Modal reasoning university of california, berkeley. Questions for a proof theory of modal logic proof analysis in modal logic firstorder modal logic completeness for kripke semantics other nonclassical logics does the deduction theorem fail for modal logic. In this section we give an axiomatic, or hilbertstyle, formulation of is4. 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 semantic perspective 3 chapters in this handbook. An overview of applications of modal logic in linguistics can be found in. A brief outline of modal predicate logic whether, how far, and in what ways various properties of sentential modal logics carry. Instead of implementing a reasoning system for this logic directly, we rather rely on existing methods and systems.
Tense logic, brings in propositional operators f and p, corresponding to whether a given proposition has been true in the past, or will be true in the future. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Introduction to modal logic cmu math carnegie mellon university. For example, the following are all modal propositions. Modal logic is a textbook on modal logic, intended for readers already acquainted with the elements of formal logic. The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new. Modal logic for philosophers second edition t his book on modal logic is especially designed for philosophy students. Modal predicate logic 27 vi6 jay is not mortal jay is immortal not jay is mortal7 the latter are all equivalent, and are straightforwardly symbolized as.
The primary goal is to provide students in philosophy 151 at stanford. We also consider the logic and semantics in classical setting. Teen pregnancy prevention state prep logic models 1 logic model tip sheet logic models overview logic models are effective tools to assist in program. Chapter 1 presents the basics of algebra and general propositional logic inasmuch as they are essential for understanding modal logic. Unfortunately, modal logics seem too limited for many important purposes. 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. Modality, in logic, the classification of logical propositions according to their asserting or denying the possibility, impossibility, contingency, or necessity of their content. Chellas pdf online free download info about modal logic. Purchase handbook of modal logic, volume 3 1st edition. These notes are meant to present the basic facts about modal logic and so to provide a common.
This article contains examples of uses of modality for which modal logic seems inadequate. Lecture notes on modal tableaux carnegie mellon school. One is to explain what modal logic is, and how it is done. Lecture notes modal logic linguistics and philosophy. Interesting introduction to logic and logical ideas. One of the core components of modal logic is the duality of the 3and. Modal logic is the study of modal propositions and the logical relationships that they bear to one another.
Modal logic midlands graduate school in foundations of cs, april 2003. Questions for a proof theory of modal logic proof analysis in modal logic firstorder modal logic completeness for. 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 in classical logic, it is only important whether a formula is true in modal logic, it is also important in which way mode state a formula is true a formula a proposition is necessarily possibly true true today tomorrow believed known. An axiomatic formulation of is4 in this paper we shall only consider propositional is4. This chapter introduces the theory of consequence relations and matrix semantics. Mattey june 11, 2001 1 the dimensions of modal predicate logic modal predicate logic mpl is based on predicate logic pl. If a the accessibility relation is serial, then m j. A brand new series dealing with three types of modal logic known as deontic logic october, temporal logic november, and doxastic logic december. A followup to the books 67 and 66 by the same authors.
Lecture 5 january 26, 2010 1 introduction to this lecture the goal of this lecture is to develop a starting point for classical modal. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. An advanced, but very accessible, textbook focusing on the main technical results in the area. Identifying the components of a logic model what is a logic model. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. Gunther propositional logic our language semantics syntax results modal logic our language. This very extensive volume represents the current statofa airs in modal logic. Semantics are given as possible world semantics, where the modal operators and are interpreted as quanti ers over possible worlds. The basic normal multi modal logic \\mathsfk\ is the minimal normal modal logic. 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. Instead of interpreting modal languages in topological spaces, as tarski did, we interpret. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Taking into account that sdl is just the modal logic k with a seriality axiom, we show that deontic logic can be translated into description logic alc.
F is called serial if for all x 2 w, there exists y 2 w such that rxy. Mj so, if the quantified sentences have the same forms as their unquantified counterparts, then they are all. Answers to two old questions are given in this paper. Modal logic is a type of formal logic primarily developed in the 1960s that extends classical. Instead, we obtain a modal logic with both normal and nonnormal modalities, together with additional axiom that speci. This book is an introduction to modal logic, more precisely, to classically.
