# Bi-Rewrite Systems

@article{Levy1996BiRewriteS, title={Bi-Rewrite Systems}, author={Jordi Levy and Jaume Agust{\'i}-Cullell}, journal={J. Symb. Comput.}, year={1996}, volume={22}, pages={279-314} }

In this article we propose an extension of term rewriting techniques to automate the deduction in monotone pre-order theories. To prove an inclusionabfrom a given setIof them, we generate fromI, using a completion procedure, abi-rewrite system, that is, a pair of rewrite relations and , and seek a common termcsuch thatacandbc. Each component of the bi-rewrite system and is allowed to be a subset of the corresponding inclusion relation or defined by the theory ofI. In order to assure the…

## 35 Citations

### Structures for Abstract Rewriting

- Computer ScienceJournal of Automated Reasoning
- 2006

This paper investigates an abstract form of rewriting, by following the paradigm of logical-system independency, and introduces convergent rewrite systems that enable one to describe deduction procedures for their corresponding theory, and proposes a Knuth-Bendix–style completion procedure.

### An Abstract Way to Define Rewriting Logic

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2006

### Term Rewriting in a Logic of Special Relations

- Philosophy, Computer ScienceAMAST
- 1998

It is shown that by applying rewrite techniques to logical theories considered as instances of a general 'logic of special relations' the authors can unify and hence simplify the computational analysis within these theories.

### Context Unification and Traversal Equations

- Mathematics, Computer ScienceRTA
- 2001

This paper proves that, if the so called rank-bound conjecture is true, then the context unification problem is decidable, and reduces context unification to solvability of traversal equations and then to word equations with regular constraints.

### Deciding Context Unification

- Computer ScienceJ. ACM
- 2019

The technique is generalized to trees, and the corresponding algorithm is generalized from word equations to context unification, which shows that context unification is in PSPACE (in EXPTIME , when tree regular constraints are also allowed).

### Abstract rewriting logic parameterized by a formal system

- Computer Science
- 2007

This work will show that there exists a valid and useful notion of rewriting logic associated to any rewriting theory fitting an abstract framework developed by two of the authors in previous papers, and study the transformation that from the equational logic has resulted in the rewriting logic.

### On some variants of second-order unification

- Computer Science, Mathematics
- 2004

The main result of this thesis is the definition of a non-trivial sufficient and necessary condition on the unifiers, for the decidability of Context Unification, called rank-bound conjecture.

### On a Generalised Logicality Theorem

- Computer ScienceAISC
- 2002

It is shown that the convertibility relation obtained via semi-commutation is equivalent to the inference relation of the logic under consideration, which is logic-independent.

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