ISO 18629-11:2005

Industrial automation systems and integration — Process specification language — Part 11: PSL core

ISO 18629-11:2005 provides a representation of the concepts of PSL Core using a set of axioms written in the basic language of ISO 18629. The representation of the concepts common to all processes is within the scope of ISO 18629-11:2005.

Systèmes d'automatisation industrielle et intégration — Langage de spécification de procédé — Partie 11: Noyau PSL

General Information

• Status: Published
• Publication Date: 25-Sep-2005
• ICS: 25.040.40 - Industrial process measurement and control
• Technical Committee: ISO/TC 184/SC 4 - Industrial data
• Drafting Committee: ISO/TC 184/SC 4/WG 15 - Digital manufacturing
• Current Stage: 9093 - International Standard confirmed
• Start Date: 15-Oct-2025
• Completion Date: 13-Dec-2025

Relations

• Splited From: ISO 18629-1:2004 - Industrial automation systems and integration — Process specification language — Part 1: Overview and basic principles
• Effective Date: 15-Apr-2008

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 18629-11
First edition
2005-10-01
Industrial automation systems and
integration — Process specification
language —
Part 11:
PSL core
Systèmes d'automatisation industrielle et intégration — Langage de
spécification de procédé —
Partie 11: Noyau PSL
Reference number
©
ISO 2005
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ii © ISO 2005 – All rights reserved

ISO 18629-11 : 2005 (E)
Contents       Page
1 Scope. 1
2 Normative references . 1
3 Terms, definitions, and abbreviations . 2
3.1 Terms and definitions . 2
3.2 Abbreviations. 7
4 ISO 18629 general . 7
5 Language specification syntax . 8
5.1 Basic symbols and Syntactic Categories. 8
5.2 Lexicon . 9
5.3 Grammar . 9
5.4 Language. 10
6 Basic elements of the PSL Core. 10
6.1 Basic features. 10
6.2 Primitive lexicon of the PSL-Core. 11
6.2.1 Primitive categories of the PSL-Core. 11
6.2.1.1 activity. 11
6.2.1.2 activity_occurrence. 11
6.2.1.3 object . 12
6.2.1.4 timepoint. 12
6.2.2 Individuals of the PSL-Core . 13
6.2.2.1 inf-. 13
6.2.2.2 inf+ . 13
6.2.3 Primitive relations of the PSL-Core . 13
6.2.3.1 before. 13
6.2.3.2 occurrence_of . 13
6.2.3.3 participates_in . 14
6.2.4 Primitive functions of the PSL-Core . 14
6.2.4.1 beginof. 14
6.2.4.2 endof. 14
6.2.5 Theories required by the PSL-Core . 15
6.3 Defined lexicon of the PSL-Core. 15
6.3.1 Formal definitions of the PSL-Core . 15
6.3.1.1 between. 15
6.3.1.2 beforeEq . 15
6.3.1.3 betweenEq . 15
6.3.1.4 exists_at. 16
6.3.1.5 is_occurring_at . 16
6.4 Axioms. 16
6.4.1 Axiom 1 . 16
6.4.2 Axiom 2 . 16
6.4.3 Axiom 3 . 17
6.4.4 Axiom 4 . 17
6.4.5 Axiom 5 . 17
6.4.6 Axiom 6 . 17
6.4.7 Axiom 7 . 17
6.4.8 Axiom 8 . 18
6.4.9 Axiom 9 . 18
6.4.10 Axiom 10 . 18
6.4.11 Axiom 11 . 19
6.4.12 Axiom 12 . 19
iii
ISO 18629-11 : 2005 (E)
6.4.13 Axiom 13 . 19
6.4.14 Axiom 14 . 19
6.4.15 Axiom 15 . 20
6.4.16 Axiom 16 . 20
6.4.17 Axiom 17 . 20
7 Conformance to PSL-Core. 21
7.1 Conformance of Ontologies. 21
7.2 Conformance of Process Descriptions. 21

