They pose some of the most difficult mathematical challenges. In manysorted logic, one can have different sorts of objectssuch as points and linesand a separate stock of variables and quantifiers ranging over each. Fitting and mendelsohn present a thorough treatment of firstorder. The focus here is on rstorder modal logic as opposed to propositional modal logic which is the focus of most of the other texts mentioned here. Now a second kind of quantification is added, over intensions. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. Purchase handbook of modal logic, volume 3 1st edition. Pdf the fitchchurch paradox and first order modal logic. Fitting and mendelsohn present a thorough treatment of first order modal logic, together with some propositional background. Modal logic is the study of modal propositions and the logical relationships that they bear to one another. Many modal logics have multiple axiomatizations that are equivalent, in the sense that they generate the same theory the same set of. We need russells scoping mechanism, and just such a device was introduced into modal logic in 10, 11.
A common approach is to express the properties to be proved in a modal logic having one or more temporal modalities. Mathematics and computer science lehman college cuny, bronx, ny 10468 depts. It elegantly straddles the line between philosophy and mathematics, without getting bogged down in the details of either as much of the rest of the modal logic literature seems to. Basic concepts in modal logic1 stanford university. Advances in modal logic is a unique forum for presenting the latest results and new directions of research in modal logic. Firstorder logic permits quantification into name position. This is a thorough treatment of firstorder modal logic. Nov 25, 20 this permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. This permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. Mendelsohn, firstorder modal logic find, read and cite all the research you need on. Buehler based on first order modal logic by fitting and mendelsohn january 5, 2015. Mendelsohn fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background.
The journal of symbolic logic volume 49, number 4, dec. This is a great place to get a clear introduction to firstorder modal logic. 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. Termmodal logic is the title of a paper by fitting, thalmann and voronkov. Thus, qk is the weakest or basic firstorder modal logic and any firstorder modal logic may be regarded as an extension of qk with some schemata. Based on firstorder modal logic by fitting and mendelsohn. As it happens, almost every treatment of firstorder modal logic in the literature does not. For example, the following are all modal propositions. He was a professor at city university of new york, lehman college and the graduate center 723724 from 1968 to 20. But this machinery can also be thought of as part of a move to a full higherorder modal logic. Your use of the jstor archive indicates your acceptance of. First order modal logic, topological semantics, completeness.
The most wellknown modal propositions are propositions about what is necessarily the case and what is possibly the case. A modal a word that expresses a modalityqualifies a statement. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general mathematical setting in which to analyze them. In this paper we describe tableau based theoremprovers for four modal logics, in both. These methods, in particular allow us to extend a version of the goldblattthomason theorem to. Firstorder modal logics are modal logics in which the underlying propositional logic is replaced by a firstorder predicate logic. Fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. After three introductory chapters on propositional modal logics, the next five chapters show that first order logic with relational symbols including equality poses no special problems. Computer science, philosophy, mathematics graduate center cuny, 33 west 42nd street, nyc, ny 10036.
The growth of higherorder modal logic is traced, starting with lewis and langfords quantification into sentence position in propositional modal logic, and on to the higherorder modal logics. The set of first order formulas and free variable occurrences are as follows. Firstorder modal logics, as traditionally formulated, are not expressive enough. As well as considering modalities applied to propositions in propositional modal logic, logicians have also studied modalities applied to predicate logic, or firstorder modal logic.
In 1 craig introduced a proof procedure for first order classical logic called linear reasoning. Fitting and mendelsohn present a thorough treatment of firstorder modal logic. Firstorder modal logic, topological semantics, completeness. Firstorder modal logic1 kohei kishida 1draft of november 14, 2010. He was a professor at city university of new york, lehman college and the graduate center from 1968 to 20. About the open logic project the open logic text is an opensource, collaborative textbook of formal meta logic and formal methods, starting at an intermediate level i. Typical examples can be found in fitting, 1983 where the well known tableau calculus and the sequent calculus are appropri ately extended and wallen, 1987. February 18, 1991 abstract firstorder modal logics, as traditionally.
Implementing connection calculi for firstorder modal logics. Variations and extensions firstorder modal logic t. Although we restrict the approach here to firstorder modal logic theorem proving it has been shown to be of wider interest, as e. From firstorder to higherorder modal logic oxford scholarship. Complexity of modal logic introduction ps pdf author. Buehler based on firstorder modal logic by fitting and mendelsohn january 5, 2015. He was a professor at city university of new york, lehman college and the graduate center. This book introduces some extensions of classical first order logic and applies them to reasoning about computer programs.
