An introduction to modal logic 2009 formosan summer school on logic, language, and computation. Basic concepts in modal logic1 stanford university. Canonical models for normal logics imperial college london. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. A nice introduction to modal logic though somewhat outdated.
These notes are meant to present the basic facts about modal logic and so to provide a common. Pdf a general semantics for quantified modal logic. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. 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. But quite apart from specific distances, there are also neighborhoods in london. Quine there are logicians, myself among them, to \,hom the ideas of modal logic e. This book is to be read and you can also see how the usefulness of the book modal logic. For each modal operator, one needs to transition from a world in the model to a world that is accessible through the accessibility relation.
The subject of this dissertation is manydimensional modal logic. In 9 we developed a semantics for quantified relevant logic that uses general frames. Halmos, algebraic logic, chelsea publishing company, new york, 1962. The present paper attempts to extend the results of l, in the domain of the. An overview of applications of modal logic in linguistics can be found in.
A modal logic of quantification and substitution homepages of. W e introduce the completeness problem for modal logic and examine its complexity. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. If s is canonical our models are based on propositional. Modal logic, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. Prove some interesting properties of logical consequence. For a novice this book is a mathematicallyoriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of. We also consider the logic and semantics in classical setting. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. An introduction to modal logic geared towards philosophy students. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement.
Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6. Propositional logic, predicate logic and modal logic all have different languages. The primary goal is to provide students in philosophy 151 at stanford. Prominent modal logics are constructed from a weak logic called k after saul kripke. Halmos 1962,algebraic logic, new york chelsea publishing co. Extension to other modal logics is discussed, as well as a representation theorem for. They have incorporated all the new developments that have taken place since 1968 in both modal. The most wellknown modal propositions are propositions about what is necessarily the case and what is possibly the case. A new textbook on modal logic providing a modern introduction to modal logic. This longawaited book replaces hughes and cresswells two classic studies of modal logic. Basic concepts in this chapter we recollect some basic facts concerning modal logic, concentrating on completeness theory. By an nmodal logic or modal logic1, for short we mean any set l of mln formulas that contains all valid formulas of classical propositional logic, the formulas.
A solid background in firstorder logic is essential. In all cases, what we have is a set l of sentences or. Many concepts in philosophy of language can be formalized in 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 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. The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. Modal logic was formalized for the first time by c. Modal logic is a textbook on modal logic, intended for readers already acquainted with the elements of formal logic. Lewis, who constructed five propositional systems of modal logic, given in the literature the notations s1s5 their formulations are given below.
A multimodal logic is a modal logic that has more than one primitive modal operator. Logics of modal terms for systems specification oxford academic. Moss, hansjorg tiede, applications of modal logic in linguistics, pp. Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5. However, the term modal logic may be used more broadly for a family of. A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises.
Halmos, algebraic logic,chelsea publishing company, new york, 1962. Modern origins of modal logic stanford encyclopedia of. Interestingly, the classical version of our logic is not a normal modal logic, even in the case of relational semantics. A brief outline of modal predicate logic whether, how far, and in what ways various properties of sentential modal logics carry. Lewissare not intuitively clear until explained in nonmodalterms. In this paper, we adapt that model theory to treat quantified modal logics. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. Modal logic is the study of modal propositions and the logical relationships that they bear to one another.
The modal depth of a formula indicates how far one needs to look in a kripke model when checking the validity of the formula. For example, the following are all modal propositions. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Chellas pdf online free download info about modal logic. Modal logic by patrick blackburn cambridge university press. Pdf in 9 we developed a semantics for quantified relevant logic that uses general frames. In modal logic, a striking example of this phenomenon can be found using the duality theory between. One is to explain what modal logic is, and how it is done. 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. Given a family l of modal logics and a combination method c, do certain properties. Other systems of modal logic were then constructed and investigated.
They find substantial applications in theoretical computer science a modal logic with n primitive unary modal operators. Find materials for this course in the pages linked along the left. In semantics theory that many linguists work on, modal logic helps a lot. A modala word that expresses a modalityqualifies a statement. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. Chapter 1 presents the basics of algebra and general propositional logic inasmuch as they are essential for understanding modal logic. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. Lecture notes modal logic linguistics and philosophy.
An introduction to modal logic and a companion to modal logic. Complexity of modal logic introduction ps pdf author. From it we deduce the basic completeness results in modal logic. Instead, we obtain a modal logic with both normal and nonnormal modalities, together with additional axiom that speci. Cambridge core programming languages and applied logic modal logic by patrick blackburn. This chapter introduces the theory of consequence relations and matrix semantics. Purchase handbook of modal logic, volume 3 1st edition. Notes on modal logic notes for philosophy 151 eric pacuit january 28, 2009 these short notes are intended to supplement the lectures and text ntroduce some of the basic concepts of modal logic. Introduction to modal and temporal logics 23 august 2019 6. Modal logic linguistics and philosophy mit opencourseware. But so long as modal logic stops short of quantification theory, it is possible as i. 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.