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Common Logic Standards Development

Common Logic Standards Development. Harry Delugach Univ. of Alabama in Huntsville delugach@cs.uah.edu. Outline. Common Logic Origins Structure Issues Standard Outline ISO Standards Development. Overview. First order logic language for knowledge interchange

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Common Logic Standards Development

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  1. Common Logic Standards Development Harry Delugach Univ. of Alabama in Huntsville delugach@cs.uah.edu

  2. Outline • Common Logic • Origins • Structure • Issues • Standard • Outline • ISO Standards Development

  3. Overview • 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

  4. Common Logic Participants SCL ad-hoc working group (formed Dec 2002):

  5. Origins 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

  6. First 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, …

  7. Goal 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.

  8. Issues • 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

  9. 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.

  10. Issue - Different Axiomatic Styles • 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.

  11. Example: 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 ) ) ifdate =“Jan 1”thenpay_vacation_rate not( date = “Jan 1”andnotpay_vacation_rate )

  12. Issue - 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.

  13. Issue - 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.

  14. CL 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

  15. not Girl Boy not kiss Girl Boy Surface Forms/Syntax • ()(Boy(x) ()(Girl(y) & Kissed(x,y))) • [@every *x] [If: (Boy ?x) [Then: [*y] (Girl ?y) (Kissed ?x ?y) ]]

  16. Mapping 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))

  17. Different 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)

  18. Jack married Jill Example: 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) )

  19. Semantic 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))) ) )

  20. Conformance 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

  21. Proposed Outline of Common Logic Standard (ISO Project 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

  22. ISO 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

  23. ISO WD 24707 - Normative Annexes • 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

  24. ISO WD 24707 - Informative Annexes • 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

  25. ISO Standards Organization OMG W3C Intl. Standards Organization (ISO) ANSI IEEE Joint Technical Committee (JTC1) TC37 …. …. …. SC 32 (Data Interchange) Working Group 2 (Metadata Stds) Working Group 3 (Database Languages) ….

  26. ISO Standards Development(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

  27. 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

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