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Path dissolution, a rule of inference that operates on formulas in negation normal form and that employs a representation called semantic graphs is introduced. Path dissolution has several advantages in comparison wdh many other reference technologies. In the ground case, lt preserves equivalence and is strongly complete: Any sequence of dissolution steps(More)
The prime implicate trie (pi-trie) of a logical formula is a tree whose branches are labeled with the prime implicates of the formula. The technology of reduced implicate tries is employed to analyze the structure of pi-tries. Appropriate lemmas and theorems are proved, and an algorithm that builds the pi-trie from a logical formula is developed.(More)
Completeness proofs that generalize the Anderson-Bledsoe excess literal argument are developed for calculi other than resolution. A simple proof of the completeness of regular, connected tableaux for formulas in conjunctive normal form (CNF) is presented. These techniques also provide completeness results for some inference mechanisms that do not rely on(More)