Knowledge interchange

1. KIF and Common Logic Knowledge interchange Presentation By Balaji Gourabathina nbg082000@utdallas.edu

2. Knowledge Interchange? • Exchange of knowledge among different systems

3. Why do we need to interchange knowledge? • Knowledge is power supreme!! • Basic reason: Communication • How do we do this ? • Many ways and most of them are well known

4. In the context of computing world…… • It is the same • Differs in who and how we/they do it • To be specific : We need to know how computing systems exchange knowledge

5. This presentation • Focuses on two knowledge interchange mechanisms • KIF • CL

6. Why FOL not sufficient? • The friendly features of FOL can be liabilities on open networks • Assumptions about syntactic type and signature can differ across frameworks • Inference rules must apply to names in a uniform way

7. KIF : Knowledge Interchange Format • Knowledge Interchange Format (KIF) is a language designed for use in the interchange of knowledge among disparate computer systems • ~(KIF is intended as a primary language for interaction with human users) • ~(KIF is also intended as an internal representation for knowledge within computer systems)

8. How does it work? • when a computer system reads a knowledge base in KIF, it converts the data into its own internal form • All computation is done using these internal forms • When the computer system needs to communicate with another computer system, it maps its internal data structures into KIF

9. Categorical features essential to the design of KIF • The language has declarative semantics • The language is logically comprehensive • The language provides for the representation of knowledge about knowledge • Designed to maximize,implementability and readability

10. Syntax of KIF • Three layers • Characters-Basic characters of the language • Lexemes-Combination of characters • Expressions-Grammatically legal combination of lexemes

11. Characters • Classification of KIF characters • Upper case letters • Lower case letters • Digits • Alpha characters • Special characters • White space • Other characters

12. Lexemes • Lexical analysis-Process of converting characters into lexemes is called lexical analysis • Five types of lexemes in KIF • Special lexemes • Words • Character references • Character strings • Character blocks

13. Lexemes-contd.. • Each special character is a lexeme by itself • A word is a contiguous sequence of (1) normal characters or (2) other characters preceded by the escape character \. • word ::= normal | word normal | word\character • Character reference • Charref :: = #\character

14. Lexemes-contd.. • Character string • String :: = “quotable” • quotable ::= empty | quotablestrchar | quotable\character • strchar ::= character - {",\} • A character block consists of the character # followed by the decimal encoding of a positive integer n, the character q or Q, and then n arbitrary characters • Used in encoding audio, video and special formats • Variable -A word in which the first character is ? or @ • Individual variable – beginning with ? • Sequence variable – beginning with @

15. Lexemes-contd.. • Operators-Form complex expressions of various sorts • Term Operators • Sentence Operators • Definition Operators • Constants- All other words • Object constants- Denote individual objects • Function constants-Functions on those objects • Relation constants-Denote Relations • Logical constants-True or False • NOTE: The differences between these constants is only semantic not syntactic

16. Expressions • Three disjoint types of expressions • Terms-Denote Objects • Sentences-Express facts • Definitions-Define constants • Forms- Definitions and sentences • Knowledge base – Finite set of forms

17. Terms • 9 Types • Individual variables • Constants • Character References • Character Strings • Character Blocks • Functional Terms • List Terms • Quotations • Logical Terms

18. Terms…contd • Functional Terms • Implicit functional term-Consists of a constant and an arbitrary number of argument terms, terminated by an optional sequence variable and surrounded by matching parentheses • Explicit functional term-consists of the operator value and one or more argument terms, terminated by an optional sequence variable and surrounded by matching parentheses • List term - consists of the listof operator and a finite list of terms, terminated by an optional sequence variable and enclosed in matching parentheses

19. Terms…contd • Quotations-involve the quote operator and an arbitrary list expression • Logical terms-involve the if and cond operators

20. Sentences • BNF defines the set of legal sentences in KIF • 6 Types of sentences • Constants • Equation –Consists of = and two terms • Implicit relational sentence-consists of a constant and an arbitrary number of argument terms, terminated by an optional sequence variable • Explicit relational sentence-consists of the operator holds and one or more argument terms, terminated by an optional sequence variable and surrounded by matching parentheses

21. Basics • In order to allow a user to express the idea that a function is not meaningful for certain arguments, KIF assumes that there is a special "undefined" object in the universe and provides the object constant bottom to refer to this object • Functional Terms: Computation of values is better illustrated with examples • (+ 2 3) = 2+3=5 • (+ 1 @1)= 1+2+3+4=10,where @1 is a sequence variable 2,3,4

22. Basics…contd • Relational sentences • A simple relational sentence without a terminating sequence variable is true if and only if the relation denoted by the relation constant in the sentence is true of the objects denoted by the arguments • If a relational sentence terminates in a sequence variable, the sentence is true if and only if the relation contains the tuple consisting of the values of the terms that precede the sequence variable together with the objects in the sequence denoted by the variable • Equations and Inequalities • An equation is true if and only if the terms in the equation refer to the same object in the universe of discourse. • An inequality is true if and only if the terms in the equation refer to distinct objects in the universe of discourse.

