ISO 18629-12:2005

Industrial automation systems and integration — Process specification language — Part 12: Outer core

ISO 18629-12:2005 provides a representation of the concepts that belong to the outer core of the language, through a set of axioms and definitions. These axioms provide an axiomatization of the semantics for terminology in the ISO 18629 Outer core. The following are within the scope of ISO 18629-12:2005: the aggregation of activities and sub-activities; discrete activities and state; constraints on the occurrence of activities; concurrency for primitive activities; complex activities; occurrences of complex activities.

Systèmes d'automatisation industrielle et intégration — Langage de spécification de procédé — Partie 12: Noyau externe

General Information

• Status: Published
• Publication Date: 28-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 18629-12
First edition
2005-10-01
Industrial automation systems and
integration — Process specification
language —
Part 12:
Outer core
Systèmes d'automatisation industrielle et intégration — Langage de
spécification de procédé —
Partie 12: Noyau externe
Reference number
©
ISO 2005
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ii © ISO 2005 – All rights reserved

ISO 18629-12 : 2005 (E)
Content        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 Organization of ISO 18629-12 . 8
5.1 Extensions in Outer core . 8
6 Subactivity core theory. 9
6.1 Primitive Relations of the Subactivity core theory. 9
6.2 Defined Relations of the Subactivity core theory. 9
6.3 Relationship to other sets of axioms. 10
6.4 Informal Semantics of the Subactivity core theory . 10
6.4.1 subactivity . 10
6.4.2 primitive . 10
6.5 Definitions in the Subactivity core theory. 10
6.5.1 Definition 1: . 10
6.6 Axioms of the Subactivity core theory. 11
6.6.1 Axiom 1. 11
6.6.2 Axiom 2. 11
6.6.3 Axiom 3. 11
6.6.4 Axiom 4. 11
6.6.5 Axiom 5. 12
6.6.6 Axiom 6. 12
7 Occurrence tree core theory . 13
7.1 Primitive Relations. 13
7.2 Primitive Functions . 13
7.3 Relationship to other sets of axioms. 13
7.4 Informal Semantics of the Occurrence tree core theory . 13
7.4.1 earlier. 13
7.4.2 initial. 14
7.4.3 legal . 14
7.4.4 poss. 14
7.4.5 precedes. 14
7.4.6 successor. 15
7.5 Axioms for the Occurrence tree core theory . 15
7.5.1 Axiom 1. 15
7.5.2 Axiom 2. 15
7.5.3 Axiom 3. 15
7.5.4 Axiom 4. 16
7.5.5 Axiom 5. 16
7.5.6 Axiom 6. 16
7.5.7 Axiom 7. 17
7.5.8 Axiom 8. 18
7.5.9 Axiom 9. 18
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7.5.10 Axiom 10. 18
7.5.11 Axiom 11. 18
7.5.12 Axiom 12. 19
7.5.13 Axiom 13. 19
7.5.14 Axiom 14. 19
7.5.15 Definition 1. 19
7.5.16 Definition 2. 19
8 Discrete state core theory . 20
8.1 Primitive categories in the Discrete state core theory . 20
8.2 Primitive relations in the Discrete state core theory. 20
8.3 Relationship to other sets of axioms. 20
8.4 Informal semantics of the Discrete state core theory . 20
8.4.1 state. 20
8.4.2 holds . 21
8.4.3 prior . 21
8.5 Axioms for the Discrete state core theory . 21
8.5.1 Axiom 1. 21
8.5.2 Axiom 2. 21
8.5.3 Axiom 3. 22
8.5.4 Axiom 4. 22
8.5.5 Axiom 5. 22
8.5.6 Axiom 6. 22
8.5.7 Axiom 7. 23
9 Atomic activity core theory. 23
9.1 Primitive Relations in the Atomic activity core theory . 24
9.2 Primitive Functions in the Atomic activity core theory . 24
9.3 Relationship to other sets of axioms. 24
9.4 Informal semantics of the Atomic activity core theory . 24
9.4.1 atomic . 24
9.4.2 conc . 24
9.5 Definitions in Atomic activity core theory. 24
9.6 Axioms of the Atomic activity core theory . 25
9.6.1 Axiom 1. 25
9.6.2 Axiom 2. 25
9.6.3 Axiom 3. 25
9.6.4 Axiom 4. 25
9.6.5 Axiom 5. 25
9.6.6 Axiom 6. 26
9.6.7 Axiom 7. 26
9.6.8 Axiom 8. 26
9.6.9 Axiom 9. 26
10 Complex activity core theory .27
10.1 Primitive Relations in the Complex activity core theory . 27
10.2 Defined Relations in the Complex activity core theory . 27
10.3 Relationship to other sets of axioms. 27
10.4 Informal Semantics of the Complex activity core theory. 28
10.4.1 min_precedes. 28
10.4.2 root . 28
10.4.3 subtree . 28
10.4.4 leaf. 28
10.4.5 do. 29
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10.4.6 next_subocc. 29
10.4.7 sibling . 29
10.5 Definitions in Complex activity core theory . 29
10.5.1 Definition 1. 30
10.5.2 Definition 2. 30
10.5.3 Definition 3. 30
10.5.4 Definition 4. 31
10.5.5 Definition 5. 31
10.6 Axioms of the Complex activity core theory . 31
10.6.1 Axiom 1. 32
10.6.2 Axiom 2. 32
10.6.3 Axiom 3. 32
10.6.4 Axiom 4. 33
10.6.5 Axiom 5. 33
10.6.6 Axiom 6. 33
10.6.7 Axiom 7. 34
10.6.8 Axiom 8. 34
10.6.9 Axiom 9. 34
10.6.10 Axiom 10. 35
10.6.11 Axiom 11. 35
11 Activity occurrence core theory . 35
11.1 Primitive Relations in the Activity occurrence core theory . 35
11.2 Defined Relations in the Activity occurrence core theory . 35
11.3 Relationship to other sets of axioms. 36
11.4 Informal Semantics of the Activity occurrence core theory. 36
11.4.1 subactivity_occurrence. 36
11.4.2 mono. 36
11.4.3 root_occ. 36
11.4.4 leaf_occ . 37
11.4.5 iso_occ. 37
11.4.6 hom. 37
11.4.7 same_grove. 37
11.5 Definitions for Activity occurrence core theory. 38
11.5.1 Definition 1. 38
11.5.2 Definition 2. 38
11.5.3 Definition 3. 38
11.5.4 Definition 3. 39
11.5.5 Definition 4. 39
11.5.6 Definition 5. 39
11.6 Axioms for Activity occurrence core theory . 40
11.6.1 Axiom 1. 40
11.6.2 Axiom 2. 40
11.6.3 Axiom 3. 40
11.6.4 Axiom 4. 41
11.6.5 Axiom 5. 42
11.6.6 Axiom 6. 42
11.6.7 Axiom 7. 42
11.6.8 Axiom 8. 43
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11.6.9 Axiom 9. 43
11.6.10 Axiom 10. 43
11.6.11 Axiom 11. 44
11.6.12 Axiom 12. 44
11.6.13 Axiom 13. 44
11.6.14 Axiom 14. 44
11.6.15 Axiom 15. 45

