ISO/IEC 24707:2007
(Main)Information technology — Common Logic (CL): a framework for a family of logic-based languages
Information technology — Common Logic (CL): a framework for a family of logic-based languages
ISO/IEC 24707:2007 defines Common Logic: a first-order logic framework intended for information exchange and transmission. The heart of the framework is a complete abstract syntax and abstract semantics for Common Logic, which provides the basis for many different concrete syntactic forms, called dialects, which conform to the syntax and semantics. Common Logic has some novel features, chief among them being a syntax which is signature-free and permits 'higher-order' constructions such as quantification over classes or relations while preserving a first-order model theory, and a semantics which allows theories to describe intensional entities such as classes or properties. It also fixes the meanings of a few conventions in widespread use, such as numerals to denote integers and quotation marks to denote character strings, and has provision for the use of datatypes and for naming, importing and transmitting content on the World Wide Web. ISO/IEC 24707:2007 defines the abstract syntax and semantics, and three concrete dialects are defined in the annexes. The three conforming dialects specified are Common Logic Interchange Format (CLIF), Conceptual Graph Interchange Format (CGIF) and XML for Common Logic (XCL).
Technologies de l'information — Logique commune (CL): un cadre pour une famille de langages basés sur la logique
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INTERNATIONAL ISO/IEC
STANDARD 24707
First edition
2007-10-01
Information technology — Common Logic
(CL): a framework for a family of logic-
based languages
Technologies de l'information — Logique commune (CL): un cadre pour
une famille de langages basés sur la logique
Reference number
ISO/IEC 24707:2007(E)
©
ISO/IEC 2007
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ISO/IEC 24707:2007(E)
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ISO/IEC 24707:2007(E)
Contents Page
Foreword. vi
Introduction . vii
1 Scope .1
2 Normative references .2
3 Terms and definitions .2
4 Symbols and abbreviations .5
4.1 Symbols .5
4.2 Abbreviations.6
5 Requirements and design overview .6
5.1 Requirements.6
5.2 A family of notations .8
6 Common Logic abstract syntax and semantics .8
6.1 Common Logic abstract syntax. .8
6.2 Common Logic semantics .13
6.3 Importing and identification on a network .16
6.4 Satisfaction, validity and entailment.18
6.5 Sequence markers, recursion and argument lists: discussion .18
6.6 Special cases and translations between dialects .19
7 Conformance.20
7.1 Dialect conformance .20
7.2 Application conformance.22
7.3 Network conformance .22
Annex A (normative) Common Logic Interchange Format (CLIF) .23
A.1 Introduction.23
A.2 CLIF Syntax .24
A.3 CLIF semantics .29
A.4 CLIF conformance .32
Annex B (normative) Conceptual Graph Interchange Format (CGIF).33
B.1 Introduction.33
B.2 CG Core Syntax and Semantics.39
B.3 Extended CGIF Syntax .45
B.4 CGIF conformance.51
Annex C (normative) eXtended Common Logic Markup Language (XCL).54
C.1 Introduction.54
C.2 XCL Syntax .54
C.3 XCL Semantics.72
C.4 XCL Conformance.72
Bibliography .73
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ISO/IEC 24707:2007(E)
Figures Page
Figure 1 — Structure of a text and the taxonomy of the phrase category text .10
Figure 2 — Abstract syntax of sentence and its sub-categories.10
Figure 3 — Abstract syntax of a module.10
Figure 4 — Abstract syntax of a quantified sentence .11
Figure 5 — Abstract syntax of a boolean sentence .11
Figure 6 — Abstract syntax of an atom.12
Figure 7 — Abstract syntax of a term and term sequence .12
Figure B.1 — CG display form for John is going to Boston by bus. 33
Figure B.2 — CG display form for “If a cat is on a mat, then it is a happy pet” . 34
Figure B.3 — CL functions represented by actor nodes. 35
Tables Page
Table 1 — Interpretations of Common Logic Expressions 15
Table A.1 — CLIF Semantics 30
Table A.2 — Mapping from additional CLIF forms to core CLIF forms 31
Table B.1 — Mapping from CL abstract syntax to extended CGIF syntax 52
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ISO/IEC 24707:2007(E)
Foreword
ISO (the International Organization for Standardization) and IEC (the International Electrotechnical
Commission) form the specialized system for worldwide standardization. National bodies that are members of
ISO or IEC participate in the development of International Standards through technical committees
established by the respective organization to deal with particular fields of technical activity. ISO and IEC
technical committees collaborate in fields of mutual interest. Other international organizations, governmental
and non-governmental, in liaison with ISO and IEC, also take part in the work. In the field of information
technology, ISO and IEC have established a joint technical committee, ISO/IEC JTC 1.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of the joint technical committee is to prepare International Standards. Draft International
Standards adopted by the joint technical committee are circulated to national bodies for voting. Publication as
an International Standard requires approval by at least 75 % of the national bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO and IEC shall not be held responsible for identifying any or all such patent rights.
