Affiliation:
1. Lawrence Radiation Laboratory University of California, Livermore, California
Abstract
The theory of J. A. Robinson's resolution principle, an inference rule for first-order predicate calculus, is unified and extended. A theorem-proving computer program based on the new theory is proposed and the proposed semantic resolution program is compared with hyper-resolution and set-of-support resolution programs. Renamable and semantic resolution are defined and shown to be identical. Given a model
M
, semantic resolution is the resolution of a latent clash in which each “electron” is at least sometimes false under
M
; the nucleus is at least sometimes true under
M
.
The completeness theorem for semantic resolution and all previous completeness theorems for resolution (including ordinary, hyper-, and set-of-support resolution) can be derived from a slightly more general form of the following theorem. If
U
is a finite, truth-functionally unsatisfiable set of nonempty clauses and if
M
is a ground model, then there exists an unresolved maximal semantic clash [
E
1
,
E
2
, · · ·,
E
q
,
C
] with nucleus
C
such that any set containing
C
and one or more of the electrons
E
1
,
E
2
, · · ·,
E
q
is an unresolved semantic clash in
U
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
127 articles.
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