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  1. C. Anthony Anderson & Michael Zelëny (eds.) (2001). Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Kluwer.
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  2. Itaï Ben Yaacov (2008). Topometric Spaces and Perturbations of Metric Structures. Logic and Analysis 1 (3-4):235-272.
    We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math Soc, (...)
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  3. Imme P. Berg (2008). Asymptotics of Families of Solutions of Nonlinear Difference Equations. Logic and Analysis 1 (2):153-185.
    One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.
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  4. Lars Brünjes & Christian Serpé (2007). Enlargements of Schemes. Logic and Analysis 1 (1):1-60.
    In this article we use our previous constructions (L. Brünjes, C. Serpé, Theory Appl. Categ. 14:357–398, 2005) to lay down some foundations for the application of A. Robinson’s nonstandard methods to modern algebraic geometry. The main motivation is the search for another tool to transfer results from characteristic zero to positive characteristic and vice versa. We give applications to the resolution of singularities and weak factorization.
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  5. Andrea Cantini (1996). Logical Frameworks for Truth and Abstraction: An Axiomatic Study. Elsevier Science B.V..
    This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these (...)
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  6. Mannis Charosh (1974). Number Ideas Through Pictures. New York,T. Y. Crowell.
  7. C.-T. Chong & M. J. Wicks (eds.) (1983). Southeast Asian Conference on Logic: Proceedings of the Logic Conference, Singapore, 1981. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
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  8. Arkadiusz Chrudzimski (2013). Gestalt, Equivalency, and Functional Dependency. Kurt Grelling’s Formal Ontology. In Nikolay Milkov & Volker Peckhaus (eds.), The Berlin Group and the Philosophy of Logical Empiricism. Springer. 245--261.
    In his ontological works Kurt Grelling tries to give a rigorous analysis of the foundations of the so-called Gestalt-psychology. Gestalten are peculiar emergent qualities, ontologically dependent on their foundations, but nonetheless non reducible to them. Grelling shows that this concept, as used in psychology and ontology, is often ambiguous. He distinguishes two important meanings in which the word “Gestalt” is used: Gestalten as structural aspects available to transposition and Gestalten as causally self-regulating wholes. Gestalten in the first meaning are, according (...)
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  9. Arkadiusz Chrudzimski (2006). The Young Leśniewski on Existential Propositions. In Arkadiusz Chrudzimski & Dariusz Łukasiewicz (eds.), Actions, Products, and Things: Brentano and Polish Philosophy. Ontos.
    It was one of Brentano’s central ideas that all judgements are at bottom existential. In his Psychology from an Empirical Standpoint he tried to show how all traditionally acknowledged judgement forms could be reinterpreted as existential statements. Existential propositions, therefore, were a central concern for the whole Brentano School. Kazimierz Twardowski, who also accepted this program, introduced the problem of the existential reduction to his Polish students, but not all of them found this idea plausible. In 1911 Stanisław Leśniewski published (...)
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  10. Arkadiusz Chrudzimski (2005). Drei Versionen der Meinongschen Logik. Zeitschrift für Philosophische Forschung 59 (1):49-70.
    Alexius Meinong nimmt in der Geschichte der Ontologie eine ausgezeichnete Stellung ein. Er war der erste Philosoph, der in systematischer Weise eine quasi-onto¬logische Disziplin entwickelte, die im Vergleich zu der Disziplin, die man traditionell