Equational logic and theories in sentential languages

Equational Logic and Equational Theories of Algebras

Equational Logic and Theories of Action

This is a survey on reasoning about situations, actions, and causality within equational logic. Its main feature is the representation of situations as multisets of resources. Such resources are consumed whenever the conditions of an action are satissed and are produced whenever the action is applied. It is demonstrated that the well{known frame and ramiication problems can be elegantly solved ...

Modelling theories of actions by Equational Logic Programs

A sound and complete approach for encoding the action description language A developed by M. Gelfond and V. Lifschitz in an equational logic program is given. Our results allow the comparison of the resource-oriented equational logic based approach and various other methods designed for reasoning about actions, most of them based on variants of the situation calculus, which were also related to...

A Method for Implementing Equational Theories as Logic Programs

Equational theories underly many elds of computing, including functional programming, symbolic algebra, theorem proving, term rewriting and constraint solving. In this paper we show a method for implementing many equational theories with a limited class of logic programs. We de ne regular equational theories, a useful class of theories, and illustrate with a number of examples how our method ca...

Equational Theories in CERES

Cut-elimination is the most important proof transformation in logic. Equality is a central paradigm in mathematics and plays a key role in automated deduction. Therefore its importance awakes the necessity of integrating equality into existing cut-elimination methods. In this paper we extend the resolution-based method of cut-elimination CERES to CERES-e by adding equality (and paramodulation t...