Results for 'First-order logic'

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  1.  56
    Extensions of First Order Logic.María Manzano - 1996 - Cambridge University Press.
    Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be (...)
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  2.  21
    Categorical Abstract Algebraic Logic Categorical Algebraization of First-Order Logic Without Terms.George Voutsadakis - 2004 - Archive for Mathematical Logic 44 (4):473-491.
    An algebraization of multi-signature first-order logic without terms is presented. Rather than following the traditional method of choosing a type of algebras and constructing an appropriate variety, as is done in the case of cylindric and polyadic algebras, a new categorical algebraization method is used: The substitutions of formulas of one signature for relation symbols in another are treated in the object language. This enables the automatic generation via an adjunction of an algebraic theory. The algebras of this (...)
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  3.  31
    Reasoning About Truth in First-Order Logic.Claes Strannegård, Fredrik Engström, Abdul Rahim Nizamani & Lance Rips - 2013 - Journal of Logic, Language and Information 22 (1):115-137.
    First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the (...)
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  4.  11
    An Event-Based Fragment of First-Order Logic Over Intervals.Savas Konur - 2011 - Journal of Logic, Language and Information 20 (1):49-68.
    We consider a new fragment of first-order logic with two variables. This logic is defined over interval structures. It constitutes unary predicates, a binary predicate and a function symbol. Considering such a fragment of first-order logic is motivated by defining a general framework for event-based interval temporal logics. In this paper, we present a sound, complete and terminating decision procedure for this logic. We show that the logic is decidable, and provide a NEXPTIME (...)
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  5.  35
    Is Leibnizian Calculus Embeddable in First Order Logic?Piotr BLaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry - 2016 - Foundations of Science 22.
    To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found (...)
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  6.  11
    First-Order Logic and First-Order Functions.Rodrigo A. Freire - 2015 - Logica Universalis 9 (3):281-329.
    This paper begins the study of first-order functions, which are a generalization of truth-functions. The concepts of truth-table and systems of truth-functions, both introduced in propositional logic by Post, are also generalized and studied in the quantificational setting. The general facts about these concepts are given in the first five sections, and constitute a “general theory” of first-order functions. The central theme of this paper is the relation of definition among notions expressed by formulas of first-order (...)
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  7.  3
    Is Leibnizian Calculus Embeddable in First Order Logic?Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry - forthcoming - Foundations of Science:1-15.
    To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian (...)
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  8. First-Order Logic in the Medvedev Lattice.Rutger Kuyper - 2015 - Studia Logica 103 (6):1185-1224.
    Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices. However, they only formalised this for propositional logic, while Kolmogorov also discussed the universal quantifier. We extend the work of Medvedev to first-order logic, using the notion of a first-order hyperdoctrine from categorical logic, to a structure (...)
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  9.  44
    Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom (...)
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  10.  29
    On the Expressive Power of First-Order Modal Logic with Two-Dimensional Operators.Alexander W. Kocurek - forthcoming - Synthese:1-45.
    Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these (...)
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  11.  31
    Linguistic Applications of First Order Intuitionistic Linear Logic.Richard Moot & Mario Piazza - 2001 - Journal of Logic, Language and Information 10 (2):211-232.
    In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.
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  12.  42
    First-Order Logic.Raymond M. Smullyan - 1968 - New York [Etc.]Springer-Verlag.
    This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...
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  13.  35
    First-Order Modal Logic with an 'Actually' Operator.Yannis Stephanou - 2005 - Notre Dame Journal of Formal Logic 46 (4):381-405.
    In this paper the language of first-order modal logic is enriched with an operator @ ('actually') such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system (...)
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  14. First-Order Modal Logic in the Necessary Framework of Objects.Peter Fritz - 2016 - Canadian Journal of Philosophy 46 (4-5):584-609.
    I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes (...)
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  15.  27
    First Order Mathematical Logic.Angelo Margaris - 1967 - Dover Publications.
    Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order theories are discussed in some detail, with special emphasis on number theory. After a discussion of truth and models, the completeness theorem is proved. "...an excellent text."—Mathematical Reviews. Exercises. Bibliography.
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  16. First-Order Classical Modal Logic.Horacio Arló-Costa & Eric Pacuit - 2006 - Studia Logica 84 (2):171 - 210.
    The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (...)
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  17.  3
    Semantical Completeness of First-Order Predicate Logic and the Weak Fan Theorem.Victor N. Krivtsov - 2015 - Studia Logica 103 (3):623-638.
    Within a weak system \ of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over \ the Weak Fan Theorem.
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  18.  32
    First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation.Umberto Grandi & Ulle Endriss - 2013 - Journal of Philosophical Logic 42 (4):595-618.
    In preference aggregation a set of individuals express preferences over a set of alternatives, and these preferences have to be aggregated into a collective preference. When preferences are represented as orders, aggregation procedures are called social welfare functions. Classical results in social choice theory state that it is impossible to aggregate the preferences of a set of individuals under different natural sets of axiomatic conditions. We define a first-order language for social welfare functions and we give a complete axiomatisation (...)
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  19.  16
    Sperner Spaces and First‐Order Logic.Andreas Blass & Victor Pambuccian - 2003 - Mathematical Logic Quarterly 49 (2):111-114.
    We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ∞ω-axiomatizable. We also axiomatize the first-order theory of this class.
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  20. A Philosophical Companion to First-Order Logic.R. I. G. Hughes (ed.) - 1993 - Hackett Publishing Company.
    This volume of recent writings, some previously unpublished, follows the sequence of a typical intermediate or upper-level logic course and allows teachers to enrich their presentations of formal methods and results with readings on corresponding questions in philosophical logic.
     
