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

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  1. 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.score: 729.0
    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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  2. Savas Konur (2011). An Event-Based Fragment of First-Order Logic Over Intervals. Journal of Logic, Language and Information 20 (1):49-68.score: 729.0
    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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  3. George Voutsadakis (2005). Categorical Abstract Algebraic Logic Categorical Algebraization of First-Order Logic Without Terms. Archive for Mathematical Logic 44 (4):473-491.score: 729.0
    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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  4. María Manzano (1996). Extensions of First Order Logic. Cambridge University Press.score: 720.0
    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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  5. Richard Moot & Mario Piazza (2001). Linguistic Applications of First Order Intuitionistic Linear Logic. Journal of Logic, Language and Information 10 (2):211-232.score: 711.0
    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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  6. Yannis Stephanou (2005). First-Order Modal Logic with an 'Actually' Operator. Notre Dame Journal of Formal Logic 46 (4):381-405.score: 705.0
    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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  7. Torben BraÜner (2005). Natural Deduction for First-Order Hybrid Logic. Journal of Logic, Language and Information 14 (2):173-198.score: 705.0
    This is a companion paper to Braüner (2004b, Journal of Logic and Computation 14, 329–353) 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 (...)
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  8. Angelo Margaris (1967/1990). First Order Mathematical Logic. Dover Publications.score: 702.0
    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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  9. Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.score: 696.0
    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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  10. Horacio Arlo-Costa & Eric Pacuit, First Order Classical Modal Logic.score: 696.0
    This 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.
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  11. Umberto Grandi & Ulle Endriss (2013). First-Order Logic Formalisation of Impossibility Theorems in Preference Aggregation. Journal of Philosophical Logic 42 (4):595-618.score: 681.0
    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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  12. Leigh S. Cauman (1998). First-Order Logic: An Introduction. Walter De Gruyter.score: 639.0
    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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  13. George Tourlakis (2010). On the Proof-Theory of Two Formalisations of Modal First-Order Logic. Studia Logica 96 (3):349-373.score: 639.0
    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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  14. Andreas Blass & Victor Pambuccian (2003). Sperner Spaces and First‐Order Logic. Mathematical Logic Quarterly 49 (2):111-114.score: 639.0
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  15. Geoffrey Hunter (1971). Metalogic: An Introduction to the Metatheory of Standard First Order Logic. Berkeley,University of California Press.score: 630.0
    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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  16. Raymond M. Smullyan (1968). First-Order Logic. New York [Etc.]Springer-Verlag.score: 630.0
    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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  17. Vincent F. Hendricks (ed.) (2004). First-Order Logic Revisited. Logos.score: 630.0
  18. 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.score: 576.0
    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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  19. Petr Hájek & Franco Montagna (2008). A Note on the First‐Order Logic of Complete BL‐Chains. Mathematical Logic Quarterly 54 (4):435-446.score: 573.0
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  20. Nuel Belnap & Thomas Müller (2013). BH-CIFOL: Case-Intensional First Order Logic. Journal of Philosophical Logic (2-3):1-32.score: 567.0
    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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  21. Eli Dresner (2010). Logical Consequence and First-Order Soundness and Completeness: A Bottom Up Approach. Notre Dame Journal of Formal Logic 52 (1):75-93.score: 564.0
    What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logical consequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several of the (...)
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  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.score: 558.0
    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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  23. Stéphane Demri & Hans De Nivelle (2005). Deciding Regular Grammar Logics with Converse Through First-Order Logic. Journal of Logic, Language and Information 14 (3):289-329.score: 555.0
    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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  24. 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.score: 549.0
    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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  25. 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.score: 549.0
    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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  26. Grigori Mints (1993). Resolution Calculus for the First Order Linear Logic. Journal of Logic, Language and Information 2 (1):59-83.score: 549.0
    This paper presents a formulation and completeness proof of the resolution-type calculi for the first order fragment of Girard's linear logic by a general method which provides the general scheme of transforming a cutfree Gentzen-type system into a resolution type system, preserving the structure of derivations. This is a direct extension of the method introduced by Maslov for classical predicate logic. Ideas of the author and Zamov are used to avoid skolomization. Completeness of strategies is first established for (...)