ISO/IEC 24707 was prepared by Joint Technical Committee ISO/IEC JTC 1, Information technology,
Subcommittee SC 32, Data management and interchange.
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ISO/IEC 24707:2007(E)
Introduction
Common Logic is a logic framework intended for information exchange and transmission. The framework
allows for a variety of different syntactic forms, called dialects, all expressible within a common XML-based
syntax and all sharing a single semantics.
Common Logic has some novel features, chief among them being a syntax which is signature-free and
permits 'higher-order' constructions such as quantification over classes or relations while preserving a first-
order model theory, and a semantics which allows theories to describe intensional entities such as classes or
properties. It also fixes the meanings of a few conventions in widespread use, such as numerals to denote
integers and quotation marks to denote character strings, and has provision for the use of datatypes and for
naming, importing and transmitting content on the World Wide Web using XML.
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INTERNATIONAL STANDARD ISO/IEC 24707:2007(E)
Information technology — Common Logic (CL): a framework for
a family of logic-based languages
1 Scope
This International Standard specifies a family of logic languages designed for use in the representation and
interchange of information and data among disparate computer systems.
The following features are essential to the design of this International Standard:
• Languages in the family have declarative semantics. It is possible to understand the meaning of
expressions in these languages without appeal to an interpreter for manipulating those
expressions.
• Languages in the family are logically comprehensive — at its most general, they provide for the
expression of arbitrary first-order logical sentences.
• Interchange of information among heterogeneous computer systems.
The following are within the scope of this International Standard:
• representation of information in ontologies and knowledge bases;
• specification of expressions that are the input or output of inference engines;
• formal interpretations of the symbols in the language.
The following are outside the scope of this International Standard:
• the specification of proof theory or inference rules;
• specification of translators between the notations of heterogeneous computer systems;
• computer-based operational methods of providing relationships between symbols in the logical
“universe of discourse” and individuals in the “real world”.
This International Standard describes Common Logic’s syntax and semantics.
It defines an abstract syntax and an associated model-theoretic semantics for a specific extension of first-
order logic. The intent is that the content of any system using first-order logic can be represented in this
International Standard. The purpose is to facilitate interchange of first-order logic-based information between
systems.
Issues relating to computability using this International Standard (efficiency, optimization, etc.) are not
addressed.
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ISO/IEC 24707:2007(E)
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 2382-15:1999, Information technology — Vocabulary — Part 15: Programming languages
ISO/IEC 10646:2003, Information technology — Universal Multiple-Octet Coded Character Set (UCS)
ISO/IEC 14977:1996, Information technology — Syntactic metalanguage — Extended BNF
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
atom
sentence form which has no subsentences as syntactic components
NOTE Can be either an equation, or an atomic sentence consisting of a predicate applied to an argument sequence.