Annex A (Normative) ASN.1 Identifier of ISO 18629-11. 22
Annex B (Informative) KIF Syntax and Semantics . 23
Annex C (Informative) Example of process description using PSL-Core . 31
Annex D (informative) BNF Conventions . 40

Figures
Figure C.1 : TOP level process for manufacturing a GT350 [9]. 35
Figure C.2: PROCESS for manufacturing the 350–Engine [9]. 36
Figure C.3: PROCESS for manufacturing the 350–Block [9]. 37
Figure C.4: PROCESS for manufacturing the 350–Harness [9] . 38
Figure C.5: PROCESS for manufacturing the 350–Wire [9] . 38
Figure C.6: PROCESS for manufacturing the x50–Wire. 38

Table
Table C.1: GT-350 Product Structure Table . 33

iv
ISO 18629-11 : 2005 (E)
Foreword
The International Organisation for Standardisation (ISO) is a worldwide federation of national
standards bodies (ISO member bodies). The work of preparing International Standards is normally
carried out through ISO technical committees. Each member body interested in a subject for which a
technical committee has been established has the right to be represented on that committee.
International organisations, governmental and non-governmental, in liaison with ISO, also take part in
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in ISO/IEC Directives, Part 2.
Draft International Standards (DIS) adopted by technical committees are circulated to the member
bodies for voting. Publication as an International Standard requires approval by at least 75% of the
member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this part of ISO 18629 may be the
subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 18629-11 was prepared by Technical Committee ISO/TC 184, Industrial automation systems and
integration, Sub-committee SC4, Industrial data.
A complete list of parts of ISO 18629 is available from the Internet.
http://www.tc184-sc4.org/titles
v
ISO 18629-11 : 2005 (E)
Introduction
ISO 18629 is an International Standard for the computer-interpretable exchange of information related
to manufacturing processes. Taken together, all the parts contained in the ISO 18629 Standard provide
a generic language for describing a manufacturing process throughout the entire production process
within the same industrial company or across several industrial sectors or companies, independently
from any particular representation model. The nature of this language makes it suitable for sharing
process information related to manufacturing during all the stages of a production process.
This part provides a description of the core elements of the language defined within the International
Standard.
This part of ISO 18629 and all other parts in ISO 18629 are independent of any specific process
representation or model proposed in a software application in the domain of manufacturing
management. Collectively, they provide a structural framework for improving the interoperability of
these applications.
vi
INTERNATIONAL STANDARD    ISO 18629-11 : 2005 (E)

Industrial automation systems and integration --
Process specification language --
Part 11:
PSL core
1 Scope
This part of ISO 18629 provides a representation of the concepts of PSL core using a set of axioms
written in the basic language of ISO 18629.
The following is within the scope of this part of ISO 18629:
 the representation of the concepts common to all processes.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
basic only the edition cited applies. For undated references, the latest edition of the referenced document
(including any amendments) applies.
ISO/IEC 8824-1, Information technology - Abstract Syntax Notation One (ASN.1) - Specification of
basic notation
ISO 10303-1, Industrial automation systems and integration - Product data representation and
exchange - Part 1: Overview and fundamental principles
ISO 15531-1, Industrial automation systems and integration - Industrial manufacturing management
data - Part 1: General overview
ISO 15531-42:2005, Industrial automation systems and integration - Industrial manufacturing
management data - Part 42:Time model