Our previous work see the nonrefereed, invited paper 3 has already demonstrated the feasibility of the. W, we define what does it mean for a formula to be true satisfied in a world w of a model. Kripkemodelsforknowledge inepistemiclogic,theboxrepresentsknowledge. Modal logic s4, which was informally specified by godel in 1933 as a logic for provability, meets its exact provability interpretation. In particular, duality theory came into existence see 11, xi, 26 and m ihe main novelty here is that we add a topology on any frame and extend the functors to the category of all frames. Moss, hansjorg tiede, applications of modal logic in linguistics, pp. 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.
Akrmodel m hw,r,v i consists of a serial frame hw,ri and a map v. Kripke semantics also known as relational semantics or frame semantics, and often confused with possible world semantics is a formal semantics for nonclassical logic systems created in the late 1950s and early 1960s by saul kripke and andre joyal. Modal logic, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. This semantics is intimately related to an older, topological semantics for modal logic developed by tarski in the 1940s. By seriality, for every world w there is w such that wrw. From it we deduce the basic completeness results in modal logic. A modala word that expresses a modalityqualifies a statement. Independence of the dual axiom in modal k with primitive. This book is an introduction to logic for students of contemporary philosophy. If holds at w, then holds in w0, and thus holds in w.
Today geometry is the study of a vast range of mathematical structures, closely enough related to structures once thought to. First we define a formal semantic framework for modal logic, namely, kripke. I 3d printed a ruler to help draw modal logic proofs. Complexity of modal logic introduction ps pdf author. Formulas of basic modal logic are given by the following rule.
Logic models can assist you in program evaluation by providing a picture of how your program is intended to work. A view of its evolution 3 about when, where or how sis true, or about the circumstances under which s may be true. Possibleworldsanalysisofknowledge sknowsthatpiffpistrueatallworldscompatiblewithssknowledge. Of course, these axioms cant be invalidated in kripke frames, or even in boolean propositional logic. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. Modality and language mit massachusetts institute of. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. Epistemic logic, for example, includes a propositional operator k, which symbolizes that that proposition is known. By seriality, for every world w there is w0 such that wrw0.
Ontological foundations of russells theory of modality pdf. We develop a probabilistic semantics for modal logic, which was introduced in recent years by dana scott. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. An introduction to modal logic 2009 formosan summer school on logic, language, and computation. Cotnoir northern institute of philosophy jnovember 17, 2010 1 nonnormal frames syntax for normal modal languages is identical to lk and all its extensions. I have no proof that modal logic is inadequate, so i hope modal logicians will take the examples as challenges.
References problems of proof theory in modal logic sara negri university of helsinki workshop on recent trends in proof theory. Modal logic, which studies the logical features of such concepts, originated with aristotle, was extensively studied by. Deontic logic introduction and application in computer science. Consequently formulae are given by the grammar a p j.
A new textbook on modal logic providing a modern introduction to modal logic. Can someone help me understand how to prove fibonacci sequences. Its syntax is generated by adding modal operators to the syntax of pl. Propositional modal logic modal logic is the logic of necessity, possibility and other related notions. Download pdf a new introduction to modal logic free. Logic model tip sheet administration for children and. An introduction to modal logic geared towards philosophy students. Find materials for this course in the pages linked along the left. Such a possible world is an assignment, which assigns truth. Interestingly, the classical version of our logic is not a normal modal logic, even in the case of relational semantics. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. Every effort is made to simplify the presentation by using diagrams instead of more complex mathematical apparatus. It identifies your programs main components and how they should relate to one another. Know what a logic model is, and how it can be useful to your daily program operations identify the key components of a logic model.
Modal logic introductory lecture eric pacuit university of maryland, college park ai. Modal logic is, strictly speaking, the study of the deductive behavior of the. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. 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. Completeness and definability in the logic of noncontingency evgeni e. Computational modal logic introduction ps pdf authors. D, 4, 5, with noncontingency as the sole modal primitive. 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. Descartes thought all properties were modes either of extension or thought. It provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Sentential operators are devices that take sentences to form new sentences.
Absolute modal logic iii3 smith said that jones is an idiot. However, the term modal logic may be used more broadly for a family of. The most wellknown modal propositions are propositions about what is necessarily the case and what is possibly the case. Basic concepts in modal logic1 stanford university. An introduction pdf format for free to read online. The basic logic in this setting is axiomatized, and some. The present paper applies wellinvestigated modal logics to provide. Numerous and frequentlyupdated resource results are available from this search.
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