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  1. Second-Order Logic And Foundations Of Mathematics."Anen Jouko V. "A. "An - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.
  2. Proving Theorems of the Second Order Lambek Calculus in Polynomial Time.Erik Aarts - 1994 - Studia Logica 53 (3):373 - 387.
    In the Lambek calculus of order 2 we allow only sequents in which the depth of nesting of implications is limited to 2. We prove that the decision problem of provability in the calculus can be solved in time polynomial in the length of the sequent. A normal form for proofs of second order sequents is defined. It is shown that for every proof there is a normal form proof with the same axioms. With this normal form we can give (...)
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  3. Induction and Inductive Definitions in Fragments of Second Order Arithmetic.Klaus Aehlig - 2005 - Journal of Symbolic Logic 70 (4):1087 - 1107.
    A fragment with the same provably recursive functions as n iterated inductive definitions is obtained by restricting second order arithmetic in the following way. The underlying language allows only up to n + 1 nested second order quantifications and those are in such a way, that no second order variable occurs free in the scope of another second order quantifier. The amount of induction on arithmetical formulae only affects the arithmetical consequences of these theories, whereas adding induction for arbitrary formulae (...)
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  4. Quantified Coalition Logic.Ågotnes Thomas, Hoek Wiebe van der & Wooldridge Michael - 2008 - Synthese 165 (2):269 - 294.
    We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as "every coalition satisfying property P can achieve φ" and "there exists a coalition C satisfying property P such that C can achieve φ". We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is (...)
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  5. Formalization of Reliability Block Diagrams in Higher-Order Logic.Waqar Ahmed, Osman Hasan & Sofiène Tahar - 2016 - Journal of Applied Logic 18:19-41.
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  6. Conservations of First-Order Reflections.Toshiyasu Arai - 2014 - Journal of Symbolic Logic 79 (3):814-825.
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  7. The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - forthcoming - Philosophical and Phenomenological Research.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...)
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  8. A Single Primitive Trope Relation.John Bacon - 1989 - Journal of Philosophical Logic 18 (2):141 - 154.
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  9. An Arithmetical View to First-Order Logic.Seyed Mohammad Bagheri, Bruno Poizat & Massoud Pourmahdian - 2010 - Annals of Pure and Applied Logic 161 (6):745-755.
    A value space is a topological algebra equipped with a non-empty family of continuous quantifiers . We will describe first-order logic on the basis of . Operations of are used as connectives and its relations are used to define statements. We prove under some normality conditions on the value space that any theory in the new setting can be represented by a classical first-order theory.
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  10. Independence in Higher-Order Subclassical Logic.David Ballard - 1985 - Notre Dame Journal of Formal Logic 26 (4):444-454.
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  11. Instituciones y heterogeindad.Jesús Alcolea Banegas - 1992 - Theoria 7 (1/2/3):65-85.
    The paper presents and discusses an example, namely a version of heterogeneous frrst-order logic and uses the classical theorem of Herbrand-Schmidt-Wang about the reduction of heterogeneous first-order logic to homogeneous first-order logic, in order to obtain two transformations between heterogeneous and homogeneous frrst-order logic which are different from the institution morphisms defined by Goguen and Burstall. Moreover, by considering a type of 2-cell among institution morphisms it is obtained a 2-category and also a 2-functor from this to another 2-category.
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  12. First-Order Logic.Jon Barwise - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co..
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  13. First-Order Logic, de RM Smullyan.R. Beneyto - 1971 - Teorema: International Journal of Philosophy 1 (3):136-138.
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  14. Comparing Approaches to Resolution Based Higher-Order Theorem Proving.Christoph Benzmüller - 2002 - Synthese 133 (1-2):203 - 235.
    We investigate several approaches to resolution based automated theoremproving in classical higher-order logic (based on Church's simply typed-calculus) and discuss their requirements with respect to Henkincompleteness and full extensionality. In particular we focus on Andrews'higher-order resolution (Andrews 1971), Huet's constrained resolution (Huet1972), higher-order E-resolution, and extensional higher-order resolution(Benzmüller and Kohlhase 1997). With the help of examples we illustratethe parallels and differences of the extensionality treatment of these approachesand demonstrate that extensional higher-order resolution is the sole approach thatcan completely avoid additional (...)