ISO 18629-11 : 2005 (E)
3 Terms, definitions, and abbreviations
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1.1
axiom
well-formed formula in a formal language that provides constraints on the interpretation of symbols in
the lexicon of a language
[ISO 18629-1]
3.1.2
conservative definition
definition that specifies necessary and sufficient conditions that a term shall satisfy and that does not
allow new inferences to be drawn from the theory
[ISO 18629-1]
3.1.3
core theory
set of predicates, function symbols and individual constants, associated with some axioms, the
primitive concepts of the ontology
3.1.4
data
a representation of information in a formal manner suitable for communication, interpretation, or
processing by human beings or computers
[ISO 10303-1]
3.1.5
defined lexicon
set of symbols in the non-logical lexicon which denote defined concepts
NOTE Defined lexicon is divided into constant, function and relation symbols.
EXAMPLE  terms with conservative definitions.
[ISO 18629-1]
3.1.6
extension
augmentation of PSL-Core containing additional axioms
NOTE 1  The PSL-Core is a relatively simple set of axioms that is adequate for expressing a wide range of basic
processes. However, more complex processes require expressive resources that exceed those of the PSL-Core.
Rather than clutter the PSL-Core itself with every conceivable concept that might prove useful in describing one
ISO 18629-11 : 2005 (E)
process or another, a variety of separate, modular extensions need to be developed and added to the PSL-Core as
necessary. In this way a user can tailor the language precisely to suit his or her expressive needs.
NOTE 2  All extensions are core theories or definitional extensions.
[ISO 18629-1]
3.1.7
grammar
specification of how logical symbols and lexical terms can be combined to make well-formed
formulae
[ISO 18629-1]
3.1.8
individual
element of an interpretation domain, in logic, considered as not divisible without loss of identity

EXAMPLE an individual constant is a symbol that is used to refer to some fixed individual object : it is the
equivalent in logic of the "name" in the everyday language. In first-order logic, arguments of predicates are
always individual constants.
NOTE 1  for further information, see [5].
NOTE 2  this term is commonly used in formal logic.
NOTE 3 in first order logic, the only individuals are individual constants.
3.1.9
information
facts, concepts, or instructions
[ISO 10303-1]
3.1.10
interpretation
universe of discourse and assignment of truth values (TRUE or FALSE) to all sentences in a theory