An advanced, but very accessible, textbook focusing on the main technical results in the area. Notes on modal logic notes for philosophy 151 eric pacuit january 28, 2009. Higherorder logic takes the generalization even further. The focus here is on rst order modal logic as opposed to propositional modal logic which is the focus of most of the. Melvin mel fitting born january 24, 1942 is a logician with special interests in philosophical logic and tableau proof systems. An overview of applications of modal logic in linguistics can be found in. Firstorder model theory stanford encyclopedia of philosophy. What it amounts to is separating the notion of formula and predicate. After three introductory chapters on propositional modal logics, the next five chapters show that firstorder logic with relational symbols including equality poses no special problems. In this monograph, fitting and mendelsohn give a clean treatment of firstorder modal logic.
Abstract firstorder modal logics, as traditionally formulated, are not expressive enough. Unification in firstorder transitive modal logic logic. First order modal logics are modal logics in which the underlying propositional logic is replaced by a first order predicate logic. Intensional logic stanford encyclopedia of philosophy. Computational modal logic introduction ps pdf authors. At the graduate center he was in the departments of computer science, philosophy, and mathematics, and at lehman college he was in the. Isbn 9780792353355 isbn 97894011 52921 ebook this is a thorough treatment of firstorder modal. The book covers such issues as quantification, equality including a treatment of freges morning starevening star puzzle, the notion of existence, nonrigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both fregean and. This cited by count includes citations to the following articles in scholar. In this monograph, fitting and mendelsohn give a clean treatment of first order modal logic. Interest in nonclassical theorem proving is growing and for this reason, as well as for its intrinsic interest, tableau methods deserve to be more widely known. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. This is a great place to get a clear introduction to first order modal logic. But this machinery can also be thought of as part of a move to a full higher order modal logic.
In this paper we present a sketch of just such a higher order modal logic. Henceforth in this paper attention is limited to propositional modal logic with the standard modalities possibility and necessity. Naturally the tableau rules are not complete, but they are with respect to a henkinization of the \true semantics. See fitting and mendelson 5 for details on tableau procedures for first order modal logics. The ones marked may be different from the article in the profile. Mathematics and computer science lehman college cuny, 250 bedford park boulevard west bronx, ny 104681589 email.
Problem is that theres no answers in the book for any of the exercisesquestions so its practically impossible to know how youre doing or track progress. Secondorder logic permits quantification into predicate or sentence position too. This chapter surveys basic first order modal logics and examines recent attempts to find a general mathematical setting in which to analyze them. 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. Though aimed at a nonmathematical audience in particular, students of philosophy and computer science, it is rigorous. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics. Isbn 9780792353355 isbn 9789401152921 ebook this is a thorough treatment of firstorder modal. Firstorder modal logic theorem proving and functional. The set of firstorder formulas and free variable occurrences are as follows. Details of the calculus, the implementation and performance results on the qmltp problem library are presented. But dealing with such predicates is tedious, and there is a mild extension of firstorder logic, called manysorted firstorder logic, which builds in some of the bookkeeping.
It is philosophically motivated by the epistemic reading of modal operators and, in particular, three desiderata in. A modala word that expresses a modalityqualifies a statement. Higherorder modal logica sketch melvin fitting dept. The introduction of predicate abstraction machinery provides a natural extension in which such difficulties can be addressed. Notes on modal logic notes for phil370 eric pacuit october 22, 2012. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. This very extensive volume represents the current statofa airs in modal logic. Firstorder modal logic, in the usual formulations, is not sufficiently expressive, and as a consequence problems like freges morning starevening star puzzle arise. The fitchchurch paradox and first order modal logic. We consider mainly firstorder transitive modal logics, i. Firstorder modal logic theorem proving and functional simulation. Firstorder logic formalizes fundamental mathematical concepts expressive turingcomplete not too expressive not axiomatizable.
Moss, hansjorg tiede, applications of modal logic in linguistics, pp. They are general enough to also apply to other modal systems. This is a thorough treatment of first order modal logic. First order model theory, also known as classical model theory, is a branch of mathematics that deals with the relationships between descriptions in first order languages and the structures that satisfy these descriptions. As has been noted several times, an intensional object, or individual concept, will be modeled by a function from states to objects, but now we get into the question of what functions. An excellent source on firstorder modal logic, its var ious variations and pitfalls is the book by fitting and mendelsohn fm99. Contains a detailed discussion of completeness and incompleteness. It is this that is behind the diculties in formulating a good analog of herbrands theorem, as well as. First order modal logic by melvin fitting and elliot mehdelsohn. Mendelsohn valentin shehtman 1 journal of logic, language and information volume 10, pages 403 405 2001 cite this article. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general. First order modal logic, in the usual formulations, is not sufficiently expressive, and as a consequence problems like freges morning starevening star puzzle arise. The growth of higherorder modal logic is traced, starting with lewis and langfords quantification into sentence position in propositional modal logic, and on to the higherorder modal logics of barcan marcus, carnap, montague, gallin, and others. This text provides both a philosophical and technical.
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