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Understanding Unification in First-Order Logic and Its Applications in Prolog

This note covers the concept of unification in first-order logic, highlighting examples like unifying Knows(John,x) and Knows(y,z). It explains the process of finding the most general unifier (MGU), which is essential in logic programming. The unification algorithm is linked to Prolog, a prominent logic programming language that employs backward chaining with Horn clauses. The document discusses key features of Prolog, including built-in predicates and the closed-world assumption, with practical examples such as list manipulation.

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Understanding Unification in First-Order Logic and Its Applications in Prolog

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  1. Notes 9:Inference in First-order logic ICS 171 Fall 2006

  2. Unification • To unify Knows(John,x) and Knows(y,z), θ = {y/John, x/z } or θ= {y/John, x/John, z/John} • The first unifier is more general than the second. • There is a single most general unifier (MGU) that is unique up to renaming of variables. MGU = { y/John, x/z }

  3. The unification algorithm

  4. The unification algorithm

  5. Logic programming: Prolog • Algorithm = Logic + Control • Basis: backward chaining with Horn clauses + bells & whistles Widely used in Europe, Japan (basis of 5th Generation project) Compilation techniques  60 million LIPS • Program = set of clauses = head :- literal1, … literaln. criminal(X) :- american(X), weapon(Y), sells(X,Y,Z), hostile(Z). • Depth-first, left-to-right backward chaining • Built-in predicates for arithmetic etc., e.g., X is Y*Z+3 • Built-in predicates that have side effects (e.g., input and output • predicates, assert/retract predicates) • Closed-world assumption ("negation as failure") • e.g., given alive(X) :- not dead(X). • alive(joe) succeeds if dead(joe) fails

  6. Prolog • Appending two lists to produce a third: append([],Y,Y). append([X|L],Y,[X|Z]) :- append(L,Y,Z). • query: append(A,B,[1,2]) ? • answers: A=[] B=[1,2] A=[1] B=[2] A=[1,2] B=[]

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