We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete and efficient procedure to check nominal algebra equality. This subclass includes specifications of lambda-calculus an...

Maude is a reflective language supporting both rewriting logic and membership equational logic. Reflection is systematically exploited in Maude, endowing the language with powerful metaprogramming capabilities, including declarative strategies to guide the deduction process.

We investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground), and where the logic does not permit to express...

Reasoning about atoms (names) is difficult. The last decade has seen the development of numerous novel techniques. For equational reasoning, Clouston and Pitts introduced Nominal Equational Logic (NEL), which provides judgements of equality and freshness of atoms. Just as Equational Logic (EL) can be enriched with function types to yield the lambda-calculus (LC), we introduce NLC by enriching N...

Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like EQLOG, SLOG and RITE, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditi...

In an earlier paper, one of the present authors presented a preliminary account of an equational logic called PIM. PIM is intended to function as a “transformational toolkit” to be used by compilers and analysis tools for imperative languages, and has been applied to such problems as program slicing, symbolic evaluation, conditional constant propagation, and dependence analysis. PIM consists of...

The completeness theorem of equational logic of Birkhoff asserts the coincidence of the model-theoretic and proof-theoretic consequence relations. Goguen and Meseguer, giving a sound and adequate system of inference rules for many-sorted deduction, founded ultimately on the congruences on Hall algebras, generalized the completeness theorem of Birkhoff to the completeness theorem of many-sorted ...

In our previous study, we were interested in the equational fragment of first-order fuzzy logic [2, 3]. It turned out that the models of the equational fragment (which we call algebras with fuzzy equalities) are interesting and natural structures by themselves. The present paper provides an introductory study to the structures of equational fragment of fuzzy logic. The paper is an excerpt from ...

In less than a decade, Deduction with Constraints (DwC) has opened a new universe in computer science. DwC can be viewed from two perspectives: one related to the automated deduction framework 17, 19], the other to the development and usage of programming languages based on logic 7, 14]. Within the automated deduction framework, constraints on the generic data structure \terms" have become a po...