An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. 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. They have incorporated all the new developments that have taken place since 1968 in both modal. Basic concepts in modal logic1 stanford university. Lemmon 1966, algebraic semantics for modal logics i, ii,the.
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. Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5. From it we deduce the basic completeness results in modal logic. Modal logic was formalized for the first time by c.
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. 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. An introduction to modal logic geared towards philosophy students. 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. In 9 we developed a semantics for quantified relevant logic that uses general frames. Complexity of modal logic introduction ps pdf author. Modal logic, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. Algebraic tools for modal logic university of helsinki. The present paper attempts to extend the results of l, in the domain of the. Lecture notes modal logic linguistics and philosophy. This chapter introduces the theory of consequence relations and matrix semantics. Pdf a general semantics for quantified modal logic. A brief outline of modal predicate logic whether, how far, and in what ways various properties of sentential modal logics carry.
Extension to other modal logics is discussed, as well as a representation theorem for. Illustrative chapters focus on deontic logic and conditionality. A nice introduction to modal logic though somewhat outdated. A solid background in firstorder logic is essential.
Quine there are logicians, myself among them, to \,hom the ideas of modal logic e. Find materials for this course in the pages linked along the left. Prove some interesting properties of logical consequence. These notes are meant to present the basic facts about modal logic and so to provide a common. A modala word that expresses a modalityqualifies a statement.
The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. 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. In this paper, we adapt that model theory to treat quantified modal logics. The subject of this dissertation is manydimensional modal logic. If s is canonical our models are based on propositional. Chapter 1 presents the basics of algebra and general propositional logic inasmuch as they are essential for understanding modal logic. A new textbook on modal logic providing a modern introduction to modal logic. An overview of applications of modal logic in linguistics can be found in. The primary goal is to provide students in philosophy 151 at stanford. The most wellknown modal propositions are propositions about what is necessarily the case and what is possibly the case. 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. 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. A multimodal logic is a modal logic that has more than one primitive modal operator.
Pdf in 9 we developed a semantics for quantified relevant logic that uses general frames. For example, the following are all modal propositions. The other is to give a detailed survey of the large variety of modal logic systems found in the literature, with an eye to both their formal properties consistency, completeness and their philosophi. They find substantial applications in theoretical computer science a modal logic with n primitive unary modal operators. 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.
Other systems of modal logic were then constructed and investigated. Modern origins of modal logic stanford encyclopedia of. Basic concepts in this chapter we recollect some basic facts concerning modal logic, concentrating on completeness theory. Purchase handbook of modal logic, volume 3 1st edition. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises.
A modal logic of quantification and substitution homepages of. But quite apart from specific distances, there are also neighborhoods in london. An introduction to modal logic 2009 formosan summer school on logic, language, and computation. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. Prominent modal logics are constructed from a weak logic called k after saul kripke. The modal depth of a formula indicates how far one needs to look in a kripke model when checking the validity of the formula. An introduction to modal logic and a companion to modal logic. In all cases, what we have is a set l of sentences or. Halmos, algebraic logic, chelsea publishing company, new york, 1962. The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new. Modal logic is a textbook on modal logic, intended for readers already acquainted with the elements of formal logic. This longawaited book replaces hughes and cresswells two classic studies of modal logic.
Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6. Logics of modal terms for systems specification oxford academic. W, we define what does it mean for a formula to be true satisfied in a world w of a model. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. Computational modal logic introduction ps pdf authors. Halmos, algebraic logic,chelsea publishing company, new york, 1962. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. W e introduce the completeness problem for modal logic and examine its complexity.
But so long as modal logic stops short of quantification theory, it is possible as i. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. An introduction pdf format for free to read online. One is to explain what modal logic is, and how it is done. Introduction to modal and temporal logics 23 august 2019 6. In modal logic, a striking example of this phenomenon can be found using the duality theory between.
Cambridge core programming languages and applied logic modal logic by patrick blackburn. Propositional logic, predicate logic and modal logic all have different languages. 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. Lewis, who constructed five propositional systems of modal logic, given in the literature the notations s1s5 their formulations are given below. Modal logic is the study of modal propositions and the logical relationships that they bear to one another.
Instead, we obtain a modal logic with both normal and nonnormal modalities, together with additional axiom that speci. Interestingly, the classical version of our logic is not a normal modal logic, even in the case of relational semantics. Given a family l of modal logics and a combination method c, do certain properties. Modal logic linguistics and philosophy mit opencourseware. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. Modal logic by patrick blackburn cambridge university press.
Lewissare not intuitively clear until explained in nonmodalterms. Many concepts in philosophy of language can be formalized in modal logic. However, the term modal logic may be used more broadly for a family of. Halmos 1962,algebraic logic, new york chelsea publishing co. Canonical models for normal logics imperial college london. In semantics theory that many linguists work on, modal logic helps a lot. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability.