
0 0
0
0 1
0
0
1 0
1 1
1
A simple example is ( task == "driving" /\person == "John" ) which
is true. In the next audit trail entry, this would be false, both the task and the
person are different, namely asking and Mary.
3.6.3
Or
The proposition ( A \/ B ) is true if and only if A or B is true ( if both are
true it is correct too, of course ). In a table:
A B ( A \/ B)
0 0
0
0 1
1
1 0
1
1 1
1
If the and operator in the last example is replaced with an or operator, it
stays true in the current audit trail entry. It is even true in the third audit trail
entry, where the person is John too.
3.6.4
Implication
The proposition ( A -> B ) is false if and only if A is true and B is false.
But be aware, the arrow denotes a logical value, not a causal relation or a time
relation at all. When one wants to state something about relations in time,
thus that if A holds next time should hold B, use the nexttime operator O. In
a table:
A B ( A -> B)
0 0
1
0 1
1
1 0
0
1 1
1
If a property is only important if another property hold, for example a (birth)
date must be before ”2000-06-05” when the task is driving. That is, a person
must be old enough to be permitted to drive a car, the implication is useful:
( task == "driving" -> bdate < "2000-06-05" ). But if driving does not
hold, the property with the implication is true. If you want to ensure that the
34
task is driving and if the task is driving then the date is lesser than some value,
use the and operator: ( task == driving /\bdate < "2000-06-05" ).
3.6.5
Bi-implication
The proposition ( A <-> B ) is true if and only if A and B have the same
value. This operator is also known as equivalence. In a table:
A B ( A <-> B)
0 0
1
0 1
0
0
1 0
1 1
1
As a example state that a non empty question is equivalent with a non empty
answer. Thus, if both are not in the current audit trail entry, or both are empty,
then it is true. If one of the data elements answer or question is empty or does
not exist, then it is false. If both does exist and are not empty, it is true too.
( question != "" <-> answer != "" ). This is true in the current and the
next state too.
3.6.6
Examples
In our running example we have already used some propositional logic operators,
in the next two sections, the logical operators are also used, so for now no
addition to the running example.
3.6.7
Parse errors
No errors specified.
3.7
Quantificational Logic
Quantification in this language exists of the universal (forall) and existentional
(exists) quantor. The meaning of quantification is in this context not that
clear, or to say it otherwise, formulae defined in this language can be seen as
universal quantification over all process instances of the log.
Furthermore the LTL operators always ([]) and eventually (<>) can be
compared with respectively the universal and the existentional quantor because
if there exists an audit trail entry with property A, then eventually holds A. And
if always holds A, then for all audit trail entries hold A. But quantification is
not directly about audit trail entries, but over sets, so the comparison between
those LTL operators and quantification is not complete, there are properties
which can not be specified with the LTL operators, but can with the quantors,
and vice versa.
On the other hand there is a drawback by using quantification, it is very
costly because quantification over a set S with property A results in a property of
length |S| times the length of A. So it is advisable to try to use the LTL operators
in stead of the quantors when possible. But, as said before, quantification is
sometimes needed, mostly to say something about all elements of a set. If one
wants to ask about one specific instance of a set, use the LTL operators.
35
The standard data elements of an audit trail entry, WorkflowModelElement,
EventType and Originator are the most likely candidates for quantification, and
thus for being a set attribute. But all data elements can be sets and therefor used
for quantification, so Timestamp or distance too. But then, those attributes are
sets, and the value of the element is a string rather than a date or a number.
3.7.1
Universal Quantor
The universal quantification computes if a property A holds for every element
in a set S. That is the property ∀s∈S (As ). An universal quantification is written
as follows: forall [ i: SetAttribute | Ai ]. With i: SetAttribute a local
renaming i for attribute SetAttribute of type set. The property to check for all
i is then A. If A holds for all i, this quantification is true.
3.7.2
Existentional Quantor
The existentional quantification computes if a property A holds for any element
in a set S. That is the property ∃s∈S (As ). An existentional quantification is
written as follows: exists [ i: SetAttribute | Ai ]. With i: SetAttribute
a local renaming i for attribute SetAttribute of type set. The property to check
for all i is then A. If A holds for any i, this quantification is true.
3.7.3
Examples
In the running example are now more complex properties specified using quantification. For example a formula to test if there is a person doing two different
tasks. The universal quantification is used to specify the property that all persons doing either moving or asking around, not both. Both properties are about
one process instance, and that for all process instances.