3.2
axiom
any sentence which is assumed to be true, from which others are derived, or by which they are entailed
NOTE In a computational setting, an axiom is a sentence which is never posed as a goal to be proved, but only used
to prove other sentences.
3.3
Common Logic Interchange Format
CLIF
KIF-based syntax that is used for illustration purposes in this International Standard
NOTE It is one of the concrete syntaxes as described in Annex A. The name “KIF” is not used for this syntax in order
to distinguish it from the commonly used KIF dialects. No assumptions are made in this International Standard with
respect to KIF semantics; in particular, no equivalence between CLIF and KIF is intended.
3.4
conceptual graph
CG
graphical or textual display of symbols arranged according to the style of conceptual graph theory
3.5
Conceptual Graph Interchange Format
CGIF
text version of conceptual graphs whose rules of formation conform to Annex B of this International Standard
NOTE Sometimes may refer to an example of a character string that conforms to Annex B. Intended to convey
exactly the same structure and semantics as an equivalent conceptual graph.
3.6
conceptual graph theory
form of first-order logic which represents existential quantification and conjunction via the assertion of logical
constructs called concepts and relations, which are arranged in an abstract or visually displayed graph
NOTE Conceptual graph theory was introduced by John Sowa [1].
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3.7
denotation
relationship holding between a name or expression and the thing to which it refers
NOTE Also used, with “of,” to mean the entity being named, i.e. the referent of a name or expression.
3.8 dialect
concrete instance of Common Logic syntax that shares (at least some of) the uniform semantics of Common
Logic
NOTE A dialect may be textual or graphical or possibly some other form. A dialect by definition is also a conforming
language (see 7.1 for further details).
3.9
discourse name
name whose interpretation is in the universe of discourse
NOTE There is no assumption that different names are interpreted as different individuals. A single individual in the
universe of discourse may be denoted by two or more distinct names.
3.10
domain of discourse
See universe of discourse.
3.11
eXtensible Common Logic Markup Language
XCL
XML-based syntax for Common Logic
3.12
individual
one element of the universe of discourse
NOTE The universe of discourse is the set of all individuals.
3.13
Internationalized Resource Identifier
IRI
string of Unicode characters conforming to the syntax described in [2] and intended for use as an Internet
network identifier syntax which can accommodate a wide variety of international character forms
NOTE Intended to replace Uniform Resource Identifier as an Internet standard for network identifiers.
3.14
interpretation
formal specification of the meanings of the names in a vocabulary of a Common Logic dialect in terms of a
universe of reference.
NOTE 1 An interpretation in turn determines the semantic values of all complex expressions of the dialect, in particular
the truth values of its sentences.
NOTE 2 See 6.2 for a more precise description of how an interpretation is defined.
3.15
Knowledge Interchange Format
KIF
text-based first order formalism, using a LISP-like list notation
NOTE 1 KIF, introduced by Mike Genesereth [3], originated with the Knowledge Sharing Effort sponsored by the US
DARPA.
NOTE 2 KIF forms the basis for one of the three Common Logic dialects included in this International Standard.
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ISO/IEC 24707:2007(E)
3.16
operator
distinguished syntactic role played by a specified component within a functional term
NOTE The denotation of a functional term in an interpretation is determined by the functional extension of the
denotation of the operator together with the denotations of the remaining components.
3.17
predicate
〈Common Logic〉 distinguished syntactic role played by exactly one component within an atomic sentence
NOTE The truth value of an atomic sentence in an interpretation is determined by the relational extension of the
denotation of the predicate together with the denotations of the remaining components.
3.18
segregated dialect
dialect in which some names are non-discourse names
NOTE In an interpretation of a segregated dialect, the denotations of the non-discourse names are in the universe of
reference, but not in the universe of discourse.
