However, the term modal logic may be used more broadly for a family of. Modal logic, developed as an extension of classical propositional logic and firstorder quantification theory, integrates the notions of possibility and necessity and necessary implication. Topics to be covered include some or all of the main systems of propositional modal logic, kripkean. Introductory modal logic fills the need for a basic text on modal logic, accessible to students of elementary symbolic logic. W is called our universe and elements of w are called worlds r is a relation on w. Modern origins of modal logic stanford encyclopedia of. Yet, the variety of textbooks available for the wouldbe student is not as rich as in.
Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. An introduction pdf format for free to read online. An advanced, but very accessible, textbook focusing on the main technical results in the area. A semantic perspective 3 chapters in this handbook. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. A modala word that expresses a modalityqualifies a statement. They have incorporated all the new developments that have taken place since 1968 in both modal. 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, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. The term modal logic refers to an enrichment of standard formal logic where the standard operations and, or, not, implication and perhaps forall, etc. A new textbook on modal logic providing a modern introduction to modal logic. The choice of logical connectives depends on the development of propositional logic one wants to follow. Chellas pdf online free download info about modal logic.
The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. Truth value, is a set of distinguished truth values, and,, are the operations in corresponding to the connectives. K serves as the foundation for a whole family of systems. 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. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. Reductio ad absurdum tests 315 summary 320 6 modal propositional logic 323 1. A brief outline of modal predicate logic whether, how far, and in what ways various properties of sentential modal logics carry. At the talk, dana introduced a new, probabilistic semantics for modal logica semantics about which very little was known at the time.
Model theory of modal logic introduction ps pdf authors. An introduction to modal logic and a companion to modal logic. The language l plphas the following list of symbols as alphabet. A nice introduction to modal logic though somewhat outdated. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Lewiss pioneering work starting in 1912, with the first systems devised in 1918, to s. Introductory modal logic notre dame university press. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on. Second, many results can be understood more readily in the abstract setting. Tableaux for intuitionistic logic 186 further study 193 9. Buehler based on first order modal logic by fitting and mendelsohn january 5, 2015. Covers propositional modal logic only, but has a very complete discussion of the various systems that come between k and s5. Examples for convenience, we reproduce the item logicmodal logic of principia metaphysica in which the modal logic is defined. Computational modal logic introduction ps pdf authors.
In basic modal logic we have two new sentential operators. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. 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. Pdf a new introduction to modal logic download full. Propositional modal logic any complete system of logic needs at least three components. The biintuitionistic tense logic studied in 17 can be regarded as both a tense expansion of biintuitionistic logic and an expansion of intuitionistic modal logic studied in,18 with the. An open introduction to modal logic boxes and diamonds.
One interesting application in meta physics, or mereology, is developed in the introductory chapter. It covers i basic approaches to logic, including proof theory and especially model theory, ii extensions of standard logic such as modal logic that are important in philosophy, and iii some elementary philosophy of logic. The strong modal operator is symbolized by the box, while the weak modal operator is symbolized by the diamond. For example, your hair dryer will have typically have at least two modes. A formula is called generally valid in if for every valuation of its propositional variables by elements of it takes a distinguished value. This longawaited book replaces hughes and cresswells two classic studies of modal logic. Thus, whenever we say modal logic, we always mean propositional unimodal logic, modal logics without quanti. Purchase handbook of modal logic, volume 3 1st edition. Other systems of modal logic were then constructed and investigated. Kenneth konyndyk presents a natural deduction treatment of propositional modal logic and quantified modal logic, historical information about its development, and discussions of the philosophical issues raised by. Each member of the family results from strengthening k in some way. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. Further background on modal logic can be found in the book by fitting and mendelsohn fm99. Firstordermodallogic university of california, berkeley.
Instead, we obtain a modal logic with both normal and nonnormal modalities, together with additional axiom that speci. An introduction to modal logic geared towards philosophy students. Algebraic tools for modal logic university of helsinki. Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the notruledout. Now in this, our last chapter, we concentrate our attention on the kind of propositional logic modal propositional logic within which modal concepts feature overtly. Arguments whose understanding depends on some fundamental knowledge of modal logic have always been important in philosophy of religion, metaphysics, and. Modal logics are extensions of classical logic by the operators. For an introductory survey of these and other algebras. Basic concepts in this chapter we recollect some basic facts concerning modal logic, concentrating on completeness theory. Modal logic is, strictly speaking, the study of the deductive behavior of the. Neighborhood semantics for modal logic an introduction. This book is to be read and you can also see how the usefulness of the book modal logic.
Illustrative chapters focus on deontic logic and conditionality. These notes are meant to present the basic facts about modal logic and so to provide a common ground for. Pdf in this paper we consider an intuitionistic variant of the modal logic s4 which we call is4. 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. Lewis, who constructed five propositional systems of modal logic, given in the literature the notations s1s5 their formulations are given below. The most straightforward way of constructing a modal logic is to add. Modal logic is a textbook on modal logic, intended for readers already acquainted with the elements of formal logic. Konyndyk, introductory modal logic, notre dame, 1986. Modal operators 323 nontruthfunctionality 323 modal and nonmodal propositions.
Modal logic linguistics and philosophy mit opencourseware. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. This very extensive volume represents the current statofa airs in modal logic. Prominent modal logics are constructed from a weak logic called k after saul kripke. 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. However, the term modal logic may be used more broadly for a family of related systems. We also consider the logic and semantics in classical setting. Download pdf a new introduction to modal logic free.
Another introductory formal text that places fairly high demands on the reader. Basic concepts in modal logic1 stanford university. 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. Kenneth konyndyk presents a natural deduction treatment of propositional modal logic and quantified modal logic, historical information about its development, and discussions of the philosophical issues raised by modal. Modal logic was formalized for the first time by c. 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. A solid background in firstorder logic is essential. As an excellent background on modal logic, these notes are also partly based on a manuscript by schmitt sch03 and the book by hughes and cresswell hc96. A system of modal logic s is called complete relative to a class of algebras if a. Interestingly, the classical version of our logic is not a normal modal logic, even in the case of relational semantics. This book is an introduction to logic for students of contemporary philosophy. This book presupposes that readers know the attractions and power of this approach, including the notions of logical syntax, semantics, proof, and. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability.
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