#######################################
# version : 0.6
# ...
# This part of the file is as in example version 0.5
# ...
subformula P_does_A-A_not_B( P: person, A: task, B: task ) := {
Compute if person P does task A, which is not equal to B.}
<>( ( task == A /\ ( task != B /\ person == P ) ) );
formula exists_person_doing_two_different_tasks() := {
Is there a person doing two different tasks?}
exists[ p: person
|
exists[ t: task
|
exists[ u: task |
( P_does_A-A_not_B( p, t, u) /\
P_does_A-A_not_B( p, u, t))
]
]
];
36
subformula moving( P: person ) := {
Compute if person P is moving. }
<>( ( person == P /\
(
task == "driving" \/
( task == "cycling" \/
task == "flying"
)
)
) );
subformula asking( P: person ) := {
Compute if person P is asking. }
<>( ( person == P /\ task == "asking" ) );
formula moving_or_asking() := {
All persons are either moving or asking around.}
forall[ p: person |
(
( moving( p ) /\ !( asking( p ) ) ) \/
( !( moving( p ) ) /\ asking( p ) )
)
];
3.7.4
Parse errors
• Identifier already in use in the local context.
You try to use a name for the dummy variable which is already used for
something else.
• Identifier is not a defined attribute or renaming.
The attribute you want quantify over is not defined.
• Identifier has not type set.
The attribute you want quantify over is not a set.
3.8
Linear Temporal Logic
The LTL language elements are the logical elements which express properties
about a sequence of audit trail entries of a process instance. So an LTL property
A is not a logical expression about the current audit trail entry, but over the
sequence of audit trail entries described by logic expressions about the current
audit trail entry. A and B are correct sub formulae as described earlier.
37
Figure 3.5: Again the example process instance
Again the figure of the running example, now to explain the LTL operators.
3.8.1
Nexttime
The nexttime operator is a very basic and simple operator. It express given
a current audit trail entry something about the next audit trail entry in the
sequence of audit trail entries in the current process instance. So you can
express more or less properties about subsequent states which have occurred.
The nexttime operator is an unary operator written as O( A ). In the Figure
3.5, where the current audit trail entry is D, O( person == "Mary" ) is true
because in the next audit trail entry, with name A, the person is Mary. If the
current audit trail entry was not D but the C before it, then O( O( person ==
"Mary" ) ) was true too. You see, the nexttime operator can be used repeatedly
to express some property about a specific audit trail entry given the current.
Use this nexttime operator to express recursion about states. Then, with the
always operator (see below) you can check if a property A holds for all states
of a process instance. Remark that A never hold in the last state, so to apply
such recursion, identify the last state, so that always nexttime A holds or it is
the last state. Combined with a formula call, you can use values of other states
in the current comparisons.
For finalization, it is recommended to use an end formula:
subformula end() := {
Only in the last state holds that in the next state a
WorkflowModelElement is not equal itself ( for other elements the same of
course) because in the next audit trail entry of the last state all
comparisons are false, the data elements does obviously not exist.}
!( _O( ate.WorkflowModelElement == ate.WorkflowModelElement ));
Using this end formula, it is also possible to specify properties relative to
the last state, if needed.
3.8.2
Eventually
The eventually operator checks if a property A does at least once occur in the
sequence of audit trail entries of a process instance. With <>( A ) you write
an eventually expression down. Remark the correspondence with the exists
quantor, but this eventually operator is about audit trail entries, and the exists
quantor about a set.
38
In the running example it is clear that <>( person == "John" ) holds,
there are audit trail entries with person is John, one of them the current audit
trail entry. Given this current audit trail entry, the expression <>( task ==
"asking" ) is true to, because the next audit trail entry is a asking.
3.8.3
Always
[]( A ) Express that A always, thus in all audit trail entries of a process
instance, hold. This operator can be compared with the universal quantification
as the eventually operator with the existentional. This operator is true on the
empty sequence or on the audit trail entry after the last one.
Use this operator to express that in all audit trail entries a property hold,
for example that every next audit trail entry the date of birth is lesser or equal
to the previous one. Hereby the end formula is needed to finalize the formula,
that is, that the property holds in the last state.
subformula next_older( d: bdate ) := {
Is d bigger or equal the current date? }
_O( bdate <= d );
formula always nexttime older() := {
Holds always that the birth date of the person in he next audit trail entry is
lesser or equal to the date of birth of the person performing the current
audit trail entry?}
[]( ( next_older( bdate ) end() ) );
3.8.4
Until
The until operator is the most complex operator, but it states that A holds till
B holds. When B holds, A may hold as well. You express this as ( A U B ).
Remark that if B never hold, but A does always from the current audit trail
entry, the property is true.
As example a property expressing that until there is any distance moved,
only questions are asked.
formula move_till_question() := {
}
(task == "asking" _U distance > 0
3.8.5
);
Examples
This section already contain useful examples, so here the last and complete
version of the ltl file is given to conclude this chapter. This example file can
also be found together with this manual in a file named running.ltl. A test
log is also supplied, with name running.xml.
