Tree resolution and generalized semantic tree

  • Authors:

  • S Kundu

  • Affiliations:

  • Computer Science Department, Louisiana State University, Baton Rouge, LA

  • Venue:
  • ISMIS '86 Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems
  • Year:
  • 1986

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Abstract

A resolution proof or a derivation of the empty clause from a set of clauses S = {C1, C2, …, Ck} is called a tree resolution if no clause Ci is used in more than one resolvent. We show that an unsatisfiable set of clauses S has a tree resolution proof if and only if there is a general semantic tree for S in which no clause appears in more than one terminal node. As an important application of this result, we derive a simple algorithm for obtaining a tree resolution proof, if one exists. The tree resolution proofs are important because they allow us to obtain the shortest “explanation”.