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  27. Natasha Alechina (1995). On a Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic. Journal of Logic, Language and Information 4 (3):177-189.score: 549.0
    Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifierQ into a first-order language enriched with a family of predicatesR i, for every arityi (or an infinitary predicateR) which takesQxg(x, y1,..., yn) to x(R(x, y1,..., y1) (x,y1,...,yn)) (y 1,...,yn are precisely the free variables ofQx). The logic ofQ (without ordinary quantifiers) corresponds therefore to the fragment of first-order logic which contains only specially restricted quantification. We prove that it is decidable using the method (...)
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  28. Martin Otto (2000). Epsilon-Logic is More Expressive Than First-Order Logic Over Finite Structures. Journal of Symbolic Logic 65 (4):1749-1757.score: 549.0
    There are properties of finite structures that are expressible with the use of Hilbert's ε-operator in a manner that does not depend on the actual interpretation for ε-terms, but not expressible in plain first-order. This observation strengthens a corresponding result of Gurevich, concerning the invariant use of an auxiliary ordering in first-order logic over finite structures. The present result also implies that certain non-deterministic choice constructs, which have been considered in database theory, properly enhance the expressive power (...)
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  29. Brian Rogers & Kaif Wehmeier (2012). Tractarian First-Order Logic: Identity and the N-Operator. Review of Symbolic Logic 5 (4):538-573.score: 549.0
    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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  30. Itaï Ben Yaacov (2008). Continuous First Order Logic for Unbounded Metric Structures. Journal of Mathematical Logic 8 (02):197-223.score: 549.0
    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 (which has been the common approach so far to Banach space structures in continuous logic), as well as of applying in situations where the unit ball approach does not apply (i.e., when the unit ball is not a definable set). We also (...)
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  31. 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.score: 549.0
    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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  32. Martin Otto (2001). Two Variable First-Order Logic Over Ordered Domains. Journal of Symbolic Logic 66 (2):685-702.score: 549.0
    The satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively wellordered, domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems (...)
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  33. 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.score: 549.0
    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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  34. 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.score: 549.0
    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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  35. Merrie Bergmann (2005). Finite Tree Property for First-Order Logic with Identity and Functions. Notre Dame Journal of Formal Logic 46 (2):173-180.score: 549.0
    The typical rules for truth-trees for first-order logic without functions can fail to generate finite branches for formulas that have finite models–the rule set fails to have the finite tree property. In 1984 Boolos showed that a new rule set proposed by Burgess does have this property. In this paper we address a similar problem with the typical rule set for first-order logic with identity and functions, proposing a new rule set that does have the finite (...)
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  36. Itaï Ben Yaacov & Arthur Paul Pedersen (2010). A Proof of Completeness for Continuous First-Order Logic. Journal of Symbolic Logic 75 (1):168-190.score: 549.0
    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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  37. Benjamin Rossman (2007). Successor-Invariant First-Order Logic on Finite Structures. Journal of Symbolic Logic 72 (2):601-618.score: 549.0
    We consider successor-invariant first-order logic (FO + succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (.
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  38. Don H. Faust (1982). The Boolean Algebra of Formulas of First-Order Logic. Annals of Mathematical Logic 23 (1):27-53.score: 549.0
    The algebraic recursive structure of countable languages of classical first-order logic with equality is analysed. all languages of finite undecidable similarity type are shown to be algebraically and recursively equivalent in the following sense: their boolean algebras of formulas are, after trivial factors involving the one element models of the languages have been excepted, recursively isomorphic by a map which preserves the degree of recursiveness of their models.