23. Logic • Logical Terms • (if (> a 0) a (- a)) : absolute value of a number • (if (> 1 2) 1 (> 2 1) 2 0) = 2 • Logical Sentences • Similar to rules of inference • Quantified Sentences • A simple existentially quantified sentence is true if and only if the embedded sentence is true for some value of the variables mentioned in the first argument • A simple universally quantified sentence is true if and only if the embedded sentence is true for every value of the variables mentioned in the first argument • Definitions • No truth value • (defobjects := t) (= st)

24. Numbers • The referent of every numerical constant in KIF is assumed to be the number for which that constant is the base 10 representation • Inequality of distinct numerical constants can be inferred • For every t1 and distinct t2 the following sentence is true. (/= t1t2) • Functions on Numbers : Discussed earlier • Relations on Numbers • Examples, • (defrelation number (?x) := (or (real ?x) (complex ?x)))

25. Lists • Finite sequence of objects • Any objects in the universe of discourse can be the elements of a list • (listoft1 ... tk) denotes the list of objects denoted by t1, ..., tk • nil denotes empty list and null tests whether or not an object is the empty list • The functions first, rest, last, and but last each take a single list as argument and select individual items or sublists from those lists • Some of the functions include append,reverse,adjoin,length etc

26. Characters and Strings • There are 128 distinct characters known to KIF, corresponding to the 128 possible combinations of bits in the ASCII encoding • Two ways to refer to characters • The first method is use of charref syntax, i.e. the characters # and \, followed by the character to be represented • Second, 7 bit code corresponding to the character • The relationship between characters and their numerical codes is given via the functions char-code and code-char

27. Strings • List of characters • Three ways to refer strings • Enclose it in double quotes • Use of character blocks by prefixing with # • Using listof function(Useful because it allows us to quantify over characters with strings)

28. KIF:Theoritical Problems • The formalization problem • No general model theory for all constructs of KIF • Hence, no rigorous general notion of meaning • KIF is developed before the emergence of semantic web • Not standardized • Doesn’t follow XML-based paradigm • Connections to RDF/OWL unclear

29. Common Logic • Common Logic is a framework for a family of logic-based languages with the purpose of standardizing syntax and semantics for information interchange • Provides the basis for a set of syntactic forms (dialects) all sharing a common semantics • An XML framework for encoding and transmitting in an open network.

30. CL..contd • Abstract generalization and extension to KIF • Full-FOL expressibility • Designed for easy and natural use on web • Flexibility to use in open networks • No gratuitous assumptions about logical relationships between expressions(found in different ontologies)

31. CL : Abstract Syntax • Text : Either a set or list or bag of phrases • A piece of text that can be identified with a name • Phrase: Comment ,module, sentence • A comment is a piece of data • No restrictions • Comments can be attached to other comments • Module: Consists of a name and a text called the “body text” • Indicates the local domain of discourse • Importation: Contains a name

32. CL : Abstract Syntax…contd • Sentence : An atom , a Boolean sentence or a quantified sentence • A Boolean sentence has a type, called a connective and a number of sentences ,called the components of the sentence • A quantified sentence has • a type called quantifier • a finite,nonrepeating sequence of names and sequence markers called the binding sequence, each element of which is called a binding of the quantified sentence, • and a sentence called the body of the quantified sentence.

33. CL:Abstract Syntax….contd • An atom is either an equation containing two arguments, which are terms, or an atomic sentence. • An atomic sentence consists of a term, called the predicate, and a term sequence called the argument sequence. • Each term in the term sequence of an atomic sentence is called an argument of the sentence. • Any name can be the predicate in an atomic sentence. • A term is either a name or a functional term. • Terms may have attached comments. • A functional term consists of a term, called the “operator,” and a term sequence called the “argument sequence” • A term sequence is a finite sequence of terms or sequence markers. • A term sequence may be empty.

34. Traditional Model Theory • Traditional model theories for first-, second-, and higher-order logics map each name/variable type to a different semantic construct • First-order logic permits quantification over individuals only • Higher-order logics permit quantification over functions/classes/relations

35. Traditional Model Theory • Two things prevent “collapsing” individuals, functions, classes, relations into a single domain of logical individuals • Cardinality problems: There are more functions/classes/relations over individuals than there are individuals • Well-foundedness problems: Functions/classes/relations in standard HO logic defined as sets of (ordered ntuplesof) individuals • Hence, if functions/classes/relations are treated as individuals, we have to be able to make sense of functions that apply to themselves, classes that contain themselves, and relations that relate themselves to other individuals. • This violates the well-foundedness condition in standard set theories

36. CL Model Theory • In CL’s model theory, everything is a logical individual • Only names in CL dialects; VARIABLE is a syntactic role • Each individual has function and relation extensions. • Classes treated as 1-place relations • No fixed “arity” • One relation extension can contain n-tuples, for different n • Cardinality and Well-foundedness problems avoided

37. CL and the shortcomings of KIF • Formalization • CL has a rigorous model theory for all of its constructs and a proof theory • Specification • CL specifies structure rather than any particular form • This provides a general basis for determining/establishing conformance to CL syntax, hence a basis for meaning preserving translation • CL is an international ISO standard (ISO/IEC 24707) • CL framework includes XCL, an XML-based instance of CL Includes numerous web-oriented features

38. Questions??