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. 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. 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. Philosophical issues from kripkes semantical considerations. Modal logic is a type of formal logic primarily developed in the 1960s that extends classical. Basic concepts in modal logic1 stanford university. 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 the study of modal propositions and the logical relation ships that they bear to one another. However, that discussion is less than satisfactory because it has been conducted without the necessary investigation of the. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. In part 1, the reader is introduced to some standard systems of modal logic and provided with a series of.
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. Sep 22, 2016 divers, j 2016 philosophical issues from kripkes semantical considerations on modal logic. Prominent modal logics are constructed from a weak logic called k after saul kripke. An introduction to modal logic geared towards philosophy students. This discussion presupposes familiarity with classical logic. Chapter 1 modal logics of space institute for logic. Encyclopedia of philosophy ballarin, 2008 plus the chapter logic in. Including alethic, deontic, temporal, doxastic, epistemic. In kripke semantics for modal logic, pos sible world and the. Friends of the sep society stanford encyclopedia of philosophy. A modala word that expresses a modalityqualifies a statement. Neighborhood semantics for modal logic an introduction.
This is not a book of modal logic for philosophers. This article contains examples of uses of modality for which modal logic seems inadequate. An introduction to its syntax and semantics 9780195366570. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. This book is an introduction to logic for students of contemporary philosophy.
These notes are meant to present the basic facts about modal logic and so to provide a common ground for. In semantical considerations on modal logic, kripke articulates his project in the discourse of possible worlds. Modal logic is, strictly speaking, the study of the deductive behavior of the. Philosophical aspects of multimodal logic stanford encyclopedia. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. A new textbook on modal logic providing a modern introduction to modal logic.
The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as peano arithmetic. More recently, modal logic has become a muchused tool for analyzing the logic of such various propositional operators as belief, knowledge and tense. 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. 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. It also gives an overview of nonnormal modal logics such as s1 and demonstrates various conditional and multivalued logics. Notes on modal logic stanford ai lab stanford university. An introduction to modal logic geared to wards philosophy students. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. 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. Vardi csli, ventura hall, stanford university, stanford, ca 94305 abstract. Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. Notes on modal logic stanford artificial intelligence. 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.
Csli, 1987, george hughes and max cresswell an introduction to modal logic, london. Ambitious new work by one of the worlds leading philosophers. Modern origins of modal logic stanford encyclopedia of philosophy. 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. Modal logic linguistics and philosophy mit opencourseware. 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 as metaphysics hardcover timothy williamson. Cambridgeuniversitypress,1980,robertgoldblattlogics of time andcomputation, stanford. The choice of logical connectives depends on the development of propositional logic one wants to follow. 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. However, the term modal logic may be used more broadly for a family of. Cambridge university press, 1980, robert goldblatt logics of time and computation, stanford.
Lecture 4 philosophy 150 eric pacuit stanford university ai. But what kind of structures can modal logic talk about. A semantic perspective 3 chapters in this handbook. Every effort has been made to simplify the presentation by using diagrams in place of more complex mathematical apparatus. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. The modal logic entry at the stanford encyclopedia of philosophy stanford. The axiomatisation of k is a subset of the axioms of s4 and the same proof rules of s4. Modal logic is an extension of classic propositional and predicate logic that allows the use of modal operators. Modal predicate logic an important topic in philosophical applications of modal logic that we have mostly ignored in this survey is modal predicate logic. Then ps being a necessary truth is expressed by s being true. At the talk, dana introduced a new, probabilistic semantics for modal logica semantics about which very. A nice introduction to modal logic though somewhat outdated. Thus, we can reason about knowledge rigorously in terms of partition models.
Further background on modal logic can be found in the book by fitting and mendelsohn fm99. 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. 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. 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. In the standard kripke semantics for modal logic, truth is relative to points in a set.
A philosophical conception of propositional modal logic the. Preliminary report ronald fagin ibm research laboratory, 5600 cottle road, san jose, ca 95193 moshe y. Indicative conditionals and dynamic epistemic logic. A philosophical conception of propositional modal logic. Modal logics are particularly well suited to study a wide range of philosophical. The logic begins with s5, before going into the normal modal logics. Rineke verbrugge, provability logic, from the stanford encyclopedia of philosophy. Unfortunately, modal logics seem too limited for many important purposes. 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. Modern origins of modal logic stanford encyclopedia of. Cambridgeuniversitypress,1980,robertgoldblattlogics of time and computation, stanford. In fact, normal modal logics share the same proof rules mpandg and mostly differ in the choice of axioms. To view the pdf, you must log in or become a member.
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. You can also read more about the friends of the sep society. 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. There are other examples of clear overlap between formal semantics and dynamic epistemic logic. Kripke semantics for the intuitionistic logic follows the same principles as the semantics of modal logic, but it uses a different definition of satisfaction. Ontological foundations of russells theory of modality pdf. There has been much philosophical discussion of whether endorsement of the kripke semantics brings ontological commitment to possible worlds.
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. Provability logic is a modal logic, in which the box or necessity operator is interpreted as it is provable that. Lecture notes on modal tableaux carnegie mellon school. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the. A solid background in firstorder logic is essential.
There are also more advanced books that you should keep on your radar. Preface these notes were composed while teaching a class at stanford and studying the work of brian chellas modal logic. Yet, the basic alethic modal logic of necessity and possibility already. This book is essentially split into two main sections. An introduction to its syntax and semantics amazon site. It was first conceived for modal logics, and later adapted to intuitionistic logic and other nonclassical systems.
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 for philosophers designed for use by philosophy students, this book provides an accessible yet technically sound treatment of modal logic and its philosophical applications. This entry was written by james garson and provides a nice overview of the philosophical applications of modal logic. Counterfactuals, neighborhood semantics, probability, predicative necessity, etc. This is obtained by adding to ordinary modal logic a second sort of. Lecture notes modal logic linguistics and philosophy. When i purchased the book, i thought it was going to be about how modal logic is used to solve philosophical problems. 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. I have no proof that modal logic is inadequate, so i hope modal logicians will take the examples as challenges. Friends of the sep society stanford encyclopedia of.
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