S Kundu
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”.
- 1.'Chang, C-L. and Lee, R. C-T., Symbolic logic and mechanical theorem proving, Academic Press (197~3). Google Scholar
Digital Library
- 2.L0veland, D. W., Automated theorem proving: a logical basis, North-Holland, Inc., New York (1978).Google Scholar
- 3.Nilsson, N. J., Principles of artificial intelligence, Tioga, Palo Alto, California (1980). Google ScholarDigital Library
Index Terms
- Tree resolution and generalized semantic tree
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