If you refer to the paper, please send me a message. Click download or read online button to get handbook of modal logic book now. In this paper we deal with the semantics for quantified modal logic, qml in short, and their philosophical relevance. In 9 we developed a semantics for quantified relevant logic that uses general frames. These and other innovations provide philosophers with easy access to a rich variety of topics in modal logic, including a full coverage of quantified modal logic, nonrigid designators, definite. Modal logic is, strictly speaking, the study of the deductive behavior of the. The case of quantified nonmonotone logics is left for future research. 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 authors distinguish in this section between actualism, which is based on free logic, i. Intensional logic is an approach to predicate logic that extends firstorder logic, which has quantifiers that range over the individuals of a universe, by additional quantifiers that range over terms that may have such individuals as their value. In the semantics for the quantified modal language, a model will be a quadruple.
Introductory modal logic notre dame university press. Buehler based on first order modal logic by fitting and mendelsohn. The logics rely on the philosophical tenet known as serious actualism in that within modal contexts they allow existential generalization from atomic formulas. Ordinary language is notoriously ambiguous and the analysis of ordinary language modal operators is fraught with difficulty. Proof theory for quantified monotone modal logics 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. Quantified modal logic on the rational line tspace. Handbook of modal logic download ebook pdf, epub, tuebl. There is a special predicate on individuals and situations existsi,s which is regarded as true when i names an individual existing in the situation s. Why propositional quantification makes modal logics on. On modal logic with propositional quantifiers volume 34 issue 2 r. Bull skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites.
Foundations of modal metaphysics columbia university. For modal logic, however, adding quantifiers is far from the end of the story, as we will soon see. Or we can proceed more directly, speaking explicitly of possible worlds from the start. While interpolation and beths definability theorem fail in a number of wellknown quantified modal logics for example in quantified modal k, t, d, s4, s4. Counterpart theory, quantified modal logic, and extra argument places david lewis we can couch our modal statements in the language of modal logic some times, anyway and then have recourse to possible worlds to explain the semantics of that language. The other is to give a detailed survey of the large variety of modal logic systems found in the literature, with an eye to both their formal properties consistency, completeness and their philosophi.
More specifically, we show that qctlt restricted to the temporal operator ex is. There is detailed historical discussion of how the metaphysical issues emerged in the twentiethcentury development of quantified modal logic, through the work of such figures as rudolf carnap, ruth barcan marcus, arthur prior, saul kripke, david lewis, robert stalnaker, alvin plantinga, and kit fine. In the topological semantics for propositional modal logic, s4 is known to be complete for the class of all topological spaces, for the rational line, for cantor space, and for the real line. But they may also be of interest to others who want to learn about the technical details and philosophical applications of extensions to and deviations from. The distinction between intensional and extensional entities is parallel to the distinction between sense and reference. In phil 201, you should have learned how to construct firstorder proofs for propositional and predicate logic. If we accept the historical interpretation of the network between quine, kripke and modal logic, which is to be presented here, we have to conclude that quines real philosophical animadversions against the. Zalta department of philosophy stanford university by combining the laws of classical quanti cation theory with the modal propositional logic kin the most direct manner, one produces the simplest quanti ed modal logic. Actualism the simplest quantified modal logic sqml. Quantified minimal modal logic and its applications.
A brief outline of modal predicate logic whether, how far, and in what ways various properties of sentential modal logics carry. The authors develop semantics for firstorder modal predicate logic in terms of standard model theory, the models of which we take to be settheoretic counterparts of possible worlds. Prerequisites phil 201 introduction to logic is the only prerequisite for this course. Pdf a general semantics for quantified modal logic. This semantics generalizes flaggs 1985 construction of a model of a modal version of churchs thesis and firstorder arithmetic. Pdf labelled proofs for quantified modal logic alberto. Adding quantifier machinery to classical propositional logic yields firstorder classical logic, fully formed and ready to go. Necessary existence and the semantics of quantified modal logic 1. Are there future people, who have not yet been conceived. Actualism, serious actualism, and quantified modal logic hanson, william h.
By regimenting our discourse into formal quantified modal logic we can eliminate some of these ambiguities. Propositional modal logic is a wellknown tool, since possible worlds can rep resent computational states or moments of time or ways an agent. We need russells scoping mechanism, and just such a device was introduced into modal logic in 10, 11. This is a strong motivation for the present approach. In the topological semantics for quantified modal logic, qs4 is known to be complete for the class of all topological spaces, and for the family of subspaces of the irrational line. Modal logic is used to reason about possibility and necessity, knowledge and belief, permission and obligation, past and future, and a variety of other topics. The model theory involves possible worlds with worldvariable domains. The simplest quantified modal logic sqml defines a class of firstorder modal languages, a semantic theory for those languages, and a complete system of axioms and rules of inference for the semantics. In addition to the standard connectives and quantifiers, we assume that, for every n. W and r are the same as in the semantics for propositional modal logic. A prooftheoretic study of the correspondence of classical logic and modal logic kushida, h. Questions like those raise deep issues about both the nature of being and its logical relations with contingency and change.
Today geometry is the study of a vast range of mathematical structures, closely enough related to structures once thought to. Introductory modal logic fills the need for a basic text on modal logic, accessible to students of elementary symbolic logic. Find materials for this course in the pages linked along the left. This chapter describes the syntax of firstorder modal predicate logic and develops the firstorder extensions of the different sentential modal logics constructed in chapter 2. I no longer have copies of that paper but i enclose a reference from. Kenneth konyndyk presents a natural deduction treatment of propositional modal logic and quantified modal logic, historical information about its development, and discussions of the philosophical issues raised by. Timothy williamson 2002 has offered what he believes to be a proof for his own necessary existence. Repairing the interpolation theorem in quantified modal logic.