Annex A (normative) Use of ASN.1 Identifiers in SC4 standards. 46
Annex B (informative) Relationship to Situation Calculus. 47
Annex C (informative) Example of process description using PSL-Outercore . 48

Bibliography. 56
Index. 57

Figures
Figure 1: Relationships among sets of axioms within PSL Outer core. . 9
Figure C1: TOP level process for manufacturing a GT350 [1]. 48
Figure C.2: PROCESS for manufacturing the 350–Engine [1]. 51
Figure C.3: PROCESS for manufacturing the 350–Block [1]. 52
Figure C.4: PROCESS for manufacturing the 350–Harness [1] . 53
Figure C.5: PROCESS for manufacturing the harness wire [1]. 54
Figure C.6 : Process for manufacturing the 350-Wire [1]. 54
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ISO 18629-12 : 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 18629-12 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

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ISO 18629-12 : 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.
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INTERNATIONAL STANDARD       ISO 18629-12 : 2005 (E)
Industrial automation systems and integration —
Process specification language –
Part 12:
PSL Outer core
1 Scope
This part of ISO 18629 provides a representation of the concepts that belong to the Outer core of the
language, through a set of axioms and definitions. These axioms provide an axiomatization of the
semantics for terminology in the ISO 18629 Outer core.
The following are within the scope of this part of ISO 18629:
 the aggregation of activities and sub-activities;
 discrete activities and state;
 constraints on the occurrence of activities;
 concurrency for primitive activities;
 complex activities;
 occurrences of complex activities.

2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, 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 18629-1: Industrial automation systems and integration – Process specification language –
Part 1: Overview and basic principles
ISO 18629-11: Industrial automation systems and integration – Process specification language –
Part 11: PSL core
ISO 18629-12 : 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
[ISO 18629-1]
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
definitional extension
extension of PSL-Core that introduces new linguistic items which can be completely defined in terms
of the PSL-Core
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ISO 18629-12 : 2005 (E)
NOTE: Definitional extensions add no new expressive power to PSL-Core but are used to specify the semantics

