Knowledge Interchange Format

Michael Gruninger

National Institute of Standards and Technology

gruning@cme.nist.gov

What is KIF?

• Knowledge Interchange Format (KIF) is a language designed for use in the interchange of knowledge among disparate computer systems

What is Knowledge?

• Facts– William is the brother of Harold.

– Charles is not the brother of George.

• Statements/Rules/Constraints– The mother of Charles is either Elizabeth or Ann.

– Two people are siblings if and only if they are brother or sister.

– Every person has a mother.

How Will KIF be Used?

• Specification of ontologies – Standard Upper Ontology– Process Specification Language– Semantic Web

• Software agent communication

• Automated deduction and constraint satisfaction

Features of KIF

The language has a declarative semantics.

The language is logically comprehensive.

The language provides for the representation of knowledge about knowledge.

Organization of KIF

• Part 1 (KIF-Core) : syntax and semantics of a language equivalent to first-order logic.

• Part 2 (Sorted KIF) specifies the syntax and semantics for class hierarchies.

• Part 3 (MetaKIF) syntax and semantics of the metatheory of KIF-Core.

Scope of KIF Core

Language of first-order logic:

Language with logical symbols for – connectives (conjunction, disjunction, negation,

implication, equivalence), – equality, – quantifiers (existential and universal)

Example KIF Sentences

The mother of Charles is either Elizabeth or Ann.

(forall (?x)

(=> (mother Charles ?x)

(or (= ?x Elizabeth)

(= ?x Ann))))

Everyone’s age must be greater than 0.

(forall (?x)

(greater (age ?x) 0))

Example KIF Sentences

Nobody can be both a brother and a sister.

(forall (?x ?y)

(=> (bother ?x ?y)

(not (sister ?x ?y))))

Every person has a mother.

(forall (?x)

(=> (person ?x)

(exists (?y)

(and (person ?y)

(mother ?x ?y)))))

Example KIF Sentences

Two people are siblings if and only if they are brother or sister.

(forall (?x ?y)(=> (and (person ?x)

(person ?y))(<=> (sibling ?x ?y)

(or (brother ?x ?y)(sister ?x ?y)))))

Semantics: Intuitions

• A universe of discourse is the set of all objects within some domain.

• Terms are used to denote objects in the universe.

• For every set of objects, a function associates a unique object in the universe.

• For every set of objects, a relation associates a truth value.

Semantics: Structures

• A structure consists of a nonempty set O together with the functions:– Interpretation function – Semantic valuation function – Satisfaction function

Semantics: Models

• A structure satisfies a sentence if and only if () = true

• A structure is a model of a theory T if and only if it satisfies each sentence in T

• A theory T entails a sentence if and only if every model of T satisfies .

Inference

• A proof system consists of a set of KIF sentences and a set of inference rules that transform sentences into new ones.

• A sentence is provable from a theory T if and only if can be generated by applying a finite number of inference rules to the sentences of T.

Compliance

• A proof system is compliant with KIF if and only if:– It is sound -- every sentence that is provable

from a theory is entailed by the theory.– It is complete -- every sentence that is entailed

by a theory is provable from the theory.

Additional Features

• KIF-Core also allows quantification over relations and functions that are denoted by words in the lexicon of a theory.

(forall (?r ?x ?y)

(<=> (symmetric ?r)

(<=> (?r ?x ?y)

(?r ?y ?x))))

Next Steps

• Incorporation of namespaces for KIF modules

• Semantics for sequence variables

• Syntax and semantics for Sorted-KIF

• Syntax and semantics for MetaKIF