Refutational theorem proving using term-rewriting systems
Artificial Intelligence
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
On word problems in equational theories
14th International Colloquium on Automata, languages and programming
Structuring theories on consequence
Lecture notes in Computer Science on Recent trends in data type specification
A rationale for conditional equational programming
Theoretical Computer Science - Special issue on the international conference on fifth generation computer systems. Tokyo, 1988
Canonical sets of Horn clauses
Proceedings of the 18th international colloquium on Automata, languages and programming
On word problems in horn theories
Journal of Symbolic Computation
Handbook of theoretical computer science (vol. B)
Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
Term rewrite systems for lattice theory
Journal of Symbolic Computation
Label algebras and exception handling
TAPSOFT '93 Selected papers of the colloquium on Formal approaches of software engineering
Towards a foundation of completion procedures as semidecision procedures
Theoretical Computer Science
Free objects and equational deduction for partial conditional specifications
Theoretical Computer Science
Journal of Symbolic Computation
Term rewriting and all that
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Canonical Equational Proofs
A Soft Stairway to Institutions
Selected papers from the 8th Workshop on Specification of Abstract Data Types Joint with the 3rd COMPASS Workshop on Recent Trends in Data Type Specification
On the Role of Category Theory in the Area of Algebraic Specification
Selected papers from the 11th Workshop on Specification of Abstract Data Types Joint with the 8th COMPASS Workshop on Recent Trends in Data Type Specification
Term Rewriting in a Logic of Special Relations
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
On the Word Problem for Free Lattices
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
On a Generalised Logicality Theorem
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Canonical Conditional Rewrite Systems
Proceedings of the 9th International Conference on Automated Deduction
A Stability Theorem in Rewriting Theory
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Abstract canonical presentations
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
ACM Transactions on Computational Logic (TOCL)
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When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some theories, all the rewriting theories rely on a same set of notions, properties, and methods. Rewriting techniques have been used mainly to answer the validity problem of equational theories, that is, to compute congruences. Recently, however, they have been extended in order to be applied to other algebraic structures such as preorders and orders. In this paper, we investigate an abstract form of rewriting, by following the paradigm of logical-system independency. To achieve this purpose, we provide a few simple conditions (or axioms) under which rewriting (and then the set of classical properties and methods) can be modeled, understood, studied, proven, and generalized. This enables us to extend rewriting techniques to other algebraic structures than congruences and preorders such as congruences closed under monotonicity and modus ponens. We introduce convergent rewrite systems that enable one to describe deduction procedures for their corresponding theory, and we propose a Knuth-Bendix---style completion procedure in this abstract framework.