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  15. Higher-Order Semantics and Extensionality.Christoph Benzmüller, Chad E. Brown & Michael Kohlhase - 2004 - Journal of Symbolic Logic 69 (4):1027 - 1088.
    In this paper we re-examine the semantics of classical higher-order logic with the purpose of clarifying the role of extensionality. To reach this goal, we distinguish nine classes of higher-order models with respect to various combinations of Boolean extensionality and three forms of functional extensionality. Furthermore, we develop a methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of (machine-oriented) higher-order calculi with respect to these model classes.
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  16. Order.Michael Berrill - 1966 - Perspectives in Biology and Medicine 9 (4):515-522.
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  17. Alphabetical Order.George Boolos - 1988 - Notre Dame Journal of Formal Logic 29 (2):214-215.
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  18. Review: Johan van Benthem, Kees Doets, Higher-Order Logic. [REVIEW]Kim Bruce - 1989 - Journal of Symbolic Logic 54 (3):1090-1092.
  19. Review: Stewart Shapiro, Foundations Without Foundationalism. A Case for Second-Order Logic. [REVIEW]John Burgess - 1993 - Journal of Symbolic Logic 58 (1):363-365.
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  20. Krom MR. Separation Principles in the Hierarchy Theory of Pure First-Order Logic.D. A. Clarke - 1996 - Journal of Symbolic Logic 31 (3):503-504.
  21. Review: M. R. Krom, Separation Principles in the Hierarchy Theory of Pure First-Order Logic. [REVIEW]D. A. Clarke - 1966 - Journal of Symbolic Logic 31 (3):503-504.
  22. Separation Principles in the Hierarchy Theory of Pure First-Order Logic.D. A. Clarke & M. R. Krom - 1966 - Journal of Symbolic Logic 31 (3):503.
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  23. Information Recovery Problems.John Corcoran - 1995 - Theoria 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
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  24. Circle Graphs and Monadic Second-Order Logic.Bruno Courcelle - 2008 - Journal of Applied Logic 6 (3):416-442.
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  25. The Monadic Second-Order Logic of Graphs XV: On a Conjecture by D. Seese.Bruno Courcelle - 2006 - Journal of Applied Logic 4 (1):79-114.
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  26. Monadic Second-Order Logic, Graph Coverings and Unfoldings of Transition Systems.Bruno Courcelle & Igor Walukiewicz - 1998 - Annals of Pure and Applied Logic 92 (1):35-62.
    We prove that every monadic second-order property of the unfolding of a transition system is a monadic second-order property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for one of them but not for the other.
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  27. N-Th Order Logic.Ciro de Florio - unknown
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  28. N-Order, Logic.Ciro de Florio - unknown
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  29. Geometrisation of First-Order Logic.Roy Dyckhoff & Sara Negri - 2015 - Bulletin of Symbolic Logic 21 (2):123-163.
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  30. First‐Order Logic.Roger Fellows - 1996 - Philosophical Books 37 (4):284-286.
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  31. 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 logic. We emphasize that (...)
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  32. The Complexity of First-Order and Monadic Second-Order Logic Revisited.Markus Frick & Martin Grohe - 2004 - Annals of Pure and Applied Logic 130 (1-3):3-31.
    The model-checking problem for a logic L on a class C of structures asks whether a given L-sentence holds in a given structure in C. In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic. We show that unless PTIME=NP, the model-checking problem for monadic second-order logic on finite words is not solvable in time f·p, for any elementary function f and any polynomial p. Here k denotes the size of the (...)
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  33. Spectra of Formulae with Henkin Quantifiers.Joanna Golińska & Konrad Zdanowski - 2003 - In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers. pp. 29--45.