and terminology in the domain application.
[ISO 18629-1]
3.1.7
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
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]
3.1.8
grammar
specification of how logical symbols and lexical terms can be combined to make well-formed
formulae
[ISO 18629-1]
3.1.9
idempotent
element (a) of a set under an internal binary operation (OP) with respect to which : a OP a = a
NOTE a function is idempotent when every element of the definition domain is idempotent with respect to it
EXAMPLE set-theoretic intersection and union are idempotent, since S ∩ S = S and S ∪ S = S.
3.1.10
information
facts, concepts, or instructions
[ISO 10303-1]
3.1.11
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.
3.1.12
language
combination of a lexicon and a grammar
[ISO 18629-1]
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ISO 18629-12 : 2005 (E)
3.1.13
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]
3.1.14
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]
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
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ISO 18629-12 : 2005 (E)
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
Outer core
set of core theories that are extensions of PSL-Core and that are so generic and pervasive in their
applicability that they have been put apart
NOTE  In practice, extensions incorporate the axioms of the Outer core.
[ISO 18629-1]
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
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ISO 18629-12 : 2005 (E)
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
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
semilattice
partial ordering in which every two elements have a unique least upper bound
3.1.26
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]
3.1.27
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]
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ISO 18629-12 : 2005 (E)
3.2 Abbreviations
 FOL First-Order Logic:
 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, which is a process
specification language. 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 dif and only iferent from the other languages used in the standards ISO
10303, ISO 13584, ISO 15531 and ISO 15926. In the context of an exchange of information between two
processes, PSL specifies each process independently of its behaviour. For example, an object viewed as a
resource within one process can be recognised as the same object even though it is viewed as a product within a
second process.
NOTE 2 PSL is based on Mathematical Set Core theory and Situation Calculus (see annex B). As such it follows
a significantly dif and only iferent method of description from the method used by existing languages defined in
the standard ISO 10303. The meaning of the concepts within PSL follows from a set of axioms and supporting
definitions rather than from a formal set of defined terms. A set of supporting notes and examples are provided
to aid the understanding of the primitive lexicon of the language.
The 1x series of parts of ISO 18629 specify core theories needed to give precise definitions and the
axioms of the primitive concepts of ISO 18629, thus enabling precise semantic translations between
different schemes.
The following are within the scope of ISO 18629-1x:
 the representation of the basic elements of the language;
 the provision of standardized sets of axioms that correspond to intuitive semantic primitive
concepts adequate to describe basic processes;
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ISO 18629-12 : 2005 (E)
 the set of rules to develop other core theories or extensions in compliance with PSL-Core.
The following is outside the scope of ISO 18629-1x:
 the representation of information involving concepts that are not part of core theories.

5 Organization of ISO 18629-12
This clause specifies the fundamental theories from which the ISO 18629-12 Outer core is composed.
5.1 Extensions in Outer core
The core theories that are part of the Outer core are:
 Subactivity core theory (subactivity.th);
 Occurrence tree core theory (occtree.th);
 Discrete states core theory (disc_state.th);
 Atomic activity core theory (atomic.th);
 Complex activity core theory (complex.th);
 Activity occurrence core theory (act_occ.th).

Figure 1 shows the relationships between these theories within the Outer core, in which the arrows
represent the dependencies among the theories. All theories in the Outer core are extensions of PSL-
Core. The Atomic activity core theory is an extension of both the Subactivity and the Occurrence
Trees theories, while the Discrete states core theory is an extension of the Occurrence Trees core
theory alone. The Activity occurrence core theory is an extension of the Complex Acivities core
theory, which in turn is an extension of Atomic Activities.

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ISO 18629-12 : 2005 (E)
act_occ.th
complex.th
atomic.th disc_state.th
subactivity.th occtree.th
PSL-Core
Figure 1: Relationships among sets of axioms within PSL Outer core.
6 Subactivity core theory
This core theory provides axioms for concepts for process composition. The only constraint imposed
within this core theory is that the subactivity relation is isomorphic to a discrete partial ordering.
Other core theories impose additional constraints.
6.1 Primitive Relations of the Subactivity core theory
The nonlogical lexicon of the Subactivity core theory contains one primitive relation symbol:
 subactivity.
6.2 Defined Relations of the Subactivity core theory
The nonlogical lexicon of the Subactivity core theory contains one defined relation symbol:
 primitive.
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ISO 18629-12 : 2005 (E)
6.3 Relationship to other sets of axioms
The Subactivity core theory requires psl_core.th as specified in ISO 18629-11 (PSL-Core).
No definitional extensions are required by the Subactivity core theory.
6.4 Informal Semantics of the Subactivity core theory
6.4.1 subactivity
KIF notation for subactivity:
(subactivity ?a1 ?a2)
Informal semantics for subactivity:
(subactivity ?a1 ?a2) is TRUE in an interpretation of Subactivity core theory if and only if activity ?a1
is a subactivity of activity ?a2.
The subactivity relation forms a discrete partial ordering over the set of activities.
6.4.2 primitive
KIF notation for primitive:
(primitive ?a)
Informal semantics for primitive:
(primitive ?a) is TRUE in an interpretation of Subactivity core theory if and only if the activity ?a has
no subactivities except for itself.
6.5 Definitions in the Subactivity core theory
An activity is primitive if and only i
...