3.19
sentence
〈Common Logic〉 unit of logical text which is true or false, i.e. which is assigned a truth-value in an
interpretation
3.20
sort
any subset of the universe of discourse over which some quantifier is allowed to range
NOTE Related to the definition of “type” (see 3.24). Generally used to mean a proper subset of the individuals in the
universe of discourse.
3.21
sorted logic
logic system (whether first-order or not) which requires that all nonlogical symbols be assigned to a sort
3.22
term
〈Common Logic〉 expression which denotes an individual, consisting of either a name or, recursively, a
function term applied to a sequence of arguments, which are themselves terms
3.23
traditional first-order logic
TFOL
traditional mathematical formulations of logic as introduced chiefly by Russell, Whitehead, Peano, Frege,
Peirce and Tarski dealing with n-ary predication, the Boolean operators (including negation) and
quantification, and in which every proposition is either determinately true or determinately false
NOTE Languages for traditional first-order logic specifically exclude predicate quantifiers and the use of the same
name in both predicate and argument position in atomic sentences, both of which are permitted (though not required) in
Common Logic. Languages for traditional first-order logic fall within the category of segregated dialects in CL (see 6.1.3).
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3.24
type
logical framework in which expressions in the logic are classified into syntactic or lexical categories (types)
and restricted to apply only to arguments of a fixed type
NOTE 1 In practice, a type represents a class of individuals.“Type theory” usually refers to a particular class of such
logics in which relation symbols are separated into orders, with relations of order n applying only to those of lower orders.
NOTE 2 A type is more restricted than a sort in that a type imposes intensional or categorical constraints on which
individuals are members of the type category, whereas a sort refers only to any subset of individuals in the domain over
which some quantifier is presumed to operate.
3.25
universe of discourse
domain of discourse
set of all the individuals in an interpretation, i.e. the set over which the quantifiers range
NOTE Required to be a subset of the universe of reference, and may be identical to it.
3.26
universe of reference
set of all the entities needed to define the meanings of logical expressions in an interpretation
NOTE 1 Required to be a superset of the universe of discourse, and may be identical to it.
NOTE 2 Segregated dialects are commonly described to have a universe of discourse, without mentioning the universe
of reference; and for non-segregated dialects the universes of discourse and of reference are identical. The distinction
makes it possible to provide a single semantics which can cover both styles of dialect. Non-segregated dialects which treat
the universes of discourse and of reference as identical may simply refer to ‘the universe’ of an interpretation.
3.27
Uniform Resource Identifier
URI
sequence of ASCII characters conforming to the syntax forms defined in [4]
NOTE At the time of writing, the Internet standard syntax for network identifiers. It is likely to be obsoleted by
Internationalized Resource Identifier.
4 Symbols and abbreviations
These symbols and abbreviations are generally for the main clauses of the standard. Some annexes may
introduce their own symbols and abbreviations which will be grouped together within that annex.
4.1 Symbols
Some of these symbols represent terms which are defined in clause 3.
fun a mapping from UR to functions from UD * to UD
I I I I
I an interpretation, in the model-theoretic sense
int a mapping from names in a vocabulary V to UR ; informally, a means of associating names in V to
I I
referents in UR
I
rel a mapping from UR to subsets of UD *
I I I
seq a mapping from sequence markers in V to UD *
I I
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V a vocabulary, which is a set of names and sequence markers
UD the universe of discourse; a non-empty set of individuals that an interpretation I is “about” and over
I
which the quantifiers are understood to range
UR the universe of reference, i.e. the set of all referents of names in an interpretation I
I
X* the set of finite sequences of the elements of X, for any set X
4.2 Abbreviations
These abbreviations are used in this International Standard. See clause 3 for definitions or further elaboration
on these terms.
CG Conceptual graph
CGIF Conceptual Graph Interchange Format
CL Common Logic
CLIF Common Logic Interchange Format
DF Display form (used in Annex B)
EBNF Extended Backus-Naur Format, as in ISO/IEC 14977:1996.
