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Tree resolution and generalized semantic tree

Published: 01 December 1986 Publication History

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”.

References

[1]
'Chang, C-L. and Lee, R. C-T., Symbolic logic and mechanical theorem proving, Academic Press (197~3).
[2]
L0veland, D. W., Automated theorem proving: a logical basis, North-Holland, Inc., New York (1978).
[3]
Nilsson, N. J., Principles of artificial intelligence, Tioga, Palo Alto, California (1980).

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cover image ACM Conferences
ISMIS '86: Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems
December 1986
450 pages
ISBN:0897912063
DOI:10.1145/12808
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Association for Computing Machinery

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Published: 01 December 1986

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