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