An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. An advanced, but very accessible, textbook focusing on the main technical results in the area. Basic concepts in modal logic1 stanford university. A brief introduction to modal logic introduction consider.
Illustrative chapters focus on deontic logic and conditionality. 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. A system of modal logic s is called complete relative to a class of algebras if a. Each member of the family results from strengthening k in some way. Purchase handbook of modal logic, volume 3 1st edition. The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. Prominent modal logics are constructed from a weak logic called k after saul kripke. Basic concepts in this chapter we recollect some basic facts concerning modal logic, concentrating on completeness theory. Covers propositional modal logic only, but has a very complete discussion of the various systems that come between k and s5. 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. 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. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. On the other hand, the passage from local to global semantics is achieved if one looks at truth in all states an abstraction through implicit universal. Modal logic is the study of modal propositions and the logical relation ships that they bear to one another.
The first is to explain why a particular pattern of natural deduction for modal logicsnamely that of dual contextsis suited to the necessity frag. On the minimum manyvalued modal logic over a finite. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Another introductory formal text that places fairly high demands on the reader. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Truth value, is a set of distinguished truth values, and,, are the operations in corresponding to the connectives. Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5. Model theory of modal logic introduction ps pdf authors. 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. Prove some interesting properties of logical consequence. Introduction to modal and temporal logics 6 december 2007 15. Their axioms include all propositional tautologies in.
Arguments whose understanding depends on some fundamental knowledge of modal logic have always been important in philosophy of religion, metaphysics, and. The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new. This article deals with manyvalued modal logics, based only on the necessity operator, over a residuated lattice. Thus, whenever we say modal logic, we always mean propositional unimodal logic, modal logics without quanti. This book is to be read and you can also see how the usefulness of the book modal logic. Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6. 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. 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. Yet, the variety of textbooks available for the wouldbe student is not as rich as in. A nice introduction to modal logic though somewhat outdated. The agenda introduction basic modal logic normal systems of modal logic metatheorems of normal systems variants of modal logic conclusion.
The choice of logical connectives depends on the development of propositional logic one wants to follow. Model theory of modal logic 251 over the given frame in e. A formula is called generally valid in if for every valuation of its propositional variables by elements of it takes a distinguished value. A modala word that expresses a modalityqualifies a statement.
A solid background in firstorder logic is essential. Since natural language semantics applies model theoretic methods, the role of modal logic in this context involves the application of possible worlds semantics to. 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. Neighborhood semantics for modal logic an introduction. The language l plphas the following list of symbols as alphabet. Preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal logic.
The strong modal operator is symbolized by the box, while the weak modal operator is symbolized by the diamond. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. 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. Propositional modal logic any complete system of logic needs at least three components.
A new textbook on modal logic providing a modern introduction to modal logic. Examples for convenience, we reproduce the item logicmodal logic of principia metaphysica in which the modal logic is defined. Modal logic linguistics and philosophy mit opencourseware. 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. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. Download pdf a new introduction to modal logic free. K serves as the foundation for a whole family of systems. So the basic semantic notion in modal logic is truth of a formula at a state of a kripke structure, with derived notions of validity also in kripke structures and frames. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal. All modal logics considered in the paper have two inference rules.
Modal logic, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. An introduction to modal logic geared towards philosophy students. Modal logic is meant to capture seeming entailments between such alethic and deontic notions. W is called our universe and elements of w are called worlds r is a relation on w. Modal logic for default reasoning 1 introduction computer science.
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. An introduction to modal logic and a companion to 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. Cambridgeuniversitypress,1980,robertgoldblattlogics of time andcomputation, stanford. One is to explain what modal logic is, and how it is done. The polytheistic approach to modal logics alethic modal logic. This longawaited book replaces hughes and cresswells two classic studies of modal logic. Model theory of modal logic 3 over the given frame in e.
Modal logic is a textbook on modal logic, intended for readers already acquainted with the elements of formal logic. This very extensive volume represents the current statofa airs in modal logic. A semantic perspective 3 chapters in this handbook. Csli, 1987, george hughes and max cresswell an introduction to modal logic, london. An introduction pdf format for free to read online. Computational modal logic introduction ps pdf authors. We will define several varieties of modal logic, providing both their semantics and their axiomatic proof systems, and prove their standard soundness and. Modal logic, developed as an extension of classical propositional logic and firstorder quantification theory, integrates the notions of possibility and necessity and necessary implication. In this tutorial, we give examples of the axioms, consider some rules of inference and in particular, the derived rule. But we can also use a logical proof calculus, once we have settled on one, independently to reveal more of the abstract system of principles governing modality. In basic modal logic we have two new sentential operators. A new introduction to modal logic is an entirely new work, completely rewritten by the authors.
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