The Model Evolution Calculus with Equality [chapter]

Peter Baumgartner, Cesare Tinelli
2005 Lecture Notes in Computer Science  
In many theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper we show how to integrate a modern treatment of equality in the Model Evolution calculus (ME), a first-order version of the propositional DPLL procedure. The new calculus, ME E , is a proper extension of the ME calculus without equality. Like ME it maintains an explicit candidate model, which is searched for by DPLL-style splitting. For equational reasoning ME E uses an adapted
more » ... version of the ordered paramodulation inference rule, where equations used for paramodulation are drawn (only) from the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many simplification techniques known from superposition-style theorem proving. Our main result is the correctness of the ME E calculus in the presence of very general redundancy elimination criteria.
doi:10.1007/11532231_29 fatcat:4zmryafkqzct5g3kskjhn2ja4y