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- Neil V. Murray, Erik Rosenthal
- J. ACM
- 1993

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)

- Neil V. Murray, Erik Rosenthal
- Theor. Comput. Sci.
- 1994

- Neil V. Murray, Erik Rosenthal
- AAAI
- 1987

- Andrew Matusiewicz, Neil V. Murray, Erik Rosenthal
- TABLEAUX
- 2009

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)

- Reiner Hähnle, Neil V. Murray, Erik Rosenthal
- ISMIS
- 1997

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)

- Neil V. Murray, Erik Rosenthal
- J. ACM
- 1987

A graphical representation of quantifier-free predicate calculus formulas in negation normal form and a new rule of inference that employs this representation are introduced. The new rule, <italic>path resolution</italic>, is an amalgamation of resolution and Prawitz analysis. The goal in the design of path resolution is to retain some of the advantages of… (More)

- James J. Lu, Neil V. Murray, Erik Rosenthal
- ISMVL
- 1993

- James J. Lu, Neil V. Murray, Erik Rosenthal
- J. Autom. Reasoning
- 1998

- Neil V. Murray, Erik Rosenthal
- TABLEAUX
- 2005

The goal of knowledge compilation is to enable fast queries. Prior approaches had the goal of small (i.e., polynomial in the size of the initial knowledge bases) compiled knowledge bases. Typically, query-response time is linear, so that the efficiency of querying the compiled knowledge base depends on its size. In this paper, a target for knowledge… (More)

- Reiner Hähnle, Neil V. Murray, Erik Rosenthal
- ISMIS
- 2005

A class of formulas called factored negation normal form is introduced. They are closely related to BDDs, but there is a DPLL-like tableau procedure for computing them that operates in PSPACE.Ordered factored negation normal form provides a canonical representation for any boolean function. Reduction strategies are developed that provide a unique reduced… (More)