Basic Paramodulation

A New Approach to Inferences of Semantic Constraints

Chase procedures are well-known decision and semi-decision procedures for the implication problem among dependencies, a specific type of first-order logic formulas, that are used for expressing database constraints. Of course, the implication problem can also be treated by general refutationally complete inference systems, like resolution with paramodulation. Recently the inference rule of basi...

Decidability and Complexity Analysis by Basic Paramodulation

It is shown that for sets of Horn clauses saturated under basic paramodulation the word and unifiability problems are in NP, and the number of minimal unifiers is simply exponential (i). For Horn sets saturated w.r.t. a special ordering under the more restrictive inference rule of basic superposition, the word and unifiability problems are still decidable and unification is finitary (ii). These...

Stadtwald D 66123 Saarbrücken Germany

We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the ter...

Basic Paramodulation and Decidable Theories (Extended Abstract)

We prove that for sets of Horn clauses saturated under basic paramodulation, the word and uniiabil-ity problems are in NP, and the number of minimal uniiers is simply exponential (i). For Horn sets saturated wrt. a special ordering under the more restrictive inference rule of basic superposition, the word and uniiability problems are still decidable and uniication is nitary (ii). We deene stand...

Model Elimination with Basic Ordered Paramodulation