FO First-order
IRI Internationalized Resource Identifier
KIF Knowledge Interchange Format
OWL Web Ontology Language
RDF Resource Definition Framework
RDFS Resource Definition Framework Schema
TFOL traditional first order logic
URI Uniform Resource Identifier
XCL eXtensible Common Logic Markup Language
XML eXtensible Markup Language
5 Requirements and design overview
This clause is informative. Its purpose is to briefly describe the purposes of Common Logic and the overall
guiding principles and constraints on its content.
5.1 Requirements
Common Logic has been designed and developed with several requirements in mind, all arising from its
intended role as a medium for transmitting logical content on an open communication network. The use of
“should” in the rest of clause 5 indicates a desired goal but is not required of either CL or its conforming dialect
(in accordance with Annex H of ISO/IEC Directives – Part 2).
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5.1.1 Common Logic should include full first-order logic with equality.
Common Logic syntax and semantics shall provide for the full range of first-order syntactic forms, with their
usual meanings. Any conventional first-order syntax will be directly translatable into Common Logic without
loss of information or alteration of meaning.
5.1.2 Common Logic should provide a general-purpose syntax for communicating logical
expressions.
a. There should be a single XML syntax for communicating Common Logic content.
b. The language should be able to express various commonly used 'syntactic sugarings' for logical forms
or commonly used patterns of logical sentences.
c. The syntax should relate to existing conventions; in particular, it should be capable of rendering any
content expressible in RDF, RDFS, or OWL.
d. There should be at least one compact, human-readable syntax defined which can be used to express
the entire language.
5.1.3 Common Logic should be easy and natural for use on the Web
a. The XML syntax should be compatible with the published specifications for XML, URI syntax, XML
Schema, Unicode, and other conventions relevant to transmission of information on the Web.
b. URIs and URI references should be usable as names in the language.
c. URIs should be usable to give names to expressions and sets of expressions, in order to facilitate Web
operations such as retrieval, importation, and cross-reference.
5.1.4 Common Logic should support open networks
a. Transmission of content between Common Logic-aware agents should not require negotiation about
syntactic roles of symbols, or translations between syntactic roles.
b. Any piece of Common Logic text should have the same meaning, and support the same entailments,
everywhere on the network. Every name should have the same logical meaning at every node of the
network.
c. No agent should be able to limit the ability of another agent to refer to any entity or to make assertions
about any entity.
d. The language should support ways to refer to a local universe of discourse and be able to relate it to
other such universes.
e. Users of Common Logic should be free to invent new names and use them in published Common
Logic content.
5.1.5 Common Logic should not make arbitrary assumptions about semantics
a. Common Logic does not make gratuitous or arbitrary assumptions about logical relationships between
different expressions.
b. If possible, Common Logic agents should express these assumptions in Common Logic directly.
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ISO/IEC 24707:2007(E)
5.2 A family of notations
This (informative) section describes what is meant by a “family” of languages and gives some of the rationale
behind the development of Common Logic.
If we follow the convention whereby any language has a grammar, then Common Logic is a family of
languages rather than a single language. Different Common Logic languages, referred to in this International
Standard as dialects, may differ sharply in their surface syntax, but they have a single uniform semantics and
can all be transcribed into the common abstract syntax. Membership in the family is defined by being inter-
translatable with the other dialects while preserving meaning, rather than by having any particular syntactic
form. Several existing logical notations and languages, therefore, can be considered to be Common Logic
dialects.
A Common Logic dialect called CLIF based on KIF (see Annex A) is used in giving examples throughout this
International Standard. CLIF can be considered an updated and simplified form of KIF 3.0 [3], and hence a
separate language in its own right, and so a complete self-contained description is given which can be
understood without reference to the rest of the specification. Conceptual graphs [1] are also a well-known form
of first-order logic for machine processing; the CGIF language is specified in Annex B. An XML dialect us
...
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