NOTE  See annex C for an example of an interpretation.
3.1.11
language
combination of a lexicon and a grammar
[ISO 18629-1]
ISO 18629-11 : 2005 (E)
3.1.12
lexicon
set of symbols and terms
NOTE The lexicon consists of logical symbols (such as Boolean connectives and quantifiers) and non-logical
symbols. For ISO 18629, the non logical part of the lexicon consists of expressions (constants, function symbols,
and relation symbols) chosen to represent the basic concepts of the ontology.
[ISO 18629-1]
3.1.13
linear ordering
set of elements with a binary relation between any two elements that is transitive, irreflexive and
antisymmetric
EXAMPLE the less-than relation in mathematics : 3 < 5.
3.1.14
manufacturing
function or act of converting or transforming material from raw material or semi-finished state to a
state of further completion
[ISO 15531-1]
3.1.15
manufacturing process
structured set of activities or operations performed upon material to convert it from the raw material or
a semifinished state to a state of further completion
NOTE Manufacturing processes may be arranged in process layout, product layout, cellular layout or
fixed position layout. Manufacturing processes may be planned to support make-to-stock, make-to-
order, assemble-to-order, etc., based on strategic use and placements of inventories.
[ISO 15531-1]
ISO 18629-11 : 2005 (E)
3.1.16
model
combination of a set of elements and a truth assignment that satisfies all well-formed formulae in a
theory
NOTE 1 The word "model" is used, in logic, in a way that differs from the way it is used in most scientific and
everyday contexts: if a sentence is true in a certain interpretation, it is possible to say that the interpretation is a
model of the sentence. The kind of semantics presented here is often called model-theoretical semantics.
NOTE 2  A model is typically represented as a set with some additional structure (partial ordering, lattice, or
vector space). The model then defines meanings for the terminology and a notion of truth for sentences of the
language in terms of this model. Given a model, the underlying set of axioms of the mathematical structures used
in the set of axioms then becomes available as a basis for reasoning about the concepts intended by the terms of
the language and their logical relationships, so that the set of models constitutes the formal semantics of the
ontology.
[ISO 18629-1]
3.1.17
ontology
a lexicon of specialised terminology along with some specification of the meaning of terms in the
lexicon
NOTE 1: structured set of related terms given with a specification of the meaning of the terms in a formal
language. The specification of meaning explains why and how the terms are related and conditions how the set
is partitioned and structured.
NOTE 2:  The primary component of a process specification language such as ISO 18629 is an ontology  The
primitive concepts is the ontology according to ISO 18629 are adequate for describing basic manufacturing,
engineering, and business processes.
NOTE 3:  The focus of an ontology is not only on terms, but also on their meaning. An arbitrary set of terms is
included in the ontology, but these terms can only be shared if there is an agreement about their meaning. It is
the intended semantics of the terms that is being shared, not simply the terms.
NOTE 4:  Any term used without an explicit definition is a possible source of ambiguity and confusion. The
challenge for an ontology is that a framework is needed for making explicit the meaning of the terms within it.
For the ISO 18629 ontology, it is necessary to provide a rigorous mathematical characterisation of process
information as well as a precise expression of the basic logical properties of that information in the ISO 18629
language.
[ISO 18629-1]
3.1.18
point in time
location of something noticeable within a time domain
th
EXAMPLE 1 Wednesday, 15 of March, 2003.
EXAMPLE 2 9.30 a.m.
[ISO 15531-42]
ISO 18629-11 : 2005 (E)
3.1.19
primitive concept
lexical term that has no conservative definition
[ISO 18629-1]
3.1.20
primitive lexicon
set of symbols in the non-logical lexicon which denote primitive concepts
NOTE Primitive lexicon is divided into constant, function and relation symbols.
[ISO 18629-1]
3.1.21
process
structured set of activities involving various enterprise entities, that is designed and organised for a
given purpose
NOTE The definition provided here is very close to that given in ISO 10303-49. Nevertheless ISO 15531 needs
the notion of structured set of activities, without any predefined reference to the time or steps. In addition, from
