November 11, 2004

Common Logic Standards Common Logic Standards DevelopmentDevelopment

Common Logic Standards Common Logic Standards DevelopmentDevelopment

Harry Delugach

Univ. of Alabama in Huntsville

delugach@cs.uah.edu

November 11, 2004

OutlineOutlineOutlineOutline

• Common Logic– Origins– Structure– Issues

• Standard– Outline– ISO Standards Development

November 11, 2004

OverviewOverviewOverviewOverview

• First order logic language for knowledge interchange

• Provides a core semantic framework for logic

• Provides the basis for a set of syntactic forms (dialects) all sharing a common semantics

November 11, 2004

Common Logic ParticipantsCommon Logic ParticipantsCommon Logic ParticipantsCommon Logic ParticipantsSCL ad-hoc working group (formed Dec 2002):

Pat Hayes IHMC, USA

Christopher Menzel Texas A&M U., USA

John Sowa VivoMind, USA

Tanel Tammet U. Goteborg, Sweden

Bill Anderson OntologyWorks, USA

Murray Altheim Open University, UK

Harry Delugach U. Alabama Huntsville, USA

Mike Gruninger NIST, USA

November 11, 2004

Origins of Common LogicOrigins of Common LogicOrigins of Common LogicOrigins of Common Logic

• Conceptual Graphs, 1984– Linear (textual form) – Display (graphic form)– Natural language processing, knowledge based

systems

• Knowledge Interchange Format (KIF) c. 1990– Part of the Ontolingua project at Stanford to develop

ontologies

• KIF-CGIF collaboration, 1994-c. 1998• Common Logic (CL) 1998-2002• Simplified Common Logic (SCL) 2002-present

November 11, 2004

First Order SemanticsFirst Order SemanticsFirst Order SemanticsFirst Order Semantics• Entities - things, states, attributes

– Harry, idleness, color, etc.

• Relations - between entities, attributes– Marriage, eye-color, etc.

• Quantification - single or multiple instance– Definition, uniqueness, etc.

• Negation - explicit falsehood– Harry is not President of the United States

• Iteration - over elements a set– Age of each member of a population

• NOT INCLUDED: – actors, ontologies, knowledge bases, …

November 11, 2004

Goal of Common LogicGoal of Common LogicGoal of Common LogicGoal of Common Logic• Two agents, A and B, each have a first-order

formalization of some knowledge • A and B wish to communicate their

knowledge to each other so as to draw some conclusions. – Any inferences which B draws from A's input

should also be derivable by A using basic logical principles, and vice versa

• The goal of Common Logic is to provide a logical framework which can support this kind of use and communication without requiring complex negotiations between the agents.

November 11, 2004

IssuesIssuesIssuesIssues• Syntax

– A and B may have different surface syntactic forms

• Different axiomatic styles– Differing assumptions about how to model– E.g., Rule-based vs. logical formulae

• Multiple domains– Differing vocabularies, ontologies, granularity

• Shareable semantics– Requires agreement between parties about

some part of the universe

November 11, 2004

Issue - Syntax Issue - Syntax Issue - Syntax Issue - Syntax • A and B may have used different surface

syntactic forms to express their knowledge. – A well-known problem– Usually solved by defining a standard syntax into

which others can be translated, such as KIF– CL provides a common 'interlingua' syntax XCL into

which the others can be translated. – XCL uses XML concepts and design principles

• Provides a clean separation between the description of logical form and the surface syntactic form appropriate to a particular usage.

• Allows for linking of CL text across documents and conveying CL written in non-XCL syntaxes between applications using XML protocols.

November 11, 2004

Issue - Different Axiomatic Issue - Different Axiomatic StylesStyles

Issue - Different Axiomatic Issue - Different Axiomatic StylesStyles

• A and B may have made divergent assumptions about the logical signatures of their formalizations. – A uses relation name where B uses function– A and B use same relation with different argument

orderings or different numbers of arguments. – A particular concept, such as marriage, might be

represented by A as an individual, but by B as a relation.

