Nfirst-order modal logic fitting pdf

This cited by count includes citations to the following articles in scholar. On the expressive power of firstorder modal logic with twodimensional operators alex kocurek forthcoming in synthese. Details of the calculus, the implementation and performance results on the qmltp problem library are presented. On the expressive power of firstorder modal logic with. 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. What it amounts to is separating the notion of formula and predicate. Firstorder logic permits quantification into name position. Contains a detailed discussion of completeness and incompleteness. He was a professor at city university of new york, lehman college and the graduate center from 1968 to 20. As it happens, almost every treatment of firstorder modal logic in the literature does not. This is a great place to get a clear introduction to firstorder modal logic. 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. These methods, in particular allow us to extend a version of the goldblattthomason theorem to.

First order modal logic, on the other hand, is underrepresented in the literature and. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general. Firstorder modal logic theorem proving and functional. Firstorder modal logic, topological semantics, completeness. Firstorder modal logic introduction ps pdf authors.

Although we restrict the approach here to firstorder modal logic theorem proving it has been shown to be of wider interest, as e. Though aimed at a nonmathematical audience in particular, students of philosophy and computer science, it is rigorous. Fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. This text provides both a philosophical and technical. We consider mainly firstorder transitive modal logics, i. List of errors in and suggested modi cations for firstorder modal logic melvin fitting and richard l. Melvin mel fitting born january 24, 1942 is a logician with special interests in philosophical logic and tableau proof systems. 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. Many authors have noted that there are types of english modal sentences that cannot be formalized in the language of basic fit order 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. Firstorder modal tableaux not only produce a proof of each tautology, but must, if carried out as far as possible. But this machinery can also be thought of as part of a move to a full higherorder modal logic. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. 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. This permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. Firstorder modal logics, as traditionally formulated, are not expressive enough. We need russells scoping mechanism, and just such a device was introduced into modal logic in 10, 11. They pose some of the most difficult mathematical challenges. List of errors in and suggested modi cations for first. 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. Download pdf a new introduction to modal logic free.

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. Buehler based on firstorder modal logic by fitting and mendelsohn january 5, 2015. Firstorder modal tableaux melvin fitting department of mathematics and computer science. The set of first order formulas and free variable occurrences are as follows. Firstorder logic formalizes fundamental mathematical concepts expressive turingcomplete not too expressive not axiomatizable.

Firstorder modal logics are modal logics in which the underlying propositional logic is replaced by a firstorder predicate logic. Higherorder logic takes the generalization even further. Notes on modal logic notes for philosophy 151 eric pacuit january 28, 2009. Implementing connection calculi for firstorder modal logics. At the graduate center he was in the departments of computer science, philosophy, and mathematics, and at lehman college he was in the. Fitting and mendelsohn present a thorough treatment of firstorder modal logic.

Variations and extensions firstorder modal logic t. First order modal logic by melvin fitting and elliot mehdelsohn. They are general enough to also apply to other modal systems. If there are n people and m locations, representing the fact that some person moved from one location to another. Predicate logic in propositional logic, each possible atomic fact requires a separate unique propositional symbol. Firstorder modal logic theorem proving and functional simulation andreas nonnengart maxplanckinstitute for computer science. The introduction of predicate abstraction machinery provides a natural extension in which such difficulties can be addressed. Many modal logics have multiple axiomatizations that are equivalent, in the sense that they generate the same theory the same set of. He was a professor at city university of new york, lehman college and the graduate center 723724 from 1968 to 20. Henceforth in this paper attention is limited to propositional modal logic with the standard modalities possibility and necessity. Unification in firstorder transitive modal logic 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. Higherorder modal logica sketch melvin fitting dept. Fitting and mendelsohn present a thorough treatment of firstorder. In this monograph, fitting and mendelsohn give a clean treatment of firstorder modal logic. The ones marked may be different from the article in the profile. 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. Firstordermodallogic free ebook download as pdf file. Request pdf 9 firstorder modal logic firstorder modal logics are modal logics in which the underlying propositional logic is replaced by a firstorder predicate logic. A modal a word that expresses a modalityqualifies a statement. Mendelsohn fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background.

Everyday low prices and free delivery on eligible orders. 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. Secondorder logic permits quantification into predicate or sentence position too. Complexity of modal logic introduction ps pdf author. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. Syntactic abstraction for reasoning in firstorder modal logics damien doligez1, jael kriener2, leslie lamport3, tomer libal2, and stephan merz4 1 inria, paris, france 2 msrinria joint centre, saclay, france 3 microsoft research, mountain view, ca, u. Firstorder modal logic, in the usual formulations, is not sufficiently expressive, and as a consequence problems like freges morning starevening star puzzle arise. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general mathematical setting in which to analyze them. 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. Nothing beyong the elementary will be needed however. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their. In studying propositional modal logicsprimarily those characterized by classes of frameswe are also studying fragments of classical firstorder. 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.

This is a thorough treatment of firstorder modal logic. Buy firstorder modal logic synthese library softcover reprint of the original 1st ed. An excellent source on firstorder modal logic, its var ious variations and pitfalls is the book by fitting and mendelsohn fm99. Garson has answered a question we raised, in a paper that is. Based on firstorder modal logic by fitting and mendelsohn.