Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. Hughes 1985, paperback at the best online prices at ebay. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their. Modal logic introduces three new symbols into classical. Narrowly construed, modal logic studies reasoning that involves the use of the expressions necessarily and possibly. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. W is called our universe and elements of w are called worlds r is a relation on w. In a companion paper we will introduce natural deduction systems for the. However, the term modal logic is used more broadly to cover a family of logics with similar rules and a variety of different symbols. An introduction to modal logic and a companion to modal logic.
However, unlike other empirical discoveries about language made in the. A companion to philosophical logic provides a comprehensive stateoftheart handbook for students and professional researchers in philosophical logic. We use a simple modal logic, which is an extension of the wellknowns5 logic, and base the contrastive operators proposed by francez in 2 on the basic modalities that appear in this. That is, it presents modal logic as a tool for talking about structures or models. Logical approach a companion to philosophical logic wiley online library. Assignments modal logic linguistics and philosophy. A modala word that expresses a modalityqualifies a statement. Introduction to philosophylogicmodal logic wikibooks. Pdf on intuitionistic modal and tense logics and their.
Lewiss pioneering work starting in 1912, with the first systems devised in 1918, to s. Intuitionistic and modal predicate logic as categorical doctrines 43. A modal a word that expresses a modalityqualifies a statement. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal this longawaited book replaces hughes and cresswells two classic studies of modal logic. T opological semantics for intuit ionistic logic and for the classical modal logic s4 have a long history going back to tarski an d coworkers i n the 1930s and 40s, predating the relational. Hughes of an introduction to modal logic and a companion to modal logic, the standard works in the field. Given a class c of models, a binary relation r on c, and a modeltheoretic language l, we consider the modal logic and the modal algebra of the theory of c in l where the modal operator is. A nice introduction to modal logic though somewhat outdated. Basic concepts in this chapter we recollect some basic facts concerning modal logic, concentrating on completeness theory. Counterfactuals, neighborhood semantics, probability, predicative necessity, etc. Completeness results for intuitionistic and modal logic in a. Cresswell this longawaited book replaces hughes and cresswells two classic studies of modal logic. But what kind of structures can modal logic talk about.
A new introduction to modal logic george edward hughes. This book was later replaced by a new introduction to modal logic 1996. On intuitionistic modal and tense logics and their. When we wrote it, we were able to give a reasonably comprehensive survey of. He is the author of philosophy of mind 1994, meinongian logic. A list describing the best known of these logics follows. Introduction to modal and temporal logics 6 december 2007 3 logic syntax and semantics or calculus syntax.
A companion to the philosophy of language hale and wright, ed. Some of the high points are temporality the possible world semantics as given by stig kanger and saul kripke connects formal systems for modal logic and geometrical assumptions about the temporal relation. Please refer to the assigned text for homework assignments and the take home final. Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality. The material presented here is not a direct component of the course but is offered to you as an incentive and a support to understand and master the concepts and exercises presented during the course. Konyndyk, introductory modal logic, notre dame, 1986. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle. Proof theory of modal logic has always been a delicate subjectthe intension.
Chellas pdf online free download info about modal logic. In logic, a modal companion of a superintuitionistic intermediate logic l is a normal modal logic which interprets l by a certain canonical translation, described below. Evenif 1 and 2 are themselves normal modal logics, 1. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. Names and rigid designation a companion to the philosophy. A new textbook on modal logic providing a modern introduction to modal logic. In this tutorial, we give examples of the axioms, consider some rules of inference and in particular, the derived rule of necessitation, and then draw out some consequences. Modal logic for philosophers designed for use by philosophy students, this book provides an accessible yet technically sound treatment of modal logic and its philosophical applications. An approach to the logic of action normative act positions actions and normative positions. Neighborhood semantics for modal logic an introduction. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. The semantics of existence and nonexistence 1996, wittgensteins thought in transition 1998, symbolic logic 2001, david humes critique of infinity 2001, and on boole.
Cresswell, a companion to modal logic, methuen, 1984. Note that the cylindric operators 9 and,their irreflexive companions 6, and the. Book note ge hughes and mj cresswell, a companion to modal. Aristotles modal logic, first published in 1995, presents an interpretation of aristotles logic by arguing that a proper understanding of the system depends on an appreciation of its connection to the metaphysics. When we wrote it, we were able to give a reasonably comprehensive survey of the state of modal logic at that time.