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  21.  52
    First-Order Logic: An Introduction.Leigh S. Cauman - 1998 - De Gruyter.
    Introduction This is an elementary logic book designed for people who have no technical familiarity with modern logic but who have been reasoning, ...
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  22.  80
    Metalogic: An Introduction to the Metatheory of Standard First Order Logic.Geoffrey Hunter - 1971 - Berkeley: University of California Press.
    This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard (i.e., basically ...
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  23. The Language of First-Order Logic Including the Program Tarski's World.Jon Barwise & John Etchemendy - 1990
     
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  24. The Language of First-Order Logic Including the Ibm-Compatible Windows Version of Tarski's World 4.0.Jon Barwise & John Etchemendy - 1992
     
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  25. The Language of First-Order Logic Including the Macintosh Version of Tarski's World 4.0.Jon Barwise & John Etchemendy - 1993
     
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  26. First-Order Logic a Concise Introduction.John Heil - 1994
     
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  27. First-Order Logic Revisited.Vincent F. Hendricks (ed.) - 2004 - Logos.
  28.  4
    Recursive Complexity of the Carnap First Order Modal Logic C.Amélie Gheerbrant & Marcin Mostowski - 2006 - Mathematical Logic Quarterly 52 (1):87-94.
    We consider first order modal logic C firstly defined by Carnap in “Meaning and Necessity” [1]. We prove elimination of nested modalities for this logic, which gives additionally the Skolem-Löwenheim theorem for C. We also evaluate the degree of unsolvability for C, by showing that it is exactly 0′. We compare this logic with the logics of Henkin quantifiers, Σ11 logic, and SO. We also shortly discuss properties of the logic C in finite models.
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  29.  8
    Investigations on Fragments of First Order Branching Temporal Logic.Montagna Franco, Pinna G. Michele & B. P. Tiezzi - 2002 - Mathematical Logic Quarterly 48 (1):51-62.
    We investigate axiomatizability of various fragments of first order computational tree logic showing that the fragments with the modal operator F are non axiomatizable. These results shows that the only axiomatizable fragment is the one with the modal operator next only.
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  30.  28
    BH-CIFOL: Case-Intensional First Order Logic.Nuel Belnap & Thomas Müller - 2013 - Journal of Philosophical Logic (2-3):1-32.
    This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that (...)
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  31. First-Order Logic, Second-Order Logic, and Completeness.Marcus Rossberg - 2004 - In Vincent Hendricks, Fabian Neuhaus, Stig Andur Pedersen, Uwe Scheffler & Heinrich Wansing (eds.), First-Order Logic Revisited. Logos. pp. 303-321.
    This paper investigates the claim that the second-order consequence relation is intractable because of the incompleteness result for SOL. The opponents’ claim is that SOL cannot be proper logic since it does not have a complete deductive system. I argue that the lack of a completeness theorem, despite being an interesting result, cannot be held against the status of SOL as a proper logic.
     