#######################################
# version : 1.0
39
# date : 01122004
# author : HT de Beer
##
##
# Defining attributes:
##
set ate.WorkflowModelElement;
set ate.Originator;
date ate.dob := "yyyy-MM-dd"; # dates have the format ’year-month-day’.
number ate.distance;
string ate.question;
string ate.answer;
string pi.name;
number pi.case;
##
# Renamings
##
rename ate.WorkflowModelElement as task;
rename ate.Originator as person;
rename ate.dob as bdate;
rename ate.distance as distance;
rename ate.question as question;
rename ate.answer as answer;
rename pi.name as name;
rename pi.case as case;
##
# Formulae
##
formula eventually_task_A_is_done_by_person_P( A : task, P: person ):=
{
<h2>Does eventually P task A?</h2>
<p>Is there a audit trail entry in a process instance in which person P
does task A?</p>
<p>
<ul>
<li><b>A</b> is a task, of attribute <i>ate.WorkflowModelElement</i>.
For this argument fill in the task you want to check for.</li>
<li><b>P</b> is a person, of attribute <i>ate.Originator</i>. Fill in
the person you want to know if he or she perform task A.</li>
</ul>
</p>
}
<>( ( task == A /\ person == P ) );
40
formula does_John_drive() :=
{ Does John drive in a process instance? }
eventually_task_A_is_done_by_person_P( "driving", "John" );
subformula has_Answer() := {
If the task is asking, then there is a answer not equal to the empty string.
This formula results in true for all task other than asking and for those
task equal to asking with a non empty answer.
}
( task == "asking" -> answer != "");
subformula distance_between( lbound: distance, ubound: distance ) := {
The distance of the current audit trail entry lies between the lower bound
and the upper bound. }
( distance >= lbound / distance <= ubound );
subformula reasonable_distance() := {
If the task is cycling, the distance must be between 0 and 65, if the task
is driving is must be between 0 and 300, if the task is flying, the distance
must be between 150 and 1340. }
(
( task == "cycling" -> distance_between( 0, 65 )
) /\
( ( task == "driving" -> distance_between( 0, 300 )
) /\
( task == "flying" -> distance_between( 150, 1340 ) )
)
);
subformula permitted_to_drive() := {
A person is permitted to drive if he or she is born before 2004-6-01. }
bdate < "2004-06-01";
subformula a_important_case() := {
Case is important if the word ’important’ is used in the name. }
name ~= ".*important.*";
subformula P_does_A-A_not_B( P: person, A: task, B: task ) := {
Compute if person P does task A, which is not equal to B.}
<>( ( task == A /\ ( task != B /\ person == P ) ) );
formula exists_person_doing_two_different_tasks() := {
Is there a person doing two different tasks?}
exists[ p: person
|
exists[ t: task
|
exists[ u: task |
( P_does_A-A_not_B( p, t, u) /\
P_does_A-A_not_B( p, u, t))
]
]
];
subformula moving( P: person ) := {
41
Compute if person P is moving. }
<>( ( person == P /\
(
task == "driving" \/
( task == "cycling" \/
task == "flying"
)
)
) );
subformula asking( P: person ) := {
Compute if person P is asking. }
<>( ( person == P /\ task == "asking" ) );
formula moving_or_asking() := {
All persons are either moving or asking around.}
forall[ p: person |
(
( moving( p ) /\ !( asking( p ) ) ) \/
( !( moving( p ) ) /\ asking( p ) )
)
];
subformula end() := {
Only in the last state holds that in the next state a
WorkflowModelElement is not equal itself ( for other elements the same of
course) because in the next audit trail entry of the last state all
comparisons are false, the data elements does obviously not exist.}
!( _O( ate.WorkflowModelElement == ate.WorkflowModelElement ));
subformula next_older( d: bdate ) := {
Is d bigger or equal the current date? }
_O( bdate <= d );
formula always nexttime older() := {
Holds always that the birth date of the person in he next audit trail entry is
lesser or equal to the date of birth of the person performing the current
audit trail entry?}
[]( ( next_older( bdate ) end() ) );
formula move_till_question() := {
}
( task == "asking" _U distance > 0
3.8.6
Parse errors
No errors specified.
42
);
Chapter 4
Grammar of the LTL
Language
4.1
Literals
<integer_literal>
::= [1 - 9] ( [0 - 9] )*
<real_literal>
::= ([0 - 9])+ . ( [0 - 9] )* <exponent>?
|
( [0 - 9] )+ <exponent>?
