Graph-Based Proof Procedures for Horn Clauses
The origins of this monograph lie in my Ph.D. dissertation of 1987 at the University of Pennsylvania, which was concerned with proof procedures for the Horn clause subset of logic. The rise of logic programming has made this an important area of study. All Prologs are based on a variant of resolution, and inherit various properties related to this proof method. This monograph studies the paradigm of logic programming in the context of graph-based proof procedures which are unrelated to resolution. The monograph is not a general introduction to logic programming, although it is self-contained with respect to the mathematics used. It should appeal to the computer scientist or mathematician interested in the general area we now call computational logic. A large part of the monograph is devoted to detailed proofs that the methods we present are sound and complete, which in the context of the logic programming, means that the operational and denotational semantics agree.
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algorithm all-solutions protocol answer substitution arity atomic formulae chapter chosen for expansion clause logic clauses with equality computation consisting defined definite clause denotational semantics denoted disjoint equational Horn clauses example ff-graph ff-refutation finite set first-order logic foreach free variables function symbol Gallier goal graph expansion step graph G graph GT(P ground HE-refutation ground Horn clauses ground terms H-graph Herbrand Base Herbrand structure Herbrand universe Herbrand's theorem Horn clause logic Hornlog method Hornlog system interpreted lemma logic program many-sorted first-order language mapping merging model-theoretic MP,Q n-tuple negation negation normal form negative clause node node chosen node labeled OP,Q operational semantics parallel pebbling processor Prolog query Q rewrite steps sentences sequence set of E-unifiers set of ground set of Horn set to true sets of variables Skolem-Herbrand-Godel theorem SLD-resolution sort soundness and completeness subset subterm TERM(P truth field unification unifier unsatisfiable iff