In studying propositional modal logicsprimarily those characterized by classes of frameswe are also studying fragments of classical firstorder. Lecture 12 february 25, 2010 1 introduction to this lecture in this lecture, we will introduce. Firstorder modal logic is a big area with a great number of di erent logics. Moss, hansjorg tiede, applications of modal logic in linguistics, pp.
This is a thorough treatment of firstorder modal logic. A modal a word that expresses a modalityqualifies a statement. Basic concepts in modal logic1 stanford university. I am unsure how to interpret these the arguments chapter 6 and 7 look ok but are they. Mendelsohn fitting and mendelsohn present a thorough treatment of first order modal logic, together with some propositional background. Firstorder modal logic theorem proving and functional. We restrict the satisfiability calculus based on tableaux for first order modal logic, presented by fitting in 46, to its termfree fragment. See fitting and mendelson 5 for details on tableau procedures for first order modal logics. First order modal logics are modal logics in which the underlying propositional logic is replaced by a first order predicate logic. In this monograph, fitting and mendelsohn give a clean treatment of firstorder modal logic. This very extensive volume represents the current statofa airs in modal logic. This formulation allows a very general notion of model sheaf models.
Firstorder modal logic, topological semantics, completeness. Ian horrocks, ullrich hustadt, ulrike sattler, renate schmidt. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. From ignorant to researcher in modal logic philosophy stack. This volume offers new essays on the theories about the logical modalities necessity and possibility held by leading philosophers from.
First order modal logic by melvin fitting and elliot mehdelsohn. A search query can be a title of the book, a name of the author, isbn or anything else. A first order modal logic and its sheaf models barnaby p. Each function and predicate symbol has an arity k0. This chapter surveys basic first order modal logics and examines recent attempts to find a general mathematical setting in which to analyze them. We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness result for the entire family of classical first order modal systems in. Natural deduction based upon strict implication for normal modal logics cerrato, claudio, notre dame journal of formal logic, 1994. 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. Abstract firstorder modal logics, as traditionally formulated, are not expressive enough. Zalerts allow you to be notified by email about the availability of new books according to your search query. Mathematics and computer science lehman college cuny, bronx, ny 10468 email. The firstorder modal logics are compared to fragments of sorted firstorder logic through appropriate. Many modal logics have multiple axiomatizations that are equivalent, in the sense that they generate the same theory the same set of. Fitting, first order intensional logic, apal, 2004.
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 723724 from 1968 to 20. Fitting and mendelsohn present a thorough treatment of firstorder modal logic. Mendelsohn fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. Modal logic is a textbook on modal logic, intended for readers already acquainted with the elements of formal logic. Lecture notes on modal tableaux carnegie mellon school. Termmodal logic is the title of a paper by fitting, thalmann and voronkov.
Implementing connection calculi for firstorder modal logics. Interest in the metaphysics and logic of possible worlds goes back at least as far as aristotle, but few books address the history of these important concepts. Lindstr om and segerberg 2007, section 1 on the history of qml in philosophy dec. Nov, 2017 we generalize two wellknown modeltheoretic characterization theorems from propositional modal logic to firstorder modal logic fml, for short. The logic of proofs with quantifiers over proofs is not recursively enumerable yavorsky 2001. We first study fmldefinable frames and give a version of the goldblattthomason theorem for this logic. The advantage of this result, compared with the original goldblattthomason theorem, is that it does not need the condition of ultrafilter. It is this that is behind the diculties in formulating a good analog of herbrands theorem, as well as. In this paper we present a sketch of just such a higherorder modal logic. Lecture 14 march 2, 2010 1 introduction to this lecture in this lecture, we will consider the relationship of. Februrary 18, 2010 1 introduction to this lecture the hilbert calculus for modal logic from the last lectures is incredibly simple, but it is not entirely simple to. In part i of this chapter we give an introduction to.
Fitting and mendelsohn present a thorough treatment of first order modal logic, together with some propositional background. A common approach is to express the properties to be proved in a modal logic having one or more temporal modalities. A new s4 classical modal logic in natural deduction medeiros, maria da paz n. For example, the following are all modal propositions. Unification in firstorder transitive modal logic logic. Modal logic is the study of modal propositions and the logical relationships that they bear to one another. 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. Firstorder modal logics, as traditionally formulated, are not expressive enough.