• Can be solved by mappings between the logical forms of such divergent choices– SCL removes conventional limitations on first-order

signatures• For example, a name in SCL may serve both as an individual

name and as a relation name.

November 11, 2004

Example: Rule-based vs. logicExample: Rule-based vs. logicExample: Rule-based vs. logicExample: Rule-based vs. logic

• Rule-based system:

CL: (implies (equal date “Jan 1”) pay_vacation_rate )

• Logic system

CL: not ( (equal date “Jan 1”) and not ( pay_vacation_rate ) )

if date =“Jan 1” then pay_vacation_rate

not ( date = “Jan 1” and not pay_vacation_rate )

November 11, 2004

Issue - Multiple DomainsIssue - Multiple DomainsIssue - Multiple DomainsIssue - Multiple Domains

• A and B may have been writing with different intended universes of discourse in mind – Assertions in a domain might be interpreted to be

talking about things that they have not even conceived of

– E.g., taxonomic classifications of animals• “complement of the set of mammals” may be taken to include

fruit, sodium molecules, styles of avant-garde paintings or the names of fictional characters in movies.

• CL has a 'top-level' syntactic form called a module which automatically gives a name to the universe of discourse of a named ontology– Automatically inserts “namespace” on any contained

quantifiers when information is combined.

November 11, 2004

Issue - Shareable SemanticsIssue - Shareable SemanticsIssue - Shareable SemanticsIssue - Shareable Semantics

• Any meaningful exchange of utterances depends upon the prior existence of an agreed set of semantic and syntactic rules

-- ISO TR 9007:1987 (“Helsinki principles”) • The recipients of the utterances must use

only these rules to interpret the received utterances, if it is to mean the same as that which was meant by the utterer

-- ISO TR 9007:1987 (“Helsinki principles”) • Interpretation of the symbols forms an

ontology -- a “namespace” which must be internally self-consistent.

November 11, 2004

CL SemanticsCL SemanticsCL SemanticsCL Semantics• Based on model theory

• Assumes a universe of individuals UI and a way of associating individuals with symbols (e.g., “Jack”)

• An interpretation of vocabulary (VO,VR,VF) is defined by a set and three mappings:– A nonempty set UI called the universe;

– A mapping intI from VO to UI maps individuals to symbols

– A mapping relI from VR to the set RelI of relational extensions over UI

– A mapping funI from VF to the set FunI of functional extensions over UI.

• Once given UI and mappings, every system will have the same interpretation of CL sentences

November 11, 2004

Surface Forms/SyntaxSurface Forms/SyntaxSurface Forms/SyntaxSurface Forms/Syntax

• ()(Boy(x) ()(Girl(y) & Kissed(x,y)))• [@every *x] [If: (Boy ?x) [Then: [*y]

(Girl ?y) (Kissed ?x ?y) ]]

Girl Boykissnot Boy

not

Girl

November 11, 2004

Mapping to Common SyntaxMapping to Common SyntaxMapping to Common SyntaxMapping to Common Syntax

(forall (?x)(implies (and (P ?x) (R ?x)) (PR ?x))))

[@every *x] [If: [P(?x) R(?x)] [Then: PR(?x)]]

(∀x)(P(x)&R(x) → PR(x))

(x)not(P(x) R(x) not PR(x))

November 11, 2004

Different Axiomatic StylesDifferent Axiomatic StylesDifferent Axiomatic StylesDifferent Axiomatic Styles

• All can be represented by CL core syntax– (married Jack Jill) – (married (roleset: (husband Jack) (wife Jill))) – (exists (x)(and (married x) (husband Jack x)

(wife Jill x))) – (= (when (married Jack Jill)) (hour 3 (pm

(thursday (week 12 (year 1997))))) ) – (= (wife (married 32456)) Jill) – (ConjugalStatus married Jack) – ((ConjugalStatus Jack) Jill)

November 11, 2004

Example: InterchangeExample: InterchangeExample: InterchangeExample: Interchange

CGIF concrete syntax:[Jack: *a] [Jill: *b] (married ?a ?b)

Map to CL abstract syntax:(married Jack Jill)

Map to KIF concrete syntax(married (Jack) (Jill) )

Jack Jillmarried

November 11, 2004

Semantic ConsistencySemantic ConsistencySemantic ConsistencySemantic Consistency• System A:(married Jack Jill)• System B:

(married (roleset:(husband Jack)(wife Jill)))

• How does System B “understand” System A?

