Search results for 'First-order logic' (try it on Scholar)

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  1.  77
    Peter Fritz (forthcoming). First-Order Modal Logic in the Necessary Framework of Objects. Canadian Journal of Philosophy:1-26.
    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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  2.  17
    George Voutsadakis (2005). Categorical Abstract Algebraic Logic Categorical Algebraization of First-Order Logic Without Terms. 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.  26
    Claes Strannegård, Fredrik Engström, Abdul Rahim Nizamani & Lance Rips (2013). Reasoning About Truth in First-Order Logic. 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
    Savas Konur (2011). An Event-Based Fragment of First-Order Logic Over Intervals. 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.  3
    Piotr BLaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry (2016). Is Leibnizian Calculus Embeddable in First Order Logic? 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.  50
    María Manzano (1996). Extensions of First Order Logic. 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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  7.  8
    Rodrigo A. Freire (2015). First-Order Logic and First-Order Functions. 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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  8.  1
    Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry (forthcoming). Is Leibnizian Calculus Embeddable in First Order Logic? 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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  9. Rutger Kuyper (2015). First-Order Logic in the Medvedev Lattice. 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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  10.  27
    Richard Moot & Mario Piazza (2001). Linguistic Applications of First Order Intuitionistic Linear Logic. 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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  11.  42
    Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. 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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  12.  18
    Yannis Stephanou (2005). First-Order Modal Logic with an 'Actually' Operator. 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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  13.  24
    Angelo Margaris (1967). First Order Mathematical Logic. 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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  14.  46
    Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. 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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  15.  3
    Victor N. Krivtsov (2015). Semantical Completeness of First-Order Predicate Logic and the Weak Fan Theorem. 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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  16.  30
    Umberto Grandi & Ulle Endriss (2013). First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation. 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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  17.  10
    Andreas Blass & Victor Pambuccian (2003). Sperner Spaces and First‐Order Logic. 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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  18.  31
    Raymond M. Smullyan (1968). First-Order Logic. 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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  19.  36
    George Tourlakis (2010). On the Proof-Theory of Two Formalisations of Modal First-Order Logic. Studia Logica 96 (3):349-373.
    We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.
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  20.  41
    Leigh S. Cauman (1998). First-Order Logic: An Introduction. Walter 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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  21.  68
    Geoffrey Hunter (1971). Metalogic: An Introduction to the Metatheory of Standard First Order Logic. 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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  22. R. I. G. Hughes (1993). A Philosophical Companion to First-Order Logic. Monograph Collection (Matt - Pseudo).
     
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  23. Jon Barwise & John Etchemendy (1990). The Language of First-Order Logic Including the Program Tarski's World. Monograph Collection (Matt - Pseudo).
     
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  24. Jon Barwise & John Etchemendy (1992). The Language of First-Order Logic Including the Ibm-Compatible Windows Version of Tarski's World 4.0. Monograph Collection (Matt - Pseudo).
     
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  25. Jon Barwise & John Etchemendy (1993). The Language of First-Order Logic Including the Macintosh Version of Tarski's World 4.0. Monograph Collection (Matt - Pseudo).
     
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  26. John Heil (1994). First-Order Logic a Concise Introduction. Monograph Collection (Matt - Pseudo).
     