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  39. 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.score: 549.0
    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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  40. Tarek Sayed Ahmed (2005). Omitting Types for Algebraizable Extensions of First Order Logic. Journal of Applied Non-Classical Logics 15 (4):465-489.score: 543.0
    We prove an Omitting Types Theorem for certain algebraizable extensions of first order logic without equality studied in [SAI 00] and [SAY 04]. This is done by proving a representation theorem preserving given countable sets of infinite meets for certain reducts of ?- dimensional polyadic algebras, the so-called G polyadic algebras (Theorem 5). Here G is a special subsemigroup of (?, ? o) that specifies the signature of the algebras in question. We state and prove an independence result connecting (...)
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  41. Shalom Lappin, An Expressive First-Order Logic with Flexible Typing for Natural Language Semantics.score: 540.0
    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.1 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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  42. Arthur Paul Pedersen & Itai Ben Yaacov, A Proof of Completeness for Continuous First-Order Logic.score: 540.0
    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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  43. Ernest W. Adams (1998). Idealization in Applied First-Order Logic. Synthese 117 (3):331-354.score: 540.0
    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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  44. Stephen K. McLeod (2011). First-Order Logic and Some Existential Sentences. Disputatio 4 (31):255-270.score: 540.0
    ‘Quantified pure existentials’ are sentences (e.g., ‘Some things do not exist’) which meet these conditions: (i) the verb EXIST is contained in, and is, apart from quantificational BE, the only full (as against auxiliary) verb in the sentence; (ii) no (other) logical predicate features in the sentence; (iii) no name or other sub-sentential referring expression features in the sentence; (iv) the sentence contains a quantifier that is not an occurrence of EXIST. Colin McGinn and Rod Girle have alleged that standard (...)
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  45. Ian Hodkinson (2002). Loosely Guarded Fragment of First-Order Logic has the Finite Model Property. Studia Logica 70 (2):205 - 240.score: 540.0
    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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  46. Jan van Eijck, About Testing and Specification . . . And About First Order Logic.score: 540.0
    to a number of issues related to testing and specification. Brief review of first order logic. Use of first order logic for specification, in the specification tool Alloy.
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  47. Nuel Belnap & Thomas Müller, CIFOL: Case-Intensional First Order Logic. (I) Toward a Theory of Sorts.score: 540.0
    This is Part I of a two-part essay introducing case-intensional first-order logic (CIFOL), an easy-to-use, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of Bressan’s General interpreted modal calculus (Yale University Press 1972). CIFOL starts with a set of cases; each expression has an extension in each case and an intension, which is the function from the cases to the respective case-relative extensions. Predication is intensional; identity (...)
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  48. Beomin Kim (2008). The Translation of First Order Logic Into Modal Predicate Logic. Proceedings of the Xxii World Congress of Philosophy 13:65-69.score: 540.0
    This paper deals with the translation of first order formulas to predicate S5 formulas. This translation does not bring the first order formula itself to a modal system, but modal interpretation of the first order formula can be given by the translation. Every formula can be translated, and the additional condition such as formula's having only one variable, or having both world domain and individual domain is not required. I introduce an indexical predicate 'E' for the translation. The meaning that (...)
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  49. Graham Priest (2011). First-Order da Costa Logic. Studia Logica 97 (1):183 - 198.score: 540.0
    Priest (2009) formulates a propositional logic which, by employing the worldsemantics for intuitionist logic, has the same positive part but dualises the negation, to produce a paraconsistent logic which it calls 'Da Costa Logic'. This paper extends matters to the first-order case. The paper establishes various connections between first order da Costa logic, da Costa's own Cω, and classical logic. Tableau and natural deductions systems are provided and proved sound and complete.
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  50. J. Wolenski (2004). First-Order Logic:(Philosophical) Pro and Contra. In Vincent F. Hendricks (ed.), First-Order Logic Revisited. Logos. 369--398.score: 540.0
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