the point of view of flow management, some empty processes may be needed for a synchronisation purpose
although they are not actually doing anything (ghost task).
[ISO 15531-1]
3.1.22
product
a thing or substance produced by a natural or artificial process
[ISO 10303-1]
3.1.23
proof theory
set of theories and lexical elements necessary for the interpretation of the semantics of the language
NOTE  It consists of three components: the PSL-Core, the Outer Core and the extensions.
[ISO 18629-1]
3.1.24
PSL-Core
set of axioms for the concepts of activity, activity-occurrence, time-point, and object
NOTE  The motivation for PSL-Core is any two process-related applications shall share these axioms in
order to exchange process information, and hence is adequate for describing the fundamental concepts of
manufacturing processes. Consequently, this characterisation of basic processes makes few assumptions about
their nature beyond what is needed for describing those processes, and the PSL-Core is therefore rather weak in
ISO 18629-11 : 2005 (E)
terms of logical expressiveness. In particular, PSL-Core is not strong enough to provide definitions of the many
auxiliary notions that become necessary to describe all intuitions about manufacturing processes.
[ISO 18629-1]
3.1.25
theory
set of axioms and definitions that pertain to a given concept or set of concepts
NOTE this definition reflects the approach of artificial intelligence in which a theory is the set of assumptions on
which the meaning of the related concept is based.
[ISO 18629-1]
3.1.26
universe of discourse
the collection of concrete or abstract things that belong to an area of the real world, selected according
to its interest for the system to be modelled and for its corresponding environment.
[ISO 15531-1]
3.2 Abbreviations
For the purpose of this part of ISO 18629, the following abbreviations apply:
 BNF Backus-Naur form
 KIF Knowledge Interchange Format
 PSL Process Specification Language
4 ISO 18629 general
ISO 18629 specifies a language for the representation of process information. It is composed of a
lexicon, an ontology, and a grammar for process descriptions.
NOTE 1 PSL is a language for specifying manufacturing processes based on a mathematically well defined
vocabulary and grammar. As such, it is different from the schemas and product representations provided in the
standards ISO 10303, ISO 13584 [2], and ISO 15926 [3], it is also different from the representation provided by
ISO 15531, but strongly related to it and complementary . In the context of an exchange of information between
two software applications, PSL identifies each process independently of its behaviour. For example, an object
identified as a resource within one process can be recognised as the same object even though it is identified as a
product within a second process.
NOTE 2 PSL is based on first order logic; as such, it follows significantly different methods for specifying
semantics for modelling concepts than those used in ISO 10303. The meaning of the concepts defined within
PSL follows from sets of axioms and definitions provided within each extension of PSL-Core. A set of
supporting notes and examples are provided within each part to aid the understanding of the language.
ISO 18629-11 : 2005 (E)
The parts 1x of ISO 18629 specify foundational theories needed to give precise definitions and the
axiomatization of the primitive concepts of ISO 18629. The foundational theories enable precise
semantic translations between different schemes.
The following are within the scope of the 1x series of parts of ISO 18629:
 the representation of the basic elements of the language;
 the provision of standardised sets of axioms that correspond to intuitive semantic primitive
concepts adequate to describe basic processes;
 the set of rules to develop other foundational theories or extensions in compliance with PSL-Core.
The following is outside the scope of the 1x series of parts of ISO 18629:
 the representation of information involving concepts that are not part of foundational theories.
5 Language specification syntax
This clause specifies the definition of the ISO 18629 language using an extended Backus-Naur form
(BNF) (see Annex D). The syntax described in this section is built on the syntax of the KIF format
provided in the Annex B.
NOTE  for further information, see [7 and [8].
5.1 Basic symbols and Syntactic Categories
The set of basic symbols that shall be used to specify any PSL process description are defined in the
