Cresswell, a companion to modal logic methuen, london, 1984. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic. A modal a word that expresses a modalityqualifies a statement. Pdf a new introduction to modal logic download full. Modalities in medieval logic illc universiteit van amsterdam. 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. 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. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. A companion to philosophical logic dale jacquette ed. 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. 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.
Cambridgeuniversitypress,1980,robertgoldblattlogics of time andcomputation, stanford. 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. 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. 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.
The subject of this dissertation is manydimensional modal logic. The term modal logic refers to an enrichment of standard formal logic where the standard operations and, or, not, implication and perhaps forall, etc. On intuitionistic modal and tense logics and their. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. Lecture notes modal logic linguistics and philosophy. Introduction to philosophylogicmodal logic wikibooks. Hughes, of an introduction to modal logic, london, methuen, 1968. An introduction to modal logic geared to wards philosophy students. A new textbook on modal logic providing a modern introduction to modal logic. Oct 20, 1995 a new introduction to modal logic is an entirely new work, completely rewritten by the authors. A new introduction to modal logic george edward hughes. 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. This book presupposes that readers know the attractions and power of this approach, including the notions of logical syntax, semantics, proof, and. That is, it presents modal logic as a tool for talking about structures or models.
However, the term modal logic is used more broadly to cover a family of logics with similar rules and a variety of different symbols. 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. An introduction to its syntax and semantics 9780195366570. An introduction to its syntax and semantics amazon site. Completeness results for intuitionistic and modal logic in a. An earlier book of ours, entitled an introduction to modal logic iml, was published in 1968. A companion to the philosophy of language hale and wright, ed.
Note that the cylindric operators 9 and,their irreflexive companions 6, and the. Logical approach a companion to philosophical logic wiley online library. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. Article pdf available in annals of pure and applied logic.
Modern origins of modal logic stanford encyclopedia of. Download pdf a new introduction to modal logic free. 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. When we wrote it, we were able to give a reasonably comprehensive survey of the state of modal logic at that time. Dale jacquette is professor of philosophy at the pennsylvania state university. Cresswell this longawaited book replaces hughes and cresswells two classic studies of modal logic. However, unlike other empirical discoveries about language made in the. A modala word that expresses a modalityqualifies a statement. Hughes of an introduction to modal logic and a companion to modal logic, the standard works in the field. The model na,v satisfies the position formula as notation. 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. Second, many results can be understood more readily in the abstract setting. This book was later replaced by a new introduction to modal logic 1996. 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.
Pdf on intuitionistic modal and tense logics and their. 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. Each member of the family results from strengthening k in some way. Names and rigid designation a companion to the philosophy. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. Evenif 1 and 2 are themselves normal modal logics, 1. Lewiss pioneering work starting in 1912, with the first systems devised in 1918, to s. Introduction to modal and temporal logics 6 december 2007 3 logic syntax and semantics or calculus syntax. A list describing the best known of these logics follows. Logic as algebra 2001, as well as numerous articles on logic.
Basic concepts in this chapter we recollect some basic facts concerning modal logic, concentrating on completeness theory. Intuitionistic and modal predicate logic as categorical doctrines 43. This book is to be read and you can also see how the usefulness of the book modal logic. An advanced, but very accessible, textbook focusing on the main technical results in the area. An introduction pdf format for free to read online. Please refer to the assigned text for homework assignments and the take home final. Chellas pdf online free download info about modal logic. 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. Narrowly construed, modal logic studies reasoning that involves the use of the expressions necessarily and possibly. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. Modal logic gives a frame work for arguing about these distinctions. Counterfactuals, neighborhood semantics, probability, predicative necessity, etc. 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.
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. Neighborhood semantics for modal logic an introduction. This very extensive volume represents the current statof a airs in modal logic. He is the author of philosophy of mind 1994, meinongian logic. One is to explain what modal logic is, and how it is done. The semantics of existence and nonexistence 1996, wittgensteins thought in transition 1998, symbolic logic 2001, david humes critique of infinity 2001, and on boole. Preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal logic. 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. Konyndyk, introductory modal logic, notre dame, 1986. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. A companion to philosophical logic wiley online books. But what kind of structures can modal logic talk about.
Note that if is a normal logic and l is a language which might not contain, then. A companion to philosophical logic provides a comprehensive stateoftheart handbook for students and professional researchers in philosophical logic. The language of propositional modal logic we will begin our study of modal logic with a basic system called k in honor of the famous logician saul kripke. 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. Cresswell was the coauthor with his colleague and former teacher g. Book note ge hughes and mj cresswell, a companion to modal. Numerous and frequentlyupdated resource results are available from this search. An introduction to modal logic and a companion to modal logic. Ml2 are interpreted over the same class f of frames f. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. 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. 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.
Basic concepts in modal logic1 stanford university. In a companion paper we will introduce natural deduction systems for the. 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. On intuitionistic modal and tense logics and their classical companion logics. Csli, 1987, george hughes and max cresswell an introduction to modal logic, london. 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. Modal companions share various properties of the original intermediate logic, which enables to study intermediate logics using tools developed for modal logic. By modal decomposition i obtain completeness and other results for. Assignments modal logic linguistics and philosophy. Cresswell, a companion to modal logic, methuen, 1984. An approach to the logic of action normative act positions actions and normative positions. Richard patterson develops three striking theses in the book. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle. At the talk, dana introduced a new, probabilistic semantics for modal logica semantics about which very little was known at the time.
Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. When we wrote it, we were able to give a reasonably comprehensive survey of. Proof theory of modal logic has always been a delicate subjectthe intension. 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. W is called our universe and elements of w are called worlds r is a relation on w. 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.
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. 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. A semantic perspective 3 chapters in this handbook. Modal logic introduces three new symbols into classical. Philosophical logic princeton foundations of contemporary philosophy john p. Versions and extensions of intuitionistic and modal logic involving biheyting and. K serves as the foundation for a whole family of systems. Modal logics for qualitative possibility theory core. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal.
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