There have been active work to extend the Prolog style Horn Clause logic programming to non-Horn *** this paper,we will analyze the complexities of several such *** purpose is to understand the computational complexit...
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There have been active work to extend the Prolog style Horn Clause logic programming to non-Horn *** this paper,we will analyze the complexities of several such *** purpose is to understand the computational complexity of these inference *** analyses do not prove that any one system is better than the others all the *** they do suggest that one system may be better than the others for some particular *** also discuss the effect of caching.
The unification problem for terms containing associative and commutative functions is of importance in theorem provers based on term rewriting and resolution methods as well as in logic programming. The complexity of ...
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An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the...
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An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, and its termination can be easily established. Its complexity is easily analyzed and shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense.< >
We analyze the search space of two clause-based proof procedures, the Model Elimination procedure and Near-Horn Prolog, both of Loveland. We study how the search space changes with respect to the degree of how “non-H...
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Path dissolution is an efficient generalization of the method of analytic tableaux. Both methods feature (in the propositional case) strong completeness, the lack of reliance upon conjunctive normal form (CNF), and th...
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Path dissolution is an efficient generalization of the method of analytic tableaux. Both methods feature (in the propositional case) strong completeness, the lack of reliance upon conjunctive normal form (CNF), and the ability to produce a list of essential models (satisfying interpretations) of a formula. Dissolution can speed up every step in a tableau deduction in classical logic. The authors consider means for adapting both techniques to multiple-valued logics, and show that the speed-up theorem applies in this more general setting. These results are pertinent for modeling uncertainty and commonsense reasoning.< >
Theoretical results for identifying unnecessary inferences are discussed in the context of the use of a completion-procedure-based approach toward automated reasoning. The notion of a general superposition is introduc...
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Theoretical results for identifying unnecessary inferences are discussed in the context of the use of a completion-procedure-based approach toward automated reasoning. The notion of a general superposition is introduced and it is proved that in a completion procedure, once a general superposition is considered, all its instances are unnecessary inferences and, thus, do not have to be considered. It is also shown that this result can be combined with another criterion, called the prime superposition criterion, proposed by Kapur, Musser, and Narendran, thus implying that prime and general superpositions are sufficient. These results should be applicable to other approaches toward automated reasoning, too. These criteria can be effectively implemented, and their implementation has resulted in automatically proving instances of Jacobson's theorem (also known as the ring commutativity problems) usingRRL (Rewrite Rule Laboratory), a theorem prover based on rewriting techniques and completion.
We discuss a sequent style clause-based proof system that supports several important strategies in automatic theorem proving. The system has a goal-subgoal structure and supports back chaining with caching;it permits ...
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