following BNF :
  ::=A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W |
X | Y | Z
  ::= a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | p | q | r | s | t | u | v | w | x | y | z
  ::= |
  ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
  ::= - | ~ | # |$ | * | + | /
  ::= _ | - | ~ | ! | @ | # |$ | % | ^ | & | * | ( | ) | + | = | ` | : | ; | ' | < | > | , | . | ? | / | | |
[ | ] | { | } |
An expression is any string of basic symbols.
There are five basic categories of expression :
ISO 18629-11 : 2005 (E)
  ::= { | } { | }* {{ _ | - } { | }}*
  ::= ?[']
  ::= { | } { | }* {{ _ | - } { | }}*
  ::= {} { | }* {{ _ | - } { | }}*
  ::= " { | | | \" | \\ }* "
An expression derived from the nonterminal is a string of alphanumeric characters, dashes,
and underscores that begins with a lower case letter or digit and in which every dash and underscore is
flanked on either side by a letter or digit. A is the result of prefixing a with a
question mark and, optionally, appending a single quote (a “prime”). A is similar to a con> except that it must begin with either an , a , or an upper case letter, and a
is similar to a except that it must begin with an upper case letter. (Every is thus a
.) A is the result of quoting any string of symbols; double quotes and the
backslash can be used as well as long as they are preceded by a backslash.
5.2 Lexicon
A first-order PSL language L is given in terms of a lexicon and a grammar. The lexicon provides the
basic “words” of the language, and the grammar determines how the lexical elements may be used to
build the complex, well-formed expressions of the language.
A PSL lexicon λ consists of the following:
 The expressions , (, ), not, and, or, implies, iff, forall, and exists;
 A denumerable recursive set V of  expressions known as the variables of λ;
λ
 A recursive set C of  expressions, known as the constants of λ which includes at least
λ
the strings inf-, inf+, max-, and max+;
 A recursive set F of  expressions, known as the function symbols of λ, which includes at
λ
least the strings beginof and endof.
 A recursive set P of expressions known as the predicates of λ, which includes at least
λ
the strings = activity, activity-occurrence, object, timepoint, is-occurring-at, occurrence-of,
exists-at, before, and participates-in.
5.3 Grammar
Given an PSL lexicon λ, the grammar based on λ is given in the following BNF :
 ::=    a member of C
λ
  ::= a member of V
λ
ISO 18629-11 : 2005 (E)
  ::= a member of F
λ
  ::= a member of P
λ
 ::=  |
  ::= |
 ::=( )
  ::= | |
  ::= ( +) | (= )
  ::=(not ) | (and +) | (or
+) | (implies ) | (iff )
  ::= ({forall | exists} { | (+)} )
  ::=
5.4 Language
The PSL language L based on a lexicon λ is the set of expressions that can be derived from the
λ
nonterminal in the above grammar. The members of L are the sentences of L . User
λ λ
defined constraints shall be defined using the PSL language .
Note Example of user defined constraints are provided in annex C.
6 Basic elements of the PSL Core
This clause specifies the basic elements from which the ISO 18629-11 PSL-Core is composed.
6.1 Basic features
The basic elements of the language are :
 the primitive lexicon;
 the defined lexicon with supporting definitions;
 the axioms.
Since all these concepts provide the core elements of the language, no additional theory is needed.
The meaning of the following terms follows either from the axioms or from the supporting definitions.
ISO 18629-11 : 2005 (E)
6.2 Primitive lexicon of the PSL-Core
The primitive lexicon is made of the following :
 primitive categories;
 individuals;
 primitive relations;
 primitive functions.
NOTE In logic, primitive concepts are not given formal definitions within an ontology.
6.2.1 Primitive categories of the PSL-Core
The primitive categories are presented here with informal descriptions.
6.2.1.1 activity
The KIF notation for activity is :
(activity ?a)
The informal description for activity is :
(activity ?a) is TRUE in an interpretation of PSL-Core if and only if ?a is a member of the set of
activities in the universe of discourse of the interpretation.
6.2.1.2 activity_occurrence
The KIF notation for activity_occurrence is :
(activity_occurrence ?occ)
The informal description for activity_occurrence is :
(activity_occurrence ?occ) is TRUE in an interpretation of PSL-Core if and only if ?occ is a member
of the set of activity occurrences in the universe of discourse of the interpretation. An activity
occurrence is associated with a unique activity and begins and ends at specific points in time.
