In part 1, the reader is introduced to some standard systems of modal logic and provided with a series of. To view the pdf, you must log in or become a member. For example, modal logic can be given an algebraic semantics, and under this interpretation modal logic is a tool for talking about what are known as boolean algebras with operators. 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 modala word that expresses a modalityqualifies a statement. 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.
Notes on modal logic stanford artificial intelligence. Lecture 4 philosophy 150 eric pacuit stanford university ai. The main goal of the corse is to understand the basic techniques, results and applications of neighborhood semantics for modal logic and to understand the exact relationship with the standard relational semantics. 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 is a type of formal logic primarily developed in the 1960s that extends classical. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. Modal predicate logic an important topic in philosophical applications of modal logic that we have mostly ignored in this survey is modal predicate logic. More recently, modal logic has become a muchused tool for analyzing the logic of such various propositional operators as belief, knowledge and tense. There has been much philosophical discussion of whether endorsement of the kripke semantics brings ontological commitment to possible worlds. An introduction to modal logic geared to wards philosophy students.
A philosophical conception of propositional modal logic. Cambridgeuniversitypress,1980,robertgoldblattlogics of time and computation, stanford. Sep 22, 2016 divers, j 2016 philosophical issues from kripkes semantical considerations on modal logic. This is obtained by adding to ordinary modal logic a second sort of. Indicative conditionals and dynamic epistemic logic. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. The logic begins with s5, before going into the normal modal logics. This book is essentially split into two main sections. Modal logic as metaphysics hardcover timothy williamson. 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. In semantical considerations on modal logic, kripke articulates his project in the discourse of possible worlds. Modal logics are particularly well suited to study a wide range of philosophical.
Vardi csli, ventura hall, stanford university, stanford, ca 94305 abstract. A nice introduction to modal logic though somewhat outdated. 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. While epistemology has a long philosophical tradition dating back to ancient greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. Kripke semantics for the intuitionistic logic follows the same principles as the semantics of modal logic, but it uses a different definition of satisfaction. Modal logic is the logic of necessity and possibility, and by extension of analogously paired notions like validity and consistency, obligation and permission, the known and the notruledout. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. But what kind of structures can modal logic talk about. 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. Notes on modal logic stanford ai lab stanford university. This entry was written by james garson and provides a nice overview of the philosophical applications of modal logic. In the standard kripke semantics for modal logic, truth is relative to points in a set. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement.
A summary of all of the axioms that we have investigated in regards to all of the different kinds of modal logics that we have looked at. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. A philosophical conception of propositional modal logic the. An introduction to its syntax and semantics amazon site. In modal logic for open minds, johan van benthem provides an introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Philosophical aspects of multimodal logic stanford encyclopedia. Cambridgeuniversitypress,1980,robertgoldblattlogics of time andcomputation, stanford. As an excellent background on modal logic, these notes are also partly based on a manuscript by schmitt sch03 and the book by hughes and cresswell hc96. The axiomatisation of k is a subset of the axioms of s4 and the same proof rules of s4. A new textbook on modal logic providing a modern introduction to modal logic. In logic and philosophy, s5 is one of five systems of modal logic proposed by clarence irving lewis and cooper harold langford in their 1932 book symbolic logic.
Most philosophy students study advanced topics like modal logic for the first time in graduate school, but its to the students advantage to be exposed to modal logic as undergraduates, says calvin college professor, stephen wykstra. Modal logic is, strictly speaking, the study of the deductive behavior of the. I have no proof that modal logic is inadequate, so i hope modal logicians will take the examples as challenges. The choice of logical connectives depends on the development of propositional logic one wants to follow. In fact, normal modal logics share the same proof rules mpandg and mostly differ in the choice of axioms. An introduction to modal logic geared towards philosophy students. Modal logic is the study of modal propositions and the logical relation ships that they bear to one another.
There are other examples of clear overlap between formal semantics and dynamic epistemic logic. An introduction to its syntax and semantics 9780195366570. Counterfactuals, neighborhood semantics, probability, predicative necessity, etc. Friends of the sep society stanford encyclopedia of. A semantic perspective 3 chapters in this handbook. Furthermore, thedevelopmentofanimproved syntactical hiding for the utilized logic embedding technique allows the refutation to be presented in a humanfriendly way, suitable for nonexperts in the technicalities of higherorder theorem proving. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. When i purchased the book, i thought it was going to be about how modal logic is used to solve philosophical problems. Rineke verbrugge, provability logic, from the stanford encyclopedia of philosophy. Chapter 1 modal logics of space institute for logic.
Thus, we can reason about knowledge rigorously in terms of partition models. Modal logic linguistics and philosophy mit opencourseware. Further background on modal logic can be found in the book by fitting and mendelsohn fm99. 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. Modern origins of modal logic stanford encyclopedia of philosophy. Philosophical issues from kripkes semantical considerations. Including alethic, deontic, temporal, doxastic, epistemic. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the. It was first conceived for modal logics, and later adapted to intuitionistic logic and other nonclassical systems. Basic concepts in modal logic1 stanford university. This article contains examples of uses of modality for which modal logic seems inadequate.
There are also more advanced books that you should keep on your radar. Prominent modal logics are constructed from a weak logic called k after saul kripke. While this is faithful to the field as a whole technically, modal predicate logic is just one of many system combinations, it is a serious omission for many purposes, and we will only. However, that discussion is less than satisfactory because it has been conducted without the necessary investigation of the. At the talk, dana introduced a new, probabilistic semantics for modal logica semantics about which very. Books notes on modal logic stanford university preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal. Unfortunately, modal logics seem too limited for many important purposes. Preliminary report ronald fagin ibm research laboratory, 5600 cottle road, san jose, ca 95193 moshe y. Provability logic is a modal logic, in which the box or necessity operator is interpreted as it is provable that.
This is not a book of modal logic for philosophers. 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. Csli, 1987, george hughes and max cresswell an introduction to modal logic, london. In kripke semantics for modal logic, pos sible world and the. However, the term modal logic may be used more broadly for a family of. Defaults and nonmonotonic reasoning stanford university. Ontological foundations of russells theory of modality pdf. Ambitious new work by one of the worlds leading philosophers. Encyclopedia of philosophy ballarin, 2008 plus the chapter logic in. Lecture notes modal logic linguistics and philosophy. Then ps being a necessary truth is expressed by s being true. It also gives an overview of nonnormal modal logics such as s1 and demonstrates various conditional and multivalued logics. That is, it presents modal logic as a tool for talking about structures or models.
Van benthem begins with the basic theories of modal logic, examining its relationship to language, semantics, bisimulation, and axiomatics, and then covers more advanced topics, such as. This book is an introduction to logic for students of contemporary philosophy. Modern origins of modal logic stanford encyclopedia of. The many worlds of logic resources history of logic. Cambridge university press, 1980, robert goldblatt logics of time and computation, stanford. Friends of the sep society stanford encyclopedia of 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. You can also read more about the friends of the sep society. Preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal logic. A solid background in firstorder logic is essential. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as peano arithmetic. This discussion presupposes familiarity with classical logic.
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. Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. Yet, the basic alethic modal logic of necessity and possibility already. Lecture notes on modal tableaux carnegie mellon school. Neighborhood semantics for modal logic an introduction. These notes are meant to present the basic facts about modal logic and so to provide a common ground for. The modal logic entry at the stanford encyclopedia of philosophy stanford.
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