A General Logic

Abstract

This is an essay in logic in the traditional sense: the formal theory of inference. In it I attempt a unified account of a fairly wide range of logical systems, some very well known and others less so. These systems include classical logic, relevant logics such as Anderson and Belnap's R, close relatives of fuzzy logic, some modal logics and many weaker, but still interesting, nonstandard systems. These diverse logics, quite different in their philosophical underpinnings, are displayed as variations on a single and simple theme. Although its concern is with formal logic this paper is designed to be accessible to non- specialists. It only assumes familiarity with a natural-deduction formulation of elementary logic such as that of Lemmon's [6]. Nonclassical logics much as presented here have been introduced successfully to students with no formal logical training beyond a standard one-semester first course. Show more