Automated reasoning and nonclassical logics: Introduction

Abstract

In the mid-1980s researchers in the computer science and artificial intelligence communities began to take an interest in logics studied by logicians and philosophers since at least Aristotle in the fourth century BC. These are logics such as deontic, epistemic, intuitionistic, modal, paraconsistent, relevant, and temporal logics, all of which are usually collected under the somewhat unsatisfactory name of nonclassical, or nonstandard, logics. During the past several years, the interest in nonclassical logics in these communities has increased enormously, as anyone remotely familiar with them will know. To the reader unfamiliar with this territory we recommend [3] for a masterful historical survey of it from the time of Aristotle. A huge amount of modem work has been done in the field during this century, and the total literature would probably exceed 4000 items. Central research directions in this field have been surveyed in many places, but in our opinion the definitive work is Gabbay and Guenthner's multivolume Handbook of Philosophical Logic, the first volume of which was published in 1983 by Reidel. Recent research done on nonclassical logics in computer science and artificial intelligence is to be the subject of two further multivolume series, currently in preparation by Gabbay and others, called the Handbook of Logic in Computer Science and the Handbook of Logic in Artificial Intelligence and Logic Programming. These will be published over the next few years. Sophisticated automated reasoning systems based on classical logic have been in use for over 20 years. However, similar systems for nonclassical logics have only recently made an appearance. This special issue of the Journal of Automated Reasoning addresses the use of automated reasoning systems to solve problems in a ntmaber of nonclassical logics. Indeed, a common theme to all of the papers in this issue is that they discuss the implementations of various automated reasoning systems. Here we have in mind automated reasoning systems in possibly a broader sense than is usual. Automated reasoning systems tend to be equated with automated theorem-proving systems. At least two of the papers in this special issue, those of Slaney and Pritchard, are concerned with the automation of methods for finding non-theorems.