Fitting and mendelsohn present a thorough treatment of firstorder. First order modal logic, on the other hand, is underrepresented in the literature and. Firstorder modal logic, in the usual formulations, is not sufficiently expressive, and as a consequence problems like freges morning starevening star puzzle arise. Firstorder modal tableaux melvin fitting department of mathematics and computer science. A modal a word that expresses a modalityqualifies a statement. Melvin mel fitting born january 24, 1942 is a logician with special interests in philosophical logic and tableau proof systems. Firstorder modal logic theorem proving and functional. He was a professor at city university of new york, lehman college and the graduate center from 1968 to 20. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general mathematical setting in which to analyze them. An excellent source on firstorder modal logic, its var ious variations and pitfalls is the book by fitting and mendelsohn fm99. Firstorder logic permits quantification into name position.
They are general enough to also apply to other modal systems. In studying propositional modal logicsprimarily those characterized by classes of frameswe are also studying fragments of classical firstorder. Firstordermodallogic free ebook download as pdf file. Notes on modal logic notes for philosophy 151 eric pacuit january 28, 2009. Complexity of modal logic introduction ps pdf author. Garson has answered a question we raised, in a paper that is. Details of the calculus, the implementation and performance results on the qmltp problem library are presented. This text provides both a philosophical and technical. 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. Fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. Although we restrict the approach here to firstorder modal logic theorem proving it has been shown to be of wider interest, as e. This is a thorough treatment of firstorder modal logic.
Based on firstorder modal logic by fitting and mendelsohn. An introduction to modal logic 2009 formosan summer school on logic, language, and computation 29 june10 july, 2009. Everyday low prices and free delivery on eligible orders. 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. We consider mainly firstorder transitive modal logics, i. 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. These methods, in particular allow us to extend a version of the goldblattthomason theorem to.
This is a great place to get a clear introduction to firstorder modal logic. The ones marked may be different from the article in the profile. Variations and extensions firstorder modal logic t. Unification in firstorder transitive modal logic logic. Firstorder modal logic introduction ps pdf authors. This cited by count includes citations to the following articles in scholar. But this machinery can also be thought of as part of a move to a full higherorder 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. Many modal logics have multiple axiomatizations that are equivalent, in the sense that they generate the same theory the same set of. 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.
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. 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. Firstorder modal logics, as traditionally formulated, are not expressive enough. What it amounts to is separating the notion of formula and predicate. In this monograph, fitting and mendelsohn give a clean treatment of firstorder modal logic. Higherorder modal logica sketch melvin fitting dept. The introduction of predicate abstraction machinery provides a natural extension in which such difficulties can be addressed. Firstorder modal logic, topological semantics, completeness. Henceforth in this paper attention is limited to propositional modal logic with the standard modalities possibility and necessity. Secondorder logic permits quantification into predicate or sentence position too. Higherorder logic takes the generalization even further.
This permits a modular and elegant treatment of the considered modal logics and yields an efficient implementation. Though aimed at a nonmathematical audience in particular, students of philosophy and computer science, it is rigorous. 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. 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. If there are n people and m locations, representing the fact that some person moved from one location to another. Buehler based on firstorder modal logic by fitting and mendelsohn january 5, 2015.
Fitting and mendelsohn present a thorough treatment of firstorder 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. Firstorder modal logics are modal logics in which the underlying propositional logic is replaced by a firstorder predicate logic. List of errors in and suggested modi cations for firstorder modal logic melvin fitting and richard l. They pose some of the most difficult mathematical challenges. Firstorder modal tableaux not only produce a proof of each tautology, but must, if carried out as far as possible.
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 logic formalizes fundamental mathematical concepts expressive turingcomplete not too expressive not axiomatizable. Buy firstorder modal logic synthese library softcover reprint of the original 1st ed. Firstorder modal logic theorem proving and functional simulation andreas nonnengart maxplanckinstitute for computer science.
Nothing beyong the elementary will be needed however. On the expressive power of firstorder modal logic with twodimensional operators alex kocurek forthcoming in synthese. 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. List of errors in and suggested modi cations for first. 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. This chapter surveys basic firstorder modal logics and examines recent attempts to find a general. 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. The set of first order formulas and free variable occurrences are as follows. We need russells scoping mechanism, and just such a device was introduced into modal logic in 10, 11. First order modal logic by melvin fitting and elliot mehdelsohn. He was a professor at city university of new york, lehman college and the graduate center 723724 from 1968 to 20. Predicate logic in propositional logic, each possible atomic fact requires a separate unique propositional symbol.
Mendelsohn fitting and mendelsohn present a thorough treatment of firstorder modal logic, together with some propositional background. Implementing connection calculi for firstorder modal logics. 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. As it happens, almost every treatment of firstorder modal logic in the literature does not. A new introduction to modal logic is an entirely new work, completely rewritten by the authors. 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. Contains a detailed discussion of completeness and incompleteness.
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