1. Knowledge Interchange Format Michael Gruninger National Institute of Standards and Technology gruning@cme.nist.gov

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

3. 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.

4. How Will KIF be Used? Specification of ontologies –Standard Upper Ontology –Process Specification Language –Semantic Web Software agent communication Automated deduction and constraint satisfaction

5. Features of KIF  The language has a declarative semantics.  The language is logically comprehensive.  The language provides for the representation of knowledge about knowledge.

6. 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.

7. 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)

8. 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))

9. 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)))))

10. 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)))))

11. 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.

12. Semantics: Structures A structure consists of a nonempty set O together with the functions: – Interpretation function  –Semantic valuation function  –Satisfaction function 

13. 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 .

14. 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.

15. 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.

16. 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))))

17. Next Steps Incorporation of namespaces for KIF modules Semantics for sequence variables Syntax and semantics for Sorted-KIF Syntax and semantics for MetaKIF