English grammar online exercises and downloadable worksheets. Whereas the formulas in the rst example and exercise are ordinary modal formulas that are valid, the formulas in example 2 and. 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. The class of frames each state of which has at most one rsuccessor, that is, 8x8y8zrxyrxz. Complexity of modal logic introduction ps pdf author. To read them, youll need to have either adobe acrobat or adobe acrobat reader installed. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined. Basic concepts in modal logic1 stanford university.
Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. A modala word that expresses a modalityqualifies a statement. All downloads are in pdf format and consist of a worksheet and answer sheet to check. An introduction to modal logic 2009 formosan summer school on logic, language, and computation. A semantic perspective 3 chapters in this handbook. Modal logic, formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. 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. Identity and descriptions pdf contingent identity pdf 2425. Exercise 2 and 3 are not only valid, they are instances of tautologies in propositional logic. The chellas text in uenced me the most, though the order of presentation is inspired more by goldblatt. These notes are meant to present the basic facts about modal logic and so to provide a common. An advanced, but very accessible, textbook focusing on the main technical results in the area. Submit all the exercises above dont forget bugs in the lectures for both days 2. A new textbook on modal logic providing a modern introduction to modal logic.
Exercise 1, on the one hand, and in example 2 and exercises 2 and 3, on the other. Epistemic logic, for example, includes a propositional operator k, which symbolizes that that proposition is known. However, the term modal logic may be used more broadly for a family of. This book is an introduction to logic for students of contemporary philosophy. 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. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. 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. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. Answers to selected exercises pdf the language of modal propositional 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. Absolute modal logic iii3 smith said that jones is an idiot. Computational modal logic introduction ps pdf authors. A nice introduction to modal logic though somewhat outdated.
Modal logic was formalized for the first time by c. This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6. The language l plphas the following list of symbols as alphabet. Handbook of modal logic edited by johan van benthem, patrick blackburn and frank wolter. The purpose of this booklet is to give you a number of exercises on propositional. 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. 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. Lewis, who constructed five propositional systems of modal logic, given in the literature the notations s1s5 their formulations are given below.
Realizability logic and medvedevs logic 52 exercises \ 54 notes 56 3 modal logics 61 3. W e introduce the completeness problem for modal logic and examine its complexity. An introduction to modal logic geared towards philosophy students. In all cases, what we have is a set l of sentences or. The most straightforward way of constructing a modal logic is to add to some standard nonmodal logical system a new. Other systems of modal logic were then constructed and investigated. This is enough to say what model theory and proof theory say. The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. 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 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. A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Propositional logic, predicate logic and modal logic all have di erent languages. 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. Researchers in areas ranging from economics to computational linguistics have since realised its worth.
This very extensive volume represents the current statofa airs in modal logic. So below, we simply assume that some language l is given. 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. The polytheistic approach to modal logics alethic modal logic. Lecture notes for week 2 pdf slides for lecture 3 pdf slides for lecture 4 pdf answers to selected exercises pdf. A simple logicogrammatical account of these two quotation techniques goes as follows where we concentrate on what jones says. Modal verbs pdf worksheets english vocabulary and grammar. The material presented here is not a direct component of the course but is offered to. Jones said smith, you are an idiot subject transitive verb direct object. 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.
Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Lecture notes modal logic linguistics and philosophy. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5.