Declaration This dissertation is the result of my own work done under the guidance of my supervisor, and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. This dissertation is not substantially the same as any that I have submitted or will be submitting for a degree or diploma or other qualification at this or any other Universi...

This note shows that split-2 bisimulation equivalence (also known as timed equivalence) affords a finite equational axiomatization over the process algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981 to the recursion free fragment of Milner’s Calculus of Communicating Systems. Thus the addition of a single binary operation, viz. Hennessy’s merge, is sufficient for the...

Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications.

We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic Programming and E-generalization that includes an extension of Plotkin’s lgg theorem to the equational case. We demonstrate the potential power of E-generalization ...

This paper provides equational semantics for Dung’s argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the “extensions” of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support ...

Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications.

This paper is part of a long term eeort to increase expres-siveness of algebraic speciication languages while at the same time having a simple semantic basis on which eecient execution by rewriting and powerful theorem-proving tools can be based. In particular, our rewriting techniques provide semantic foundations for Maude's functional sublanguage, where they have been eeciently implemented. M...

In this paper we propose a new approach to theorem proving in first-order logic based on the term-rewriting method. First for propositional calculus, we introduce a canonical term-rewriting system for Boolean algebra. This system enables us to transform the first-order predicate calculus into a form of equational logic, and to develop several complete strategies (both clausal and nonclausal) fo...

Recent deductive approaches to reasoning about action and chance allow to model objects and methods in a deductive framework. In these approaches, inheritance of methods comes for free whereas overriding of methods is unsupported. In this paper , we present an equational logic framework for objects, methods, inheritance and overriding of methods. Overriding is achieved via the concept of specii...

An interpretation of the relational data model and various dependencies is given within the framework of cylindric algebras. It turns out that there is a natural translation of relational databases into cylindric set lattices, and that Codd’s relational operators have a simple interpretation in these structures. Consequently, various database constraints can be expressed in the equational langu...