Consistency Constraints for Input/Output Logic: A Comparative Review
David Makinson, Leendert van der Torre · 1999
In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. In a separate paper, we developed a general theory of such processes when they are applied without restriction. In this paper, we compare systematically several ways of restricting them by consistency constraints. 1. Background We assume familiarity with (Makinson and van der Torre, this volume), which defines and studies unrestricted output operations. Nevertheless, for convenience, we briefly recall the central points. We work in a boolean context, that is, we consider a propositional language closed under the usual truth-functional connectives. The central objects of attention are ordered pairs (a,x) of formulae, which we read forwards, i.e. with a as body and x as head. Intuitively, we think of the body a as representing a possible input, and the head