    It is known that various complexity-theoretical problems can be translated into some special spectra problems (see e.g. Fagin [Fa74] or Blass and Gurevich, [Bl-Gu86]). So questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quanti fiers in the empty vocabulary. This problem has been investigated fi rstly by Krynicki and Mostowski in [Kr-Mo 92] and [Kr- Mo 95]. All presented results can be (...)
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  34. First Order Mathematical Logic. [REVIEW]P. K. H. - 1968 - Review of Metaphysics 21 (3):556-556.
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  35. Characterizing Second Order Logic with First Order Quantifiers.David Harel - 1979 - Mathematical Logic Quarterly 25 (25‐29):419-422.
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  36. First-Order Logic a Concise Introduction.John Heil - 1994
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  37. Review: Stewart Shapiro, Second-Order Languages and Mathematical Practice. [REVIEW]Geoffrey Hellman - 1989 - Journal of Symbolic Logic 54 (1):291-293.
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  38. Shapiro Stewart. Second-Order Languages and Mathematical Practice.Geoffrey Hellman - 1989 - Journal of Symbolic Logic 54 (1):291-293.
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  39. CERES in Higher-Order Logic.Stefan Hetzl, Alexander Leitsch & Daniel Weller - 2011 - Annals of Pure and Applied Logic 162 (12):1001-1034.
    We define a generalization of the first-order cut-elimination method CERES to higher-order logic. At the core of lies the computation of an set of sequents from a proof π of a sequent S. A refutation of in a higher-order resolution calculus can be used to transform cut-free parts of π into a cut-free proof of S. An example illustrates the method and shows that can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.
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  40. On Logic and Order in the Sciences.Jeremy Horne (ed.) - forthcoming
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  41. 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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  42. On Second-Order Characterizability.T. Hyttinen, K. Kangas & J. Vaananen - 2013 - Logic Journal of the IGPL 21 (5):767-787.
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  43. Lógica Y Ontología.Ignacio Jané - 1988 - Theoria 4 (1):81-106.
    In this paper we discuss the way logical consequence depends on what sets there are. We try to find out what set-theoretical assumptions have to be made to determine a logic, i.e., to give a definite answer to whether any given argument is correct. Consideration of second order logic -which is left highly indetermined by the usual set-theoretical axioms- prompts us to suggest a slightly different but natural nation of logical consequence, which reduces second order logic indeterminacy without interfering with (...)
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  44. Nominalist Realism.Nicholas K. Jones - 2017 - Noûs.
    This paper explores the impact of quantification into predicate position on the metaphysics of properties, arguing that two familiar debates about properties are fundamentally altered by recasting them in a second-order setting. Two theories of properties are outlined, differing over whether the existence of properties is expressed using first-order or second-order quantifiers. It is argued that the second-order theory: provides good reason to regard debate about the locations of properties as contentless; resolves debate about whether properties are particulars or universals (...)
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  45. A Higher-Order Solution to the Problem of the Concept Horse.Nicholas K. Jones - 2016 - Ergo, an Open Access Journal of Philosophy 3.
    This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.
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  46. Separation Principles in the Hierarchy Theory of Pure First-Order Logic.M. R. Krom - 1963 - Journal of Symbolic Logic 28 (3):222-236.
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  47. Random Graphs in the Monadic Theory of Order.Shmuel Lifsches & Saharon Shelah - 1999 - Archive for Mathematical Logic 38 (4-5):273-312.
    We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line).
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  48. The Monadic Theory of (Ω 2, <) May Be Complicated.Shmuel Lifsches & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):207-213.
    Assume ZFC is consistent then for everyB⫅ω there is a generic extension of the ground world whereB is recursive in the monadic theory ofω 2.
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  49. Review: Angelo Margaris, First Order Mathematical Logic. [REVIEW]A. H. Lighstone - 1972 - Journal of Symbolic Logic 37 (3):616-616.
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  50. Margaris Angelo. First Order Mathematical Logic. Blaisdell Publishing Company, Waltham, Massachusetts, Toronto, and London, 1967, X + 211 Pp. [REVIEW]A. H. Lightstone - 1972 - Journal of Symbolic Logic 37 (3):616.
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