Common Logic Standards Development

1
Common Logic Standards Development

• Harry Delugach
• Univ. of Alabama in Huntsville
• delugach_at_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)

Pat Hayes IHMC, USA
Christopher Menzel Texas AM 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
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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

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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,

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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.

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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

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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.

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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.

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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 ) )

if date Jan 1 then pay_vacation_rate
not ( date Jan 1 and not pay_vacation_rate )
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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.

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Issue - Shareable Semantics

• Any meaningful exchange of utterances depends
  upon the prior existence of an agreed set of
  semantic and syntactic rules -- ISO TR
  90071987 (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 90071987 (Helsinki
  principles)
• Interpretation of the symbols forms an ontology
  -- a namespace which must be internally
  self-consistent.

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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

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Surface Forms/Syntax

• (?)(Boy(x) ?(?)(Girl(y) Kissed(x,y)))
• _at_every x If (Boy ?x) Then y (Girl ?y)
  (Kissed ?x ?y)

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Mapping to Common Syntax
(forall (?x)(implies (and (P ?x) (R ?x)) (PR
?x))))
_at_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))
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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)

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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) )

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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))) ) )

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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

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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

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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

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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

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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

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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)
.
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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

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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