Erik Rosenthal

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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 language of signed formulas offers a first-order classical logic framework for automated reasoning in multiple-valued logics. It is sufficiently general to include both annotated logics and fuzzy operator logics. Signed resolution unifies the two inference rules of annotated logics, thus enabling the development of an SLD-style proof procedure for(More)
Decomposable negation normal form (DNNF) was developed primarily for knowledge compilation. Formulas in DNNF are linkless, in negation normal form (NNF), and have the property that atoms are not shared across conjunctions. Full dissolvents are linkless NNF formulas that do not in general have the latter property. However, many of the applications of DNNF(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)
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)
The inference rule !-resolution was introduced in [27] as a technique for developing an SLD-style query answering procedure for the logic programming subset of annotated logic. The inference rule requires that the lattice of truth values be ordinary. In this paper, it is proved that all complete distributive lattices are ordinary. Properties of !-resolution(More)