A Reducing Method for Set of Clauses using Matrices.
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| Title: | A Reducing Method for Set of Clauses using Matrices. |
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| Authors: | Nishioka, Hiroaki1 |
| Source: | Systems & Computers in Japan. Jul87, Vol. 18 Issue 7, p1-10. 10p. |
| Subjects: | Matrices (Mathematics), Horn clauses, Logic programming, Computer programming, Computer systems |
| Abstract: | In resolution theory, logical formulas of a theorem and axioms must be converted to a form of a clause set (a set of clauses). For more efficient proof, it is desirable that an original clause set is a Horn set. Renaming is one of the operations which can convert a given clause set to a logically equivalent Horn set. To perform the operation for a clause set, negation signs of all literals that have the same predicate symbol should be inverted simultaneously. However, it is difficult to perform the operation systematically and efficiently. In this paper, a symbolic matrix called ‘literal reverse matrix’ is defied for each literal in a clause. Moreover, the definition of reverse matrix is extended for a clause. All renamings which convert a given claims to a Horn clause are derived from clause reverse matrix. Consequently, all renamings which convert a given clause set to a Horn set are synthesized from renamings for each clause in the set. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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