1. AI - Week 13 Knowledge Representation, Logic, Semantic Web Lee McCluskey, room 2/07 Email lee@hud.ac.uklee@hud.ac.uk http://scom.hud.ac.uk/scomtlm/cha2555/ NB I WILL BE AWAY NEXT WEEK

2. School of Computing and Mathematics, University of Huddersfield Sketch of Term 2 1. Knowledge Representation, Logic, Semantic Web - Requirements for fomalised knowledge (Semantic Web, Ontology) - First Order Logic representation and reasoning - Prolog as First Order Logic - Description Logics - OWL : Description Logic for the Semantic Web - Ontology Creation (Protégé) 2. Machine Learning - Knowledge Acquisition and Engineering - Knowledge Extraction - Data Mining - Skill Acquisition

3. School of Computing and Mathematics, University of Huddersfield Overview n We need to FORMALISE knowledge to make it independent of PROCESS or FUNCTION, so that processes can “understand” the knowledge represented. n It is very hard to represent diverse, rich, highly structured information, and allow efficient reasoning with it, using a single formalism or language

4. School of Computing and Mathematics, University of Huddersfield Semantic Web n The vision of the “Semantic Web” is to have all public (www) ‘data’ encoded in a way that ANY application program can use it – even programs that have no encoding to anticipate the meaning of the data. n A second (dual) requirement of the semantic web is to have all public (www) processes or services encoded in a way that ANY application program can use then - even programs that have no encoding to anticipate the meaning of them. n The meaning of the data / processes will therefore have to be encoded u.. To be program-independent (declarative) u.. To be accessible to the client program n So all programs using the Semantic Web will have to ‘understand’ HOW to extract the meaning of data / services encoded within it. Thus the Semantic Web will contain knowledge representation..

5. School of Computing and Mathematics, University of Huddersfield Knowledge on the Web? We want to represent CONCEPTUAL KNOWLEDGE on the WEB. How is this to be done?

6. School of Computing and Mathematics, University of Huddersfield Ontologies Knowledge in the Semantic Web will mainly be held in what are called “Ontologies” An Ontology is a a precise, structured representation of a ‘conceptualisation’ An Ontology is often written in some kind of LOGIC Reality Conceptualisation C subset of X U Y D&Y => Z Ontology X Y “an abstract, simplified view of the world”

7. School of Computing and Mathematics, University of Huddersfield First - order (predicate) logic FOL (FOPL) is a notation used widely in computing for - giving meaning to systems eg relational calculus in data bases - model of computation (with computational forms such as Prolog) - to help prove program correctness - modelling intelligent software agents - expressing and manipulating knowledge … FOPL can be used to represent conceptual knowledge

8. School of Computing and Mathematics, University of Huddersfield FOPL – grammar Syntax Classes Example Syntax constants.. a,b,c... functions.. f,g,h... - apply to constants/vars predicates.. p,q,r...- unary, binary,.. variables.. x,y,z... quantifiers.. A, E connectives.. V, &, =>,, <= Other bits.. Brackets Wffs – well formed formulae Eg Ax(p(x) => Ey q(x,y)&p(y))

9. School of Computing and Mathematics, University of Huddersfield FOPL – grammar WFF ::= ATOM | ~ ATOM | (WFF) | WFF connective WFF | quantifier variable WFF ATOM ::= predicate | predicate(ARG-LIST) ARG-LIST ::= TERM | TERM, ARG-LIST TERM ::= constant | variable | function(ARG-LIST)

10. School of Computing and Mathematics, University of Huddersfield Ontologies and FOPL: Specifying the Conceptualisation n Let constants denote object names and date type values in the world n Let unary predicates represent properties/classes eg cat(x), person(x),.. n Let binary predicates represent relations between objects, and values of attributes eg brother(bill,ben) status(tank, full) n Let the Wffs represent the logical structure of the conceptualisation

11. School of Computing and Mathematics, University of Huddersfield FOPL: interpretation Given Wffs in FOPL, an interpretation I is given by mapping the constants, function and predicate symbols to elements in the conceptualisation We say that Wff W is true in an interpretation I if W evaluates to true under I. The evaluation uses the well known meaning of connectives and quantifiers

12. School of Computing and Mathematics, University of Huddersfield FOPL: interpretation - example Universe = persons Wffs Ax,Ax,Az g(x,y) <= (f(x,z)&p(z,y)) Ax,Ay,Az u(x,y) <= (p(z,y)&b(x,z)) Ax m(x) => p(x) Ax f(x) => p(x) Example Interpretation is: g = grandfather, f = father, p = parent, b = brother, u = uncle, m = mother Are the wffs true?

13. School of Computing and Mathematics, University of Huddersfield FOPL – reasoning IN fopl we are fundamentally interested in if a wff w LOGICALLY FOLLOWS from another wff W (usually written as “..a set of WFFs”) W |= w Definition: w logically follows from W if and only if every interpretation that makes W true also makes w true

14. School of Computing and Mathematics, University of Huddersfield FOPL – more definitions A Wff is Satisfiable – at least one interpretation makes it true Unsatisfiable – no interpretation makes it true Tautological or Valid – all interpretations makes it true

15. School of Computing and Mathematics, University of Huddersfield Conclusion: n AI applications often need representations of knowledge such as ontologies n The Semantic Web will be one such application n Logic can be used to specify a conceptualisation ie to define an ontology n We have introduced FOPL and some definitions eg “Interpretation”, “Logically Follows”, “(Un)satisfiable”