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  27. Vincent F. Hendricks (ed.) (2004). First-Order Logic Revisited. Logos.
  28.  4
    Amélie Gheerbrant & Marcin Mostowski (2006). Recursive Complexity of the Carnap First Order Modal Logic C. 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.  3
    Franco Montagna, G. Michele Pinna & B. P. Tiezzi (2002). Investigations on Fragments of First Order Branching Temporal Logic. 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. Marcus Rossberg (2004). First-Order Logic, Second-Order Logic, and Completeness. In Vincent Hendricks, Fabian Neuhaus, Stig Andur Pedersen, Uwe Scheffler & Heinrich Wansing (eds.), First-Order Logic Revisited. Logos 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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  31.  24
    Nuel Belnap & Thomas Müller (2013). BH-CIFOL: Case-Intensional First Order Logic. 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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  32. Tarek Sayed Ahmed & Basim Samir (2007). An Omitting Types Theorem for First Order Logic with Infinitary Relation Symbols. 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. Tarek Sayed Ahmed (2008). Weakly Representable Atom Structures That Are Not Strongly Representable, with an Application to First Order Logic. 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.  75
    Ian Hodkinson (2002). Loosely Guarded Fragment of First-Order Logic has the Finite Model Property. 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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  35.  22
    Pietro Galliani & Allen L. Mann (2013). Lottery Semantics: A Compositional Semantics for Probabilistic First-Order Logic with Imperfect Information. 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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  36.  29
    Ernest W. Adams (1998). Idealization in Applied First-Order Logic. 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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  37. Maarten Marx & Szabolcs Mikulás (1999). Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables. 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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  38.  12
    Guillermo Badia (forthcoming). The Relevant Fragment of First Order Logic. 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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  39.  23
    Erich Grädel, Phokion G. Kolaitis & Moshe Y. Vardi (1997). On the Decision Problem for Two-Variable First-Order Logic. 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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  40.  65
    Gregory H. Moore (1980). Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory. 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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  41. Edgar Jose Andrade & Edward Samuel Becerra (2008). Establishing Connections Between Aristotle's Natural Deduction and First-Order Logic. 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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  42.  18
    Szabolcs Mikulás (1998). Taming First-Order Logic. 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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  43. John Corcoran (2001). Second-Order Logic. In M. Zeleny (ed.), Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. KLUKER 61–76.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of (...)
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  44. Tarek Sayed-Ahmed (2007). An Interpolation Theorem for First Order Logic with Infinitary Predicates. 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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  45.  12
    Samuel R. Buss & Alan S. Johnson (2010). The Quantifier Complexity of Polynomial‐Size Iterated Definitions in First‐Order Logic. Mathematical Logic Quarterly 56 (6):573-590.
    We refine the constructions of Ferrante-Rackoff and Solovay on iterated definitions in first-order logic and their expressibility with polynomial size formulas. These constructions introduce additional quantifiers; however, we show that these extra quantifiers range over only finite sets and can be eliminated. We prove optimal upper and lower bounds on the quantifier complexity of polynomial size formulas obtained from the iterated definitions. In the quantifier-free case and in the case of purely existential or universal quantifiers, we show that (...)
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  46.  23
    Brian Rogers & Kaif Wehmeier (2012). Tractarian First-Order Logic: Identity and the N-Operator. 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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  47.  16
    Itaï Ben Yaacov (2008). Continuous First Order Logic for Unbounded Metric Structures. 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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  48.  16
    Emanuel Kieroński & Martin Otto (2012). Small Substructures and Decidability Issues for First-Order Logic with Two Variables. Journal of Symbolic Logic 77 (3):729-765.
    We study first-order logic with two variables FO² and establish a small substructure property. Similar to the small model property for FO² we obtain an exponential size bound on embedded substructures, relative to a fixed surrounding structure that may be infinite. We apply this technique to analyse the satisfiability problem for FO² under constraints that require several binary relations to be interpreted as equivalence relations. With a single equivalence relation, FO² has the finite model property and is complete (...)
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  49.  7
    Robert Constable & Mark Bickford (2014). Intuitionistic Completeness of First-Order Logic. Annals of Pure and Applied Logic 165 (1):164-198.
    We constructively prove completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable in iFOL if and only if it is uniformly valid in intuitionistic evidence semantics as defined in intuitionistic type theory extended with an intersection operator.Our completeness proof provides an effective procedure that converts any uniform evidence into a formal iFOL proof. Uniform evidence can involve arbitrary concepts from type theory such as ordinals, topological structures, algebras and so forth. We have implemented that procedure (...)
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  50.  31
    Chris Fox & Shalom Lappin (2004). An Expressive First-Order Logic with Flexible Typing for Natural Language Semantics. Logic Journal of the Interest Group in Pure and Applied Logics 12 (2):135--168.
    We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like “most.” We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous type-theoretic (...)
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