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