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Theorem Proving with Ordering and Equality Constrained Clauses (1995)
| Venue: | Journal of Symbolic Computation |
| Citations: | 75 - 20 self |
BibTeX
@ARTICLE{Nieuwenhuis95theoremproving,
author = {Robert Nieuwenhuis and Albert Rubio},
title = {Theorem Proving with Ordering and Equality Constrained Clauses},
journal = {Journal of Symbolic Computation},
year = {1995},
volume = {19},
pages = {321--351}
}
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Abstract
constraint strategies and saturation Given a signature F , below we denote by S the set of all clauses built over F , and similarly by C the set of all constraints, and by EC the set of all equality constraints (which is a subset of C). Definition 3.1. An inference rule IR is a mapping of n-tuples of clauses to sets of triples containing a clause, a constraint and an equality constraint: IR : S n \Gamma! P(hS; C; ECi) An inference system is a set of inference rules. Definition 3.2. A constraint inheritance strategy is a function mapping a clause, two constraints and an equality constraint to a clause and a constraint: H : S \Theta C \Theta C \Theta EC \Gamma! S \Theta C Inference systems and constraint inheritance strategies are combined to produce inferences in the usual sense: given constrained clauses C 1 [[T 1 ]]; : : : ; Cn [[T n ]], we obtain a conclusion C [[T ]] as follows. Applying an inference rule to C 1 ; : : : ; Cn we obtain a triple hD; OT;ET i. Then the constraint...