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  32.  1
    An Omitting Types Theorem for First Order Logic with Infinitary Relation Symbols.Tarek Sayed Ahmed & Basim Samir - 2007 - Mathematical Logic Quarterly 53 (6):564-570.
    In this paper, an extension of first order logic is introduced. In such logics atomic formulas may have infinite lengths. An Omitting Types Theorem is proved.
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  33.  1
    Weakly Representable Atom Structures That Are Not Strongly Representable, with an Application to First Order Logic.Tarek Sayed Ahmed - 2008 - Mathematical Logic Quarterly 54 (3):294-306.
    Letn > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given.
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  34.  27
    Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information.Pietro Galliani & Allen L. Mann - 2013 - Studia Logica 101 (2):293-322.
    We present a compositional semantics for first-order logic with imperfect information that is equivalent to Sevenster and Sandu’s equilibrium semantics (under which the truth value of a sentence in a finite model is equal to the minimax value of its semantic game). Our semantics is a generalization of an earlier semantics developed by the first author that was based on behavioral strategies, rather than mixed strategies.
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  35.  78
    Loosely Guarded Fragment of First-Order Logic has the Finite Model Property.Ian Hodkinson - 2002 - Studia Logica 70 (2):205 - 240.
    We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic.
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  36.  1
    Loosely Guarded Fragment of First-Order Logic has the Finite Model Property.Ian Hodkinson - 2002 - Studia Logica 70 (2):205-240.
    We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic.
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  37.  27
    On the Decision Problem for Two-Variable First-Order Logic.Erich Grädel, Phokion G. Kolaitis & Moshe Y. Vardi - 1997 - Bulletin of Symbolic Logic 3 (1):53-69.
    We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it (...)
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  38.  79
    Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory.Gregory H. Moore - 1980 - History and Philosophy of Logic 1 (1-2):95-137.
    What has been the historical relationship between set theory and logic? On the one hand, Zermelo and other mathematicians developed set theory as a Hilbert-style axiomatic system. On the other hand, set theory influenced logic by suggesting to Schröder, Löwenheim and others the use of infinitely long expressions. The questions of which logic was appropriate for set theory - first-order logic, second-order logic, or an infinitary logic - culminated in a vigorous exchange between (...)
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  39.  21
    The Relevant Fragment of First Order Logic.Guillermo Badia - forthcoming - Review of Symbolic Logic:1-24.
    Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.
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  40.  57
    Idealization in Applied First-Order Logic.Ernest W. Adams - 1998 - Synthese 117 (3):331-354.
    Applying first-order logic to derive the consequences of laws that are only approximately true of empirical phenomena involves idealization of a kind that is akin to applying arithmetic to calculate the area of a rectangular surface from approximate measures of the lengths of its sides. Errors in the data, in the exactness of the lengths in one case and in the exactness of the laws in the other, are in some measure transmitted to the consequences deduced from them, (...)
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  41.  13
    Completeness and Decidability of General First-Order Logic.Antonelli Aldo - 2017 - Journal of Philosophical Logic 46 (3):233-257.
    This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.
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  42.  16
    Continuous First Order Logic for Unbounded Metric Structures.Itaï Ben Yaacov - 2008 - Journal of Mathematical Logic 8 (2):197-223.
    We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with results (...)
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  43.  1
    An Interpolation Theorem for First Order Logic with Infinitary Predicates.Tarek Sayed-Ahmed - 2006 - Logic Journal of the IGPL 15 (1):21-32.
    An interpolation Theorem is proved for first order logic with infinitary predicates. Our proof is algebraic via cylindric algebras.1.
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  44.  14
    Possible World Semantics for First-Order Logic of Proofs.Melvin Fitting - 2014 - Annals of Pure and Applied Logic 165 (1):225-240.
    In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an (...)
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  45. Establishing Connections Between Aristotle's Natural Deduction and First-Order Logic.Edgar Jose Andrade & Edward Samuel Becerra - 2008 - History and Philosophy of Logic 29 (4):309-325.
    This article studies the mathematical properties of two systems that model Aristotle's original syllogistic and the relationship obtaining between them. These systems are Corcoran's natural deduction syllogistic and ?ukasiewicz's axiomatization of the syllogistic. We show that by translating the former into a first-order theory, which we call T RD, we can establish a precise relationship between the two systems. We prove within the framework of first-order logic a number of logical properties about T RD that bear upon (...)
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  46.  11
    A Proof of Completeness for Continuous First-Order Logic.Itaï Ben Yaacov & Arthur Paul Pedersen - 2010 - Journal of Symbolic Logic 75 (1):168-190.
    Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of "algebraic" structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? The (...)
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  47.  26
    Tractarian First-Order Logic: Identity and the N-Operator.Brian Rogers & Kaif Wehmeier - 2012 - Review of Symbolic Logic 5 (4):538-573.
    In the Tractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work (...)
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  48. Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables.Maarten Marx & Szabolcs Mikulás - 1999 - Journal of Symbolic Logic 64 (4):1563-1572.
    The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on (...)
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  49.  11
    Deciding Regular Grammar Logics with Converse Through First-Order Logic.Stéphane Demri & Hans De Nivelle - 2005 - Journal of Logic, Language and Information 14 (3):289-329.
    We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide (...)
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  50.  21
    Taming First-Order Logic.Szabolcs Mikulás - 1998 - Logic Journal of the IGPL 6 (2):305-316.
    In this paper we define computationally well-behaved versions of classical first-order logic and prove that the validity problem is decidable.
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