Modal logic, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. Submit all the exercises above dont forget bugs in the lectures for both days 2. 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. A brief outline of modal predicate logic whether, how far, and in what ways various properties of sentential modal logics carry. 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 language l plphas the following list of symbols as alphabet. However, the term modal logic may be used more broadly for a family of. W e introduce the completeness problem for modal logic and examine its complexity. Basic concepts in modal logic1 stanford university. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. Exercise 1, on the one hand, and in example 2 and exercises 2 and 3, on the other. Realizability logic and medvedevs logic 52 exercises \ 54 notes 56 3 modal logics 61 3. So below, we simply assume that some language l is given.
Other systems of modal logic were then constructed and investigated. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. This is enough to say what model theory and proof theory say. Modal logic was formalized for the first time by c. Complexity of modal logic introduction ps pdf author. The class of frames each state of which has at most one rsuccessor, that is, 8x8y8zrxyrxz. All downloads are in pdf format and consist of a worksheet and answer sheet to check. This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s.
To read them, youll need to have either adobe acrobat or adobe acrobat reader installed. A nice introduction to modal logic though somewhat outdated.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. The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. A semantic perspective 3 chapters in this handbook. This book is an introduction to logic for students of contemporary philosophy. English grammar online exercises and downloadable worksheets. 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. Identity and descriptions pdf contingent identity pdf 2425. Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5. Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6.
Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. Epistemic logic, for example, includes a propositional operator k, which symbolizes that that proposition is known. An introduction to modal logic geared towards philosophy students. A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new. In all cases, what we have is a set l of sentences or. 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. Answers to selected exercises pdf the language of modal propositional logic. The material presented here is not a direct component of the course but is offered to. 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. These notes are meant to present the basic facts about modal logic and so to provide a common. Lecture notes modal logic linguistics and philosophy. The material presented here is not a direct component of the course but is offered to you as an incentive and a support to understand and master the concepts and exercises presented during the course.
The purpose of this booklet is to give you a number of exercises on propositional. Jones said smith, you are an idiot subject transitive verb direct object. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. Absolute modal logic iii3 smith said that jones is an idiot. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. A simple logicogrammatical account of these two quotation techniques goes as follows where we concentrate on what jones says. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. A modala word that expresses a modalityqualifies a statement. Computational modal logic introduction ps pdf authors. Lewis, who constructed five propositional systems of modal logic, given in the literature the notations s1s5 their formulations are given below.
The handbook of modal logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. Characterized by clear and concrete explanations, appropriate examples, and varied and challenging exercises, introductory modal logic makes both modal logic and the possibleworlds metaphysics readily available to the introductory level student. Classical logic 3 syntax and semantics 3 semantic tableaux 6 classical calculus 9 basic properties of cl 15 exercises 19 notes 21 intuitionistic logic 23 motivation 23 kripke frames and models 25 truthpreserving operations 28 hintikka systems 35 intuitionistic frames and formulas 40 intuitionistic calculus 45 embeddings of cl into int 46. A new textbook on modal logic providing a modern introduction to modal logic. An introduction to modal logic 2009 formosan summer school on logic, language, and computation. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, modal logics and philosophy focuses on showing how useful modal logic can be as a tool for formal philosophical analysis. Modal logic for philosophers designed for use by philosophy students, this book provides an accessible yet technically sound treatment of modal logic and its philosophical applications. Whereas the formulas in the rst example and exercise are ordinary modal formulas that are valid, the formulas in example 2 and. An advanced, but very accessible, textbook focusing on the main technical results in the area. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The polytheistic approach to modal logics alethic modal logic. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. 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. Propositional logic, predicate logic and modal logic all have di erent languages.782 145 691 1123 324 910 1216 1179 657 633 1248 103 922 903 736 174 899 923 196 876 1528 904 853 412 1397 428 540 1197 846 854 925 1 1276 1464 1431