Abstract A logic is said to admit an equational completeness theorem when it can be interpreted into the consequence relative some class of algebras. We characterize logics admitting that are either locally tabular or have tautology. In particular, shown a protoalgebraic admits precisely has two distinct logically equivalent formulas. While problem determining whether decidable both for present...

We present an outline of a refinement calculus for strict functional programming, based on four-valued logic and equational reasoning. The languages imitates the features known from the imperative Refinement Calculus in a language of expressions.

We present a complete axiomatisation for four-valued sequential logic. It consists of nine axioms, from which all valid laws can be derived by equational reasoning. These nine axioms are independent of each other. © 2011 Elsevier B.V. All rights reserved.

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 ...

This dissertation describes a novel method for deriving logical consequences of first-order formulas using resolution and unskolemization. A complete unskolemization algorithm is given and its properties analyzed. This method is then applied to a number of different fields, namely program verification, machine learning, and mathematical induction. The foremost problem in automating program veri...

Appetizer. Algebraic logic (AL) is a well established discipline yet some natural questions remain out of its scope. For instance, it is well known that the Horn and universal fragments of FOL are original logics close to equational logic rather than just sublogics of FOL, and, very similarly, Gentzen's axiomatization of FOL seems has much in common with the universal equational logic: how can ...

1987 ABSTRACT In 1975 I started a small project to explore the consequences of implementing equational programs with no semantic compromises. Latest results include a compiler that executes exactly the logical consequences of an equa-tional program, with run-time speed comparable to compiled Franz LISP. This paper describes the accomplishments of the project very brieey, concentrating on shortc...

Orthogonal term rewriting systems (also known as regular systems) provide an elegant framework for programming in equational logic. O'Donnell showed that the parallel-outermost strategy, which replaces all outermost redexes in each step, is complete for such systems. Many of the reductions performed by this strategy could be wasteful in general. A lazy normalization algorithm that completely el...

For a programming system based on term rewrite rules such as equational logic programming, a serious eeciency problem of the generated code is the creation of terms that only serve to drive further pattern matching. In this paper, we deene a terminating call unfolding strategy based on ne-grain partial evaluation that removes much of this unnecessary term allocation for programs in intermediate...