<exponent>
::= [e,E] ( [+,-] )? ( [0 - 9] )+
<string_literal>
::= " ( ~[",\,\n,\r] | ( \ ( [n,t,b,r,f,\,’,"] ) ) )* "
<desc_literal>
::= { ( ~[{,}] | ( \ ( [n,t,b,r,f,\,’,",},{] ) ) )* }
4.2
Identifier
<identifier>
::= <startletter> ( <letter> | <digit> )*
<startletter>
::= [a - z,A - Z]
<letter>
::= [a - z,A - Z,-,_]
<digit>
::= [0 - 9]
4.3
LTL File
<ltlfile>
::= ( <attribute> | <renaming> | <formulae> )*
<attribute>
::= ( ’number’ | ’string’ | ’set’ ) <attr_name> ’;’
|
’date’ <attr_name> ’:=’ <date_pattern> ’;’
<date_pattern>
::= <string_literal>
43
<attr_name>
::= ( ’ate.’ | ’pi.’ )?<identifier>
<renaming>
::= ’rename’ <attr_name> ’as’ <identifier> ’;’
<formulae>
::= ( formula | subformula ) <identifier> ’(’ <arg_list>? ’)’
’:=’ <desc_literal> <prop> ’;’
<arg_list>
::= <arg> ( ’, ’<arg> )*
<arg>
::= <identifier> ’:’ <attr_name>
4.4
Propositions
<prop>
::=
|
|
|
|
<unary_prop>
<binary_prop>
<quantification>
<comparison>
<formula_call>
<unary_prop>
::= ( ’!’ | ’[]’ | ’<>’ | ’_O’ ) ’(’ <prop> ’)’
<binary_prop>
::= ’(’ <prop> ( ’/\’ | ’\/’ | ’->’ | ’<->’ | ’_U’ ) <prop> ’)’
<quantification>
::= ( forall | exists ) ’[’ <identifier> : <name> ’|’ <prop> ’]’
<comparison>
::= <attr_name>
( ’==’ | ’!=’ | ’<=’ | ’>=’ | ’<’ | ’>’ | ’~=’ )
<expr>
|
<attr_name> ’in’ ’[’ <string_list>? ’]’
<string_list>
::= <string_literal> ( ’,’ <string_literal> )*
<formula_call>
::= <identifier> ’(’ <param_list>? ’)’
<param_list>
::= <literal> ( ’,’ <literal> )*
<literal>
::= <integer_literal> | <real_literal> | <string_literal>
<expr>
::=
|
|
|
’-’ <expr>
’(’ <expr> ( ’+’ | ’-’ | ’*’ | ’/’ ) <expr> ’)’
<literal>
<attr_name>
44
Index
Comparisons, 28
Examples, 31
Parse errors, 32
List of arguments, 24
Parse errors, 26
Grammar, 43
Identifier, 43
Literal, 43
LTL File, 43
Propositions, 44
Defining attributes
Date, 21
Examples, 22
Number, 20
Parse errors, 22
Set, 21
String, 21
Importing in the ProM framework
LTL Template files, 5
Importing LTL Template files, 5
Error
Comments, 20
Comparisons, 32
Defining attributes, 22
Formula calls, 28
Formula definitions, 26
LTL, 42
Propositional logic, 35
Quantification, 37
Renamings, 24
Examples
Comments, 20
Comparisons, 31
Defining Attributes, 22
Description, 19
Formula calls, 27
Formula definitions, 25
LTL, 39
Propositional logic, 35
Quantification, 36
Renamings, 23
Exporting in the ProM framework, 14
LTL, 37
Always, 39
Eventually, 38
Examples, 39
Nexttime, 38
Parse errors, 42
Until, 39
LTL Checker Plugin
Default
How to start, 8
Exporting the results, 14
How to use the Template GUI, 10
LTL Checker Plugin
How to start, 9
Reusing the results, 14
Viewing the results of a check, 13
LTL Language, 17
Comments, 19
Comparisons, 28
Date, 31
Defining attributes
Date, 21
Number, 20
String, 21
Formula definitions, 24
Description, 24
List of arguments, 24
Grammar, 43
Formula call, 26
Examples, 27
Parse errors, 28
Formulae, 24
Description, 24
Examples, 25
45
LTL, 37
Always, 39
Eventually, 38
Nexttime, 38
Until, 39
Name, 23
Number, 31
Propositional logic, 33
And, 34
Bi-implication, 35
Implication, 34
Not, 33
Or, 34
Quantification, 35, 36
Renamings, 23
Running example, 19
Set, 31
String, 30
LTL language
Environment, 17
LTL Parser
Error messages, 7
Use on the command line, 7
LTL Template Import Plugin
How to use, 5
Propositional logic, 33
And, 34
Bi-implication, 35
Examples, 35
Implication, 34
Not, 33
Or, 34
Parse errors, 35
Quantification, 35, 36
Renamings, 23
Examples, 23
Parse errors, 24
Results window, 13
Standard LTL Template file, 9
Template GUI, 10
46
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