lecch09 - CS2710,ISSP2610 Chapter9...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
1 CS 2710, ISSP 2610 Chapter 9 Inference in First-Order Logic
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Pages to skim Storage and Retrieval (p. starts bottom 328) Efficient forward chaining (starts p. 333) through  Irrelevant facts (ends top 337) Efficient implementation of logic programs (starts p. 340)  through Constraint logic programming (ends p. 345) Completeness of resolution (starts p. 350) (though see  notes in slides)
Background image of page 2
3 Inference with Quantifiers Universal Instantiation:  Given  2200 X (person(X)   likes(X, sun)) Infer person(john)   likes(john,sun)  Existential Instantiation: Given  5 x likes(x, chocolate) Infer: likes(S1, chocolate) S1 is a “Skolem Constant” that is not found anywhere  else in the KB and refers to (one of) the individuals  that likes sun.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Reduction to Propositional Inference Simple form (pp. 324-325) not efficient.  Useful conceptually. Replace each universally quantified sentence by all possible  instantiations All X (man(X)   mortal(X))  replaced by man(tom)   mortal(tom) man(chocolate)   mortal(chocolate)  Now, we essentially have propositional logic.   Use propositional reasoning algorithms from Ch 7
Background image of page 4
5 Reduction to Propositional Inference Problem:  when the KB includes a function symbol, the  set of term substitutions is infinite.   father(father(father(tom))) … Herbrand 1930:  if a sentence is entailed by the original  FO KB, then there is a proof using a finite subset of the  propositionalized KB Since any subset has a maximum depth of nesting in  terms,  we can find the subset  by generating all  instantiations with constant symbols, then all with depth  1, and so on
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Reduction to Propositional Inference We have an approach to FO inference via propositionalization that  is complete:   any entailed sentence can be proved Entailment for FOPC is semi-decidable : algorithms exist that say  yes to every entailed sentence, but no algorithm exists that also says  no to every nonentailed sentence. Our proof procedure could go on and on, generating more and more  deeply nested terms, but we will not know whether it is stuck in a  loop, or whether the proof is just about to pop out
Background image of page 6
7 Generalized Modus Ponens This is a general inference rule for FOL that does  not require instantiation  Given:   p1’, p2’ … pn’ (p1   … pn)   q Subst(theta, pi’) = subst(theta, pi) for all i Conclude: Subst(theta, q)
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
GMP is a lifted version of MP GMP “lifts” MP from  propositional  to  first-order   logic Key advantage of lifted inference rules over  propositionalization is that they 
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 42

lecch09 - CS2710,ISSP2610 Chapter9...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online