(forall (x y) (implies (married x y) (married

(roleset:(husband x) (wife y))) ) )

November 11, 2004

Conformance IssuesConformance IssuesConformance IssuesConformance Issues

• What if a system/notation is a superset of CL?– E.g., Conceptual Graphs have procedural

nodes called actors that serve as functional relations

• Only that subset of the system/notation that is first-order will be preserved via interchange– E.g., actor will be exchanged as simple

relation

November 11, 2004

Proposed Outline of Common Proposed Outline of Common Logic Standard (ISO Project Logic Standard (ISO Project

24707)24707)

Proposed Outline of Common Proposed Outline of Common Logic Standard (ISO Project Logic Standard (ISO Project

24707)24707)Three stages proposed

• Stage 1: NormativeAbstract syntax, semantics, and annexes

• Stage 2: InformativeTechnical report on other logical formalisms

• Stage 3: InformativeOntology merging, use of multiple knowledge bases

November 11, 2004

ISO WD 24707 - Main bodyISO WD 24707 - Main bodyISO WD 24707 - Main bodyISO WD 24707 - Main body

• Scope, normative references, terms, symbols• Common Logic Core

– Abstract syntax– Abstract Semantics

• How to conform?• Three specific surface syntaxes are conformant

• KIF, CGIF, XCL

• Provide a mapping from your language to one of those

• Prove that semantics of your language are preserved for every mapping into CL abstract syntax

November 11, 2004

ISO WD 24707 - Normative ISO WD 24707 - Normative AnnexesAnnexes

ISO WD 24707 - Normative ISO WD 24707 - Normative AnnexesAnnexes

• KIF (1st order)– Concrete syntax - KIF – EBNF grammar -– Show KIF to CL abstract syntax

• CGIF (1st order)– CGIF – EBNF grammar– Show CGIF to CL abstract syntax

• XCL– XML-based markup – EBNF grammar – Show XCL to CL abstract syntax

November 11, 2004

ISO WD 24707 - Informative ISO WD 24707 - Informative AnnexesAnnexes

ISO WD 24707 - Informative ISO WD 24707 - Informative AnnexesAnnexes

• Relationship to other standards and practices– Prolog, Z, OCL (non-ISO-std), OWL (non-ISO-std)– Distinguish CL from Horn clause, description logics,

others

• A benchmark “fact set” of all the kinds of facts that one can have

• Especially: meaning of negation, reasoning over sets – see well founded semantics

• Use Cases

November 11, 2004

ISO Standards OrganizationISO Standards OrganizationISO Standards OrganizationISO Standards Organization

TC37 ….

SC 32 (Data Interchange) …. ….

Working Group 2(Metadata Stds)

Working Group 3(Database Languages)

….

W3C OMGANSI IEEE

Intl. Standards Organization(ISO)

Joint TechnicalCommittee (JTC1)

November 11, 2004

ISO Standards DevelopmentISO Standards Development(Metadata Standards)(Metadata Standards)

ISO Standards DevelopmentISO Standards Development(Metadata Standards)(Metadata Standards)

• 7 countries (national bodies) involved:– USA, UK, CAN, KOR, PRC, JAP, AUS

• Working Group 2 (ISO JTC1 / SC32 / WG2) develops working draft (WD)– submitted June 2004

• Subcommittee 32 (SC32) Data Mgt and Interchange approves Committee Draft (CD)– expected Apr. 2005

• ISO approves final draft and standard (IS)– Expected 2006

November 11, 2004

From Here…From Here…From Here…From Here…

• If you are interested in the progress of the standard, you can:– Participate in the technical email discussions– Get your national body to participate – Send in your comments to your national body– Attend standards meetings