Validity modal logic pdf

Model checking and validity in propositional and modal. Pdf frame constructions, truth invariance and validity. In propositional logic, validity can be defined using truth tables. The concept of form 301 sentences and sentential forms in a logic 301 the relationship between sentences and sentenceforms 302 7. 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. We just write n a if formula a holds in all interpretations and say that a is valid. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. A new deduction system for deciding validity in modal logic k. Our modal logic languages will be interpreted over graphlike structures. An argument is valid if in every model in which all of the premises are true, the conclusion is also true. In particular, the following two principles are intuitively valid. An introduction to modal logic geared towards philosophy students.

Before tackling this question, i want to say a bit about why i think it is important. A modala word that expresses a modalityqualifies a statement. But in what sense, exactly, is logic normative for thought. Whatever other merits prooftheoretic and modeltheoretic accounts of validity may have, they are not remotely plausible as accounts of the meaning of valid. In what sense if any is logic normative for thought. In what follows we will introduce a very simple modal. Modal logic frank pfenning lecture 16 march 23, 2010 1 introduction. This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Pdf modal inclusion logic is a formalism that belongs to the family of logics based on team semantics. This article investigates the model checking and validity problems of these logics. Modal logics are extensions of classical logic by the operators. 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. Cotnoir northern institute of philosophy jnovember 17, 2010 1 nonnormal frames syntax for normal modal languages is identical to lk and all its extensions.

A necessary condition for angelo coming to the party, is that, if bruno and carlo arent coming, davide comes 7. Zalta center for the study of language and information stanford university table of contents preface chapter 1 introduction x1. Kripkes formulation of modal logic chapter 2 the language chapter 3 semantics and model theory x1. Basic concepts in modal logic1 stanford university. 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. Lecture notes on kripke semantics for validity 15816.

Modal logic is the study of modal propositions and the logical relation ships that they bear to one another. Validity is to do with the logical form of arguments rather than the truth of the propositions it contains. Modern origins of modal logic stanford encyclopedia of. In semantics theory that many linguists work on, modal logic helps a lot. This book is an introduction to logic for students of contemporary philosophy. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The most crucial criterion in classical logic is that logical reasoning. Validity is to do with the logical form of arguments rather than the truth of the. Modal reasoning university of california, berkeley. Advanced truthtable techniques 294 corrected truthtables 294 reduced truthtables 297 6. However, the term modal logic may be used more broadly for a family of. Robert loftis robert trueman remixed and revised by aaron thomasbolduc richard zach.

Reducing ctllive model checking to firstorder logic validity checking amirhossein vakili and nancy a. 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. 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 logics could be very helpful in modelling dynamic and reactive. Icard, iii 1 logical dynamics lab, center for the study of language and information. Propositional and modal inclusion logic are formalisms that belong to the family of logics based on team semantics. A logic is supposed to tell us which inferences are valid. One of the most important concepts of formal logic is that of logical validity. An overview of applications of modal logic in linguistics can be found in. Pdf a new deduction system for deciding validity in modal. Interest in regionbased, qualitative spatial logics of this kind was rekindled, however, in the early 1990s, within arti. However, truth and validity are different things and it is important in logical reasoning to distinguish the differences. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. Modal logic is, strictly speaking, the study of the deductive behavior of the.

A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. An open introduction to modal logic boxes and diamonds. One of the most central topics in philosophy of logicand one of the most confusingis the concept of validity. Angelo, bruno and carlo come to the party if and only if davide doesnt come, but, if neither angelo nor bruno come, then davide comes only if carlo comes. The valid formulas form the minimal modal logic, true solely in virtue of local quanti. Frame constructions, truth invariance and validity preservation in manyvalued modal logic pantelis e. A new textbook on modal logic providing a modern introduction to modal logic. 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. Modal logics could be very helpful in modelling dynamic and reactive systems such as bioinspired systems and process algebras.

A guide one of the most important concepts in logic is validity. Modal syntax and semantics the great advantage of ordinary propositional logic is that all of its connectives are truthfunctional. In the last section we saw some examples of valid formulas, i. A new deduction system for deciding validity for the minimal decidable normal modal logic k is presented in this article. These notes are meant to present the basic facts about modal logic and so to provide a common. Revealing modal status and modal relations 279 modal status 279 modal relations 284 deductive validity 290 5. Propositions and modal validity oxford scholarship. One of the most important concepts in logic is validity. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Frame constructions, truth invariance and validity preservation in manyvalued modal logic. And not just because they involve technical notions like model and proof that neednt be possessed by a speaker who. 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. Lecture notes modal logic linguistics and philosophy. Find materials for this course in the pages linked along the left.

Pdf model checking and validity in propositional and modal. 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. Whenever the premises are true, the conclusion must be true, because of the form of the argument. This book is an elementary introduction to the logic that students of contemporary philosophy ought to know. This article investigates the model checking and validity.