UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Using Definite Knowledge Notes for Ch.3 of Poole et al. CSCE 580 Marco Valtorta

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Definite Clause Language A database language A question-answering system A programming language A representation and reasoning systems (RRS)

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Definite Clauses as RRS Which concepts and individuals to represent? At what level of detail? Is each clause true in the intended interpretation? –If so, a sound proof procedure will generate only answers that are true in the intended interpretation! Do the rules for the predicates cover all cases?

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering House Wiring (elect.pl) Review Fig. 3.1 (same as 1.3) Level of detail (abstraction) influenced by goals of modeling and available information –Determine whether light are on or off –Voltage and frequency are irrelevant –Common-sense level: we may ignore Kirkhoff’s law

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Individuals and Relations Wires, switches, lights, outlets, circuit breakers. Relationships represented by predicates: –light(L)---L is a light –lit(L)---L, a light, is lit –live(W)---W, a wire, has current –up(S)---S, a switch, is up –down(S) –ok(E)---E, a circuit breaker or a light, is not blown –connected_to(X,Y)---current (if present at Y) would flow to X.

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Axiomatize! Write what is true in the intended interpretation, using constant and predicate names. Start with facts. –light(l1)---l1 is a light –down(s1)---switch s1 is down –ok(l2)---l2 is not blown There is a “light” predicate but no “switch” predicate. Why? –Because we distinguish lights when we define “lit” –Because switches cannot be broken

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Keep axiomatizing! Rules, e.g.: –connected_to(w0,w1) <- up(s2) Is this true in the intended interpretation? Check it! –Check what? The figure! –connected_to(w5, outside). Should connected_to be transitive? Symmetric? Reflexive? –Maybe, but it is not in elect.pl!

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering More Rules for House Wiring lit(L) <- light(L) & ok(L) & live(L). A recursive definition: –live(Y) <- connected_to(Y,Z) ^ live(Z). –live(outside).

UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Is this axiomatization good? Every clause is true in the intended interpretation. Some “true” facts are not represented at all. –Some are impossible to represent in definite clause logic without introducing new predicates or constants, e.g.: “If a light is ok and live and it is not lit, then it is blown” requires a negated atom in the body of a clause!