These notes are meant to present the basic facts about modal logic and so to provide a common. Moss, hansjorg tiede, applications of modal logic in linguistics, pp. One of the most central topics in philosophy of logicand one of the most confusingis the concept of validity. An open introduction to modal logic boxes and diamonds. A new deduction system for deciding validity for the minimal decidable normal modal logic k is presented in this article. Lecture notes on kripke semantics for validity 15816. Validity is to do with the logical form of arguments rather than the truth of the. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. Modal logic frank pfenning lecture 16 march 23, 2010 1 introduction. A new textbook on modal logic providing a modern introduction to modal logic. 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. Frame constructions, truth invariance and validity preservation in manyvalued modal logic. A modala word that expresses a modalityqualifies a statement.
Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. 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. 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. A new deduction system for deciding validity in modal logic k. A guide one of the most important concepts in logic is validity. One of the most important concepts of formal logic is that of logical validity. The primary goal is to provide students in philosophy 151 at stanford university with a study guide that will complement the lectures on modal logic. Researchers in areas ranging from economics to computational linguistics have since realised its worth. Our modal logic languages will be interpreted over graphlike structures. An introduction to modal logic geared towards philosophy students.
The most crucial criterion in classical logic is that logical reasoning. Reducing ctllive model checking to firstorder logic. Modern origins of modal logic stanford encyclopedia of. Validity is to do with the logical form of arguments rather than the truth of the propositions it contains. Modal logics could be very helpful in modelling dynamic and reactive. Cotnoir northern institute of philosophy jnovember 17, 2010 1 nonnormal frames syntax for normal modal languages is identical to lk and all its extensions. 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. In what sense if any is logic normative for thought. The valid formulas form the minimal modal logic, true solely in virtue of local quanti. Lecture notes modal logic linguistics and philosophy. Robert loftis robert trueman remixed and revised by aaron thomasbolduc richard zach. Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6. Pdf frame constructions, truth invariance and validity. An argument is valid if in every model in which all of the premises are true, the conclusion is also true.
Frame constructions, truth invariance and validity preservation in manyvalued modal logic pantelis e. Find materials for this course in the pages linked along the left. Kripkes formulation of modal logic chapter 2 the language chapter 3 semantics and model theory x1. Zalta center for the study of language and information stanford university table of contents preface chapter 1 introduction x1. In semantics theory that many linguists work on, modal logic helps a lot. In what follows we will introduce a very simple modal.
A logic is supposed to tell us which inferences are valid. The most wellknown modal propo sitions are propositions about what is necessarily the case and what is possibly the case. In the last section we saw some examples of valid formulas, i. Modal syntax and semantics the great advantage of ordinary propositional logic is that all of its connectives are truthfunctional. This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. This book is an introduction to logic for students of contemporary philosophy. A nice introduction to modal logic though somewhat outdated. Modal logic is the study of modal propositions and the logical relation ships that they bear to one another. Icard, iii 1 logical dynamics lab, center for the study of language and information. Propositions and modal validity oxford scholarship. However, truth and validity are different things and it is important in logical reasoning to distinguish the differences. Pdf model checking and validity in propositional and modal. However, the term modal logic may be used more broadly for a family of.
The polytheistic approach to modal logics alethic modal logic. Modal logics could be very helpful in modelling dynamic and reactive systems such as bioinspired systems and process algebras. But in what sense, exactly, is logic normative for thought. And not just because they involve technical notions like model and proof that neednt be possessed by a speaker who. Whatever other merits prooftheoretic and modeltheoretic accounts of validity may have, they are not remotely plausible as accounts of the meaning of valid. We just write n a if formula a holds in all interpretations and say that a is valid. Basic concepts in modal logic1 stanford university. Validity, in logic, the property of an argument consisting in the fact that the truth of the premises logically guarantees the truth of the conclusion. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. This book is an elementary introduction to the logic that students of contemporary philosophy ought to know. Topology, connectedness, and modal logic 3 formal semantics for the languages in question impeded their mathematical development, despite sporadic revivals in the following decades 10, 11, 7.
Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5. An individual user may print out a pdf of a single chapter of a monograph in oso for personal use. Frame constructions, truth invariance and validity. Interest in regionbased, qualitative spatial logics of this kind was rekindled, however, in the early 1990s, within arti. The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. Reducing ctllive model checking to firstorder logic validity checking amirhossein vakili and nancy a. One of the most important concepts in logic is validity. A necessary condition for angelo coming to the party, is that, if bruno and carlo arent coming, davide comes 7. Pdf modal inclusion logic is a formalism that belongs to the family of logics based on team semantics. An overview of applications of modal logic in linguistics can be found in. Pdf a new deduction system for deciding validity in modal. Pdf model checking and validity in propositional and. In particular, the following two principles are intuitively valid. This article investigates the model checking and validity problems of these logics.
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