Extensional Theories and Rewriting

A rewriting approach to satisfiability procedures

We show how a well-known superposition-based inference system for first-order equational logic can be used almost directly for deciding satisfiability in various theories including lists, encryption, extensional arrays, extensional finite sets, and combinations of them. We also give a superposition-based decision procedure for homomorphism. 2003 Elsevier Science (USA). All rights reserved.

POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

Extensional Rewriting with Sums

Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simply-typed λ-calculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simply-typed λ-calculus extended with sum types. Unlike previous decidability results, which rely on advanced rewr...

On Modular Properties of Higher Order Extensional Lambda Calculi

We prove that confluence and strong normalisation are both modular properties for the addition of algebraic term rewriting systems to Girard’s F! equipped with either -equality or -equality. The key innovation is the use of -expansions over the more traditional -contractions. We then discuss the difficulties encountered in generalising these results to type theories with dependent types. Here c...

Query Rewriting under Extensional Constraints in DL-Lite