Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic of henceforth, next, and until, and to the propositional dynamic logic of regular programs.

Modern modal logic originated as a branch of philosophical logic in which the concepts of necessity and possibility were investigated by means of a pair of dual operators that are added to a propositional or first-order language. The field owes much of its flavor and success to the introduction in the 1950s of the “possible-worlds” semantics in which the modal operators are interpreted via some “accessibility relation” connecting possible worlds. In subsequent years, modal logic has received attention as an attractive (...) approach towards formalizing such diverse notions as time, knowledge, or action. Nowadays, modal logics are applied in various disciplines, ranging from economics to linguistics and computer science. Consequently, there is by now a large variety of modal languages, with an even greater wealth of interpretations. For instance, many applications require a poly-modal framework consisting of a language with a family of modal operators and a semantics in which the corresponding accessibility relations are connected somehow. (shrink)

Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed ...

This new edition of the classic Contemporary Theories of Knowledge has been significantly updated to include analyses of the recent literature in epistemology.

This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.

We present two finitely axiomatized modal propositional logics, one betweenTandS4 and the other an extension ofS4, which are incomplete with respect to the neighbourhood or Scott-Montague semantics.Throughout this paper we are referring to logics which contain all the classical connectives and only one modal connective □ (unary), no propositional constants, all classical tautologies, and which are closed under the rules of modus ponens (MP), substitution, and the rule RE (fromA↔Binfer αA↔ □B). Such logics are calledclassicalby Segerberg [6]. Classical logics which (...) contain the formula □p∧ □q→ □(p∧q) (denoted byK) and its “converse,” □{p∧q)→ □p∧ □q(denoted byR) are called regular;regularlogics which are closed under the rule of necessitation, RN (fromAinfer □A), are callednormal. The logics that we are particularly concerned with are all normal, although some of our results will be true for all regular or all classical logics. It is well known thatKandRand closure under RN imply closure under RE and also that normal logics are also those logics closed under RN and containing □{p→q) → {□p→ □q). (shrink)

This paper presents a partial analysis of perceptual knowledge, an analysis that will, I hope, lay a foundation for a general theory of knowing. Like an earlier theory I proposed, the envisaged theory would seek to explicate the concept of knowledge by reference to the causal processes that produce (or sustain) belief. Unlike the earlier theory, however, it would abandon the requirement that a knower's belief that p be causally connected with the fact, or state of affairs, that p.

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

This edition includes new essays by philosopher Michael Williams and literary scholar David Bromwich, as well as Rorty's previously unpublished essay "The ...

This multiplex semantics incorporates multiple relations of deontic accessibility or multiple preference rankings on alternative worlds to represent distinct normative standards. This provides a convenient framework for deontic logic that allows conflicts of obligation, due either to conflicts between normative standards or to incoherence within a single standard. With the multiplex structures, two general senses of "ought" may be distinguished, an indefinite sense under which something is obligatory when it is enjoined by some normative standard and a core sense for (...) when something is enjoined by all normative standards. Multiple normative standards may themselves be given a preferential order; this leads to a concept of ranked obligation. This paper presents the foundations of this multiplex semantics and the propositional deontic logics they define. (shrink)

In this paper we show that the Hilbert system of agency and ability presented by Dag Elgesem is incomplete with respect to the intended semantics. We argue that completeness result may be easily regained. Finally, we shortly discuss some issues related to the philosophical intuition behind his approach. This is done by examining Elgesem's modal logic of agency and ability using semantics with different flavours.

A history of the logic of action is outlined, beginning with St Anselm. Five modern authors are discussed in some detail: von Wright, Fitch, Kanger, Chellas and Pratt.