NOTE An activity occurrence is not an instance of an activity. Although there may exist activities that have no
activity occurrence, all activity occurrences must be associated with an activity
EXAMPLE: The activity denoted by the term (paint House1 Paintcan1) is an instance of the class of Painting
activities:
(Painting (paint House1 Paintcan1))
There may be multiple distinct occurrences of this instance:
(occurrence_of Occ1 (paint House1 Paintcan1))
ISO 18629-11 : 2005 (E)
(occurrence_of Occ2 (paint House1 Paintcan1))
(= (beginof Occ1) 1100)
(= (endof Occ1) 1200)
(= (beginof Occ2) 1500)
(= (endof Occ2) 1800)
There may be another instance of the class of Painting activities
(Painting (paint House1 Paintcan2))
that has no occurrences.
6.2.1.3 object
The KIF notation for object is :
(object ?x)
The informal description for object is :
(object ?x) is TRUE in an interpretation of PSL-Core if and only if ?x is a member of the set of objects
in the universe of discourse of the interpretation. An object is anything that is not a timepoint, nor an
activity nor an activity-occurrence.
NOTE Intuitively, an object is a concrete or abstract thing that can participate in an activity. Objects can come
into existence (be created) and go out of existence (be "used up" as a resource) at certain points in time. In such
cases, an object has a begin and an end point. In some contexts it may be useful to consider some ordinary
objects as having no such points either.
EXAMPLE 1 The most typical examples of objects are ordinary, tangible things, such as people, chairs, car
bodies, NC-machines. Abstract objects, such as numbers are also objects.
EXAMPLE 2 Some objects, for instance numbers, do not have finite begin and end points.
6.2.1.4 timepoint
The KIF notation for timepoint is :
(timepoint ?t)
The informal description for timepoint is :
(timepoint ?t) is TRUE in an interpretation of PSL-Core if and only if ?t is a member of the set of
timepoints in the universe of discourse of the interpretation.Timepoints form a linear ordering.
ISO 18629-11 : 2005 (E)
6.2.2 Individuals of the PSL-Core
6.2.2.1 inf-
The informal description for inf- is :
(= ?t inf-) is TRUE in an interpretation of PSL-Core if and only if ?t is the unique timepoint that is
before all other timepoints in the linear ordering over timepoints in the universe of discourse of the
interpretation.
NOTE inf- plays the role of negative infinity. It is needed to specify objects that have not been created within
the universe of discourse of the interpretation.
6.2.2.2 inf+
The informal description for inf+ is :
(= ?t inf+) is TRUE in an interpretation of PSL-Core if and only if ?t is the unique timepoint that is
after all other timepoints in the linear ordering over timepoints in the universe of discourse of the
interpretation.
NOTE inf+ plays the role of positive infinity. It is needed to specify objects that have not been destroyed within
the universe of discourse of the interpretation.
6.2.3 Primitive relations of the PSL-Core
6.2.3.1 before
The KIF notation for before is :
(before ?t1 ?t2)
The informal description for before is :
(before ?t1 ?t2) is TRUE in an interpretation of PSL-Core if and only if the timepoint ?t1 is earlier
than ?t2 in the linear ordering over timepoints in the interpretation.
NOTE In PSL-Core, the set of timepoints is not dense (between any two distinct timepoints there is a third
timepoint), although in PSL-Core the set of timepoints is infinite. Denseness can be added by a user as an
additional postulate. Time intervals are not included among the primitives of PSL-Core; intervals can be defined
with respect to timepoints and activities.
EXAMPLE the concept of intervals made of timepoints is a fundamental element of the parts ISO 15531-42
(Time model) and ISO IS 10303-41 (Product description and support).
6.2.3.2 occurrence_of
The KIF notation for occurrence_of is :
(occurrence_of ?occ ?a)
The informal description for occurrence_of is :
ISO 18629-11 : 2005 (E)
(occurrence_of ?occ ?a) is TRUE in an interpretation of PSL-Core if and only if ?occ is a particular
occurrence of the activity ?a. occurrence_of is the basic relation between activities and activity
occurrences. Every activity occurrence is associated with a unique activity. An activity may have no
occurrences or multiple occurrences.
6.2.3.3 participates_in
The KIF notation for participates_in is :
(participates_in ?x ?occ ?t)
The informal description for participates_in is :