The focus here is on rst order modal logic as opposed to propositional modal logic which is the focus of most of the. Computational modal logic introduction ps pdf authors. This semantics generalizes flaggs 1985 construction of a model of a modal version of churchs thesis and firstorder arithmetic. Details of the calculus, the implementation and performance results on the qmltp problem library are presented. Kx j x m it is true of kay that jay believes that she is the murderer. As it happens, almost every treatment of firstorder modal logic in the literature does not. Firstorder logic permits quantification into name position. 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.
The most wellknown modal propositions are propositions about what is necessarily the case and what is possibly the case. He was a professor at city university of new york, lehman college and the graduate center from 1968 to 20. Melvin mel fitting born january 24, 1942 is a logician with special interests in philosophical logic and tableau proof systems. Picture from the handbook meeting in amsterdam in 2004. This is a great place to get a clear introduction to firstorder modal logic. He was a professor at city university of new york, lehman college and the graduate center. This is a great place to get a clear introduction to first order modal logic. At the graduate center he was in the departments of computer science, philosophy, and mathematics, and at lehman college he was in the. First order modal logic, topological semantics, completeness. Logical modalities from aristotle to carnap edited by max. Higherorder logic takes the generalization even further. Firstorder logic formalizes fundamental mathematical concepts expressive turingcomplete not too expressive not axiomatizable. This cited by count includes citations to the following articles in scholar. An advanced, but very accessible, textbook focusing on the main technical results in the area.
What it amounts to is separating the notion of formula and predicate. Firstorder model theory stanford encyclopedia of philosophy. 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. 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. In this paper we present a sketch of just such a higher order modal logic. Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth. The set of first order formulas and free variable occurrences are as follows. 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. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general mathematical setting in which to analyze them. Lecture notes on firstorder reductions of firstorder modal logic 15816. This permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. Modern origins of modal logic stanford encyclopedia of.
They pose some of the most difficult mathematical challenges. Henceforth in this paper attention is limited to propositional modal logic with the standard modalities possibility and necessity. In this version, we show that the use first order modal logic with no higher order constructs suffices for many modelling tasks. A modala word that expresses a modalityqualifies a statement. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. We can formulate the first reading within our logical system as follows. An overview of applications of modal logic in linguistics can be found in. After a rocky start in the first half of the twentieth century, modal logic hit its stride in. Variations and extensions firstorder modal logic t. These methods, in particular allow us to extend a version of the goldblattthomason theorem to. Complexity of modal logic introduction ps pdf author. Firstorder modal logics are modal logics in which the underlying propositional logic is replaced by a firstorder predicate logic. They are general enough to also apply to other modal systems.
This is a thorough treatment of first order modal logic. I have been reading some introductory metaphysics van inwagens book of the same name and i encounter arguments using modal logic. Earlier this year, artemov yavorskaya found the firstorder logic of proofs folp capable of realizing firstorder modal logic fos4 and there fore, the firstorder intuitionistic logic hpc. Notes on modal logic notes for philosophy 151 eric pacuit january 28, 2009. Lecture notes on firstorder reductions of firstorder modal. 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. Although we restrict the approach here to firstorder modal logic theorem proving it has been shown to be of wider interest, as e. For example, the statement john is happy might be qualified by saying that john is usually happy, in which. Buehler based on first order modal logic by fitting and mendelsohn january 5, 2015. Naturally the tableau rules are not complete, but they are with respect to a henkinization of the \true semantics. Roles, rigidity, and quantification in epistemic logic. Many concepts in philosophy of language can be formalized in modal logic. What would be a good place to start to learn formal modal logic so that i can evaluate modal logic based arguments. Fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background.
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. Some have concluded that names cannot be treated as rigid designators in epistemic logic, as they are in alethic modal logic. This text provides both a philosophical and technical. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. Secondorder logic permits quantification into predicate or sentence position too. A modal logic for ceteris paribus preferences, journal of philosophical logic, 38. Contains a detailed discussion of completeness and incompleteness. A semantics for quantified modal logic is presented that is based on kleenes notion of realizability. Based on firstorder modal logic by fitting and mendelsohn. The set of firstorder formulas and free variable occurrences are as follows.
Buy firstorder modal logic synthese library softcover reprint of the original 1st ed. In this paper we describe tableau based theoremprovers for four modal logics, in both. We consider mainly firstorder transitive modal logics, i. 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. We need russells scoping mechanism, and just such a device was introduced into modal logic in 10, 11. We restrict the satisfiability calculus based on tableaux for firstorder modal logic, presented by fitting in 46, to its termfree fragment. 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. We present a new way of formulating rst order modal logic which circumvents the usual di culties associated with variables changing their reference on moving between states.
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