Decidability and Complexity Analysis by Basic Paramodulation

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...

Basic Paramodulation

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...

Complexity, decidability and completeness

We give resource bounded versions of the Completeness Theorem for propositional and predicate logic. For example, it is well known that every computable consistent propositional theory has a computable complete consistent extension. We show that, when length is measured relative to the binary representation of natural numbers and formulas, every polynomial time decidable propositional theory ha...

Model Elimination with Basic Ordered Paramodulation