Basic Paramodulation

Abstract

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 terms which are available for inferences. These refinements are compatible with standard ordering restrictions and are complete without paramodulation into variables or using functional reflexivity axioms. We prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption, and of techniques for eliminating redundant inferences.

Oriented Equational Logic Programming is Complete

“…Bachmair et al (1995). That inference system is complete when using a selection rule in F. However, it is not known to be complete for any selection rule outside of F. This was previously also the best known result for Horn clauses with equality.…”

“…Bachmair and Ganzinger (1994) and . Bachmair et al (1995). In this method, the literals in the body of a definite clause must be solved before the head can be used in an inference with the goal.…”

“…We have presented the inference system in an abstract setting which should make it possible to combine it with other theorem proving strategies, like the redex restrictions from . Bachmair et al (1995). One practical problem with our method (as in SLD-resolution) is that the goal-directedness might blow up the search space.…”

Superposition-based Equality Handling for Analytic Tableaux

“…A more restrictive form of equality handling is known in the resolution community as basic ordered paramodulation [5]. In comparison to basic superposition, the basicness restriction is strengthened: One forbids paramodulation below a position where a previous paramodulation step has taken place.…”

Reasoning in Description Logics by a Reduction to Disjunctive Datalog

“…Basic superposition [6,31] is a clausal calculus optimized for theorem proving with equality. We use standard definitions of terms, atoms, and literals.…”