These are important in his discussion of modal logic and tense logic. Books notes on modal logic stanford university preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal. A new introduction to modal logic is an entirely new work, completely rewritten by the authors to incorporate all the new developments that have taken places since 1968 both in modal propositional logical and modal predicate logic, but without sacrificing the clarity of exposition and approachability that were essential features of the earlier. Relational sheaves and predicate intuitionistic modal logic. Article pdf available in annals of pure and applied logic. A companion to philosophical logic dale jacquette ed. Basic concepts in modal logic1 stanford university. Modal logic attempts to include the notions of modality necessary, contingent, possible and impossible, among others into the structure of classical logic propositional logic and predicate calculus and is therefore an extension of classical logic. The scope of this entry is the recent historical development of modal logic, strictly understood as the logic of necessity and possibility, and particularly the historical development of systems of modal logic, both syntactically and semantically, from c. Modern origins of modal logic stanford encyclopedia of.
Preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal logic. This book presupposes that readers know the attractions and power of this approach, including the notions of logical syntax, semantics, proof, and metatheory of formal systems. Richard patterson develops three striking theses in the book. An introduction pdf format for free to read online. An introduction to its syntax and semantics amazon site. Ml2 are interpreted over the same class f of frames f. Dale jacquette is professor of philosophy at the pennsylvania state university. Philosophical logic princeton foundations of contemporary philosophy john p. Oct 01, 2015 a brand new series dealing with three types of modal logic known as deontic logic october, temporal logic november, and doxastic logic december.
Numerous and frequentlyupdated resource results are available from this search. A companion to philosophical logic wiley online books. For example, modal logic can be given an algebraic semantics, and under this interpretation modal logic is a tool for talking about what are known as boolean algebras with operators. Pdf a new introduction to modal logic download full. An advanced, but very accessible, textbook focusing on the main technical results in the area. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal. Topological semantics for intuitionistic logic and for the classical modal logic s4 have a long history going back to tarski and coworkers in the 1930s and 40s, predating the relational kripke semantics for both 29, 36.
Oct 20, 1995 a new introduction to modal logic is an entirely new work, completely rewritten by the authors. Download pdf a new introduction to modal logic free. Modal logic gives a frame work for arguing about these distinctions. One is to explain what modal logic is, and how it is done.
In this paper we present a modal approach to contrastive logic, the logic of contrasts as these appear in natural language conjunctions such as but. An introduction to modal logic geared to wards philosophy students. A semantic perspective 3 chapters in this handbook. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. The main goal of the corse is to understand the basic techniques, results and applications of neighborhood semantics for modal logic and to understand the exact relationship with the standard relational semantics. K serves as the foundation for a whole family of systems. Modal logics for qualitative possibility theory core. Lecture notes modal logic linguistics and philosophy. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus.
Modal companions share various properties of the original intermediate logic, which enables to study intermediate logics using tools developed for modal logic. This book presupposes that readers know the attractions and power of this approach, including the notions of logical syntax, semantics, proof, and. Second, many results can be understood more readily in the abstract setting. Modal companions a modal logic m s4 is amodal companionof an intermediate logic l ipc if for any propositional formula we have l iff m. Hughes, of an introduction to modal logic, london, methuen, 1968. Logic as algebra 2001, as well as numerous articles on logic. Cresswell was the coauthor with his colleague and former teacher g. An earlier book of ours, entitled an introduction to modal logic iml, was published in 1968. An introduction to its syntax and semantics 9780195366570.
For example, the statement john is happy might be qualified by saying that john is usually happy, in which case the term usually is functioning as a modal. In handbook of logic in artificial intelligence and logic programming. By modal decomposition i obtain completeness and other results for. On intuitionistic modal and tense logics and their classical companion logics. The subject of this dissertation is manydimensional modal logic. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Cresswell, a companion to modal logic methuen, london, 1984.
At the talk, dana introduced a new, probabilistic semantics for modal logica semantics about which very little was known at the time. Aristotle may also be credited with the formulation of several metalogical theses, most notably the law of noncontradiction, the principle of the excluded middle, and the law of bivalence. Csli, 1987, george hughes and max cresswell an introduction to modal logic, london. Note that if is a normal logic and l is a language which might not contain, then. This very extensive volume represents the current statof a airs in modal logic. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. We now say that v is an allowable valueassignment ilf, for every variable p, all the worlds in which p is true form an allowable subset of w.
He is the author of logics and languages, in which he developed an alternative version of montague grammar, as well as many articles on possibleworlds semantics. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic. This book is to be read and you can also see how the usefulness of the book modal logic. Each member of the family results from strengthening k in some way.
977 1508 255 827 653 1169 1344 1517 883 494 116 884 1373 1021 254 327 372 898 909 711 1126 466 925 427 568 1208 1382 414 559 745 471 860 143 205