(participates_in ?x ?occ ?t) is TRUE in an interpretation of PSL-Core if and only if ?x plays some role
that is not pre-specified in an occurrence of the activity occurrence ?occ at the timepoint ?t in the
interpretation. An object can participate in an activity occurrence only at those timepoints at which
both the object exists and the activity is occurring.
6.2.4 Primitive functions of the PSL-Core
6.2.4.1 beginof
The KIF notation for beginof is :
(beginof ?x)
The informal description for beginof is :
The domain of the beginof function is the set of activity occurrences and objects.
If ?x is an activity occurence in the universe of discourse of an interpretation of PSL-Core, then
(beginof ?x) has the value t if and only if t is the timepoint at which the activity occurrence ?x begins.
EXAMPLE (= 10 (beginof milling_occurrence)) where milling_occurrence begins at timepoint 10.
If ?x is an object in the universe of discourse of an interpretation of PSL-Core, then (beginof ?x) has
the value x if and only if t is the timepoint at which the object ?x becomes possible to participate in an
activity.
EXAMPLE (= 15 (beginof screw)) where the object screw can participate in an activity at timepoint 15.
6.2.4.2 endof
The KIF notation for endof is :
(endof?x)
The informal description for endof is :
The domain of the endof function is the set of activity occurrences and objects.
ISO 18629-11 : 2005 (E)
If ?x is an activity occurrence in the universe of discourse of an interpretation of PSL-Core, then
(endof?x) has the value x if and only if t is the timepoint at which the activity occurrence ?x ends.
EXAMPLE (= 25 (endof milling_occurrence)) where milling_occurrence ends at timepoint 25.
If ?x is an object in the universe of discourse of an interpretation of PSL-Core, then (endof?x) has the
value x if and only if t is the timepoint at which the object ?x becomes no longer possible to participate
in an activity.
EXAMPLE (= 30 (endof screw)) where screw can no longer participate in an activity at timepoint 30.
6.2.5 Theories required by the PSL-Core
No other theory is required for the primitive lexicon.
6.3 Defined lexicon of the PSL-Core
6.3.1 Formal definitions of the PSL-Core
NOTE  The lexicon ‘defrelation’, ‘exists’, ‘forall’, ‘and’, ‘or’, ‘not’, ‘=’, ‘Ù’, and ‘implies’ are defined in the
KIF Reference Manual [8]
6.3.1.1 between
Definition 1: Timepoint t2 is between timepoints t1 and t3 if and only if t1 is before t2 and t2 is before
t3.
(forall (?t1 ?t2 ?t3) (iff (between ?t1 ?t2 ?t3)
(and (before ?t1 ?t2) (before ?t2 ?t3)))))
6.3.1.2 beforeEq
Definition 2: Timepoint t1 is beforeEq timepoint t2 if and only if t1 is before or equal to t2.
(forall (?t1 ?t2) (iff (beforeEq ?t1 ?t2)
(and (timepoint ?t1) (timepoint ?t2)
(or (before ?t1 ?t2) (= ?t1 ?t2))))))
6.3.1.3 betweenEq
Definition 3: Timepoint t2 is between or equal to timepoints t1 and t3 if and only if t1 is before or
equal to t2, and t2 is before or equal to t3.
(forall (?t1 ?t2 ?t3) (iff (betweenEq ?t1 ?t2 ?t3)
(and (beforeEq ?t1 ?t2)
(beforeEq ?t2 ?t3)))))
ISO 18629-11 : 2005 (E)
6.3.1.4 exists_at
Definition 4: An object exists at a timepoint t1 if and only if t1 is between or equal to its begin and end
points.
(forall (?x ?t) (iff (exists_at ?x ?t)
(and (object ?x)
(betweenEq (beginof ?x) ?t (endof ?x))))))
6.3.1.5 is_occurring_at
Definition 5: An activity is occurring at a timepoint t1 if and only if t1 is between or equal to the
activity occurrence’s begin and end points.
(forall (?occ ?t) (iff (is-occuring-at ?occ ?t)
(and (activity_ooccurrence ?occ)
(betweenEq (beginof ?occ) ?t (endof ?occ)))))
6.4 Axioms
The following axioms (axiom 1 to axiom 17) are the fundamental axioms of the PSL-Core.
NOTE  The lexicon ‘defrelation’, ‘exists’, ‘forall’, ‘and’, ‘or’, ‘not’, ‘=’, ‘iff’, and ‘implies’ are defined in the
KIF Reference Manual [8]
6.4.1 Axiom 1
The before relation only holds between timepoints.
(forall (?t1 ?t2)
(implies   (before ?t1 ?t2)
(and   (timepoint ?t1)
(timepoint ?t2))))
6.4.2 Axiom 2
The before relation is a total ordering.
(forall (?t1 ?t2)
(implies   (and   (timepoint ?t1)
(timepoint ?t2))
ISO 18629-11 : 2005 (E)
(or    (= ?t1 ?t2)
(before ?t1 ?t2)
(before ?t2 ?t1))))
6.4.3 Axiom 3
The before relation is irreflexive.
(forall (?t)  (not (before ?t ?t)))
6.4.4 Axiom 4
The before relation is transitive.
(forall (?t1 ?t2 ?t3)
(implies   (and  (before ?t1 ?t2)
(before ?t2 ?t3))
(before ?t1 ?t3)))
6.4.5 Axiom 5
The timepoint inf- is before all other timepoints.
(forall (?t)
(implies (and (timep
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