Handout semantics for quantified modal logic april 3april 8 pages 5355. The cost of the messier house plus the assumption that no object can be abstract in some worlds and concrete in others must be counted against their view, even as the simplicity of their logic counts for it. An admissible semantics for propositionally quantified relevant logics. Unfortunately, this choice does not correspond to a intuitively satisfying semantics.
A modala word that expresses a modalityqualifies a statement. These sentences, i will argue, have a threefold ambiguity. Modal logic autumn 2019 this is a followon course to logic 1, focusing on modal extensions of classical propositional and predicate logic. Foundations of modal metaphysics phil c3912 fall 2015 friday 24pm description. When it comes to kripkestyle semantics for quantified modal logic, theres a choice to be made concerning the interpretation of the quantifiers. In defense of the simplest quanti ed modal logic bernard linsky department of philosophy university of alberta and edward n. Modal logic as metaphysics hardcover timothy williamson. These are special cases of the main result of the paper. There are several reasons for this, including multiplicity of versions and inadequate syntax. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. Pdf quine and quantified modal logic against the received. Counterpart theory and quantified modal logic authors. The reason we want to utilize modal logic is to precisify ordinary language.
However, the term modal logic may be used more broadly for a family of. Labelled proofs for quantified modal logic uq espace. In order to translate quantified modal logic, with its difficulties of referential opacity, we must complicate the situation calculus to a degree which makes it rather clumsy. Many of the readings are online, and all can be obtained from the college or other libraries in oxford, but if you are struggling to get hold of anything, email me, as i have pdf copies of nearly everything. While interpolation and beths definability theorem fail in a number of wellknown quantified modal logics, their counterparts in quantified hybrid logic have these properties. Necessary existence and the semantics of quantified modal logic. In this paper, we adapt that model theory to treat quantified modal logics. Counterpart theory, quantified modal logic, and extra. Semantics of quantified modal logic oxford scholarship. One is to explain what modal logic is, and how it is done. Buehler based on first order modal logic by fitting and mendelsohn january 5, 2015. The modal generalization to the vocabulary, add one logical expression. In this seminar, we will discuss foundational questions in the theory of metaphysical possibility. Quantified hybrid logic is quantified modal logic extended with apparatus for naming states and asserting that a formula is true at a named state.
While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope. This site is like a library, use search box in the widget to get ebook that you want. Essentialism in quantified modal logic springerlink. The book contains detailed historical discussion of how the metaphysical issues emerged in the twentieth century development of quantified modal logic, through the work of such figures as rudolf. A general strategy for proving completeness theorems for quantified modal logics is provided. Firstordermodallogic university of california, berkeley. Propositional modal logic is a standard tool in many disciplines, but firstorder modal logic is not. By combining the laws of classical quantification theory with the modal propositional logic k in the most direct manner, one produces the sim plest quantified. But certainly adding quantifiers is the place to start. Though mainly the last few years have witnessed a huge amount of historical work that aimed to.
These are the core lectures for students taking fhs paper 127. Basic tense logic and combining modality and tense. What it amounts to is separating the notion of formula and predicate. A semantics for quantified modal logic is presented that is based on kleenes notion of realizability. Quantified modal logic and the plural dere 375 world the president at that world is a u. For this purpose, however, kripkes semantics for quantified modal logic is inadequate. Are there such things as merely possible people, who would have lived if our ancestors had acted differently. The paper discusses several firstorder modal logics that extend the classical predicate calculus. Is the notion of metaphysical possibility intelligible. Quantified modal logic on the rational line 441 it is well known that. Objections 1 a system of modal propositional logic is a bona fide logic only if it has a quantificational extension. This proof, though, is not an exercise in existential immodesty on a grand scale since it generalises to be an argument for the seemingly. The semantics of modal propositional logic philosophy 431 spring 20 this handout draws on sider, logic for philosophy, ch.
Counterpart theory w t te can conduct formalized discourse about most topics perfectly well bv means of our allpurpose extensional. A primary semantics for logical necessity as based on the notion of all possible worlds of a logical space is also described and shown to be essentially incomplete. He rejects the search for a metaphysically neutral logic as futile. What are the controversies behind systems of quantified modal logic. Counterpart theory w t te can conduct formalized discourse about most topics perfectly well bv means of our allpurpose extensional logic, provided with predicates and a domain of quanti fication suited to the subject matter at hand. A modal is an expression like necessarily or possibly that is used to qualify the truth of a judgement. Examples for convenience, we reproduce the item logic modal logic of principia metaphysica in which the modal logic is defined.
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. Quantified minimal modal logic and its applications, logic journal of the igpl, volume 11, issue 5. As for quantified normal modal logics, labelled calculi allow for an elegant and uniform proof of completeness for all the qmml considered. To read them, youll need to have either adobe acrobat or adobe acrobat reader installed. Ockhamism and quantified modal logic logique et analyse 2015. In 1947 in a paper on identity in modal logic in the journal of symbolic logic 12 jsl, there is a formal proof of the necessity of identity for systems of quantified modal logic. The textbooklike history of analytic philosophy is a history of myths, received views and dogmas. Pdf ockhamism and quantified modal logic logique et. Pdf semantics and ontology in quantified modal logic. Logic for philosophy logic michigan state university.
Lecture notes modal logic linguistics and philosophy. Starting from free quantified modal logic k, with or without identity. Handout 18 modal description theory april 24 pages 6871. Quantified modal logic and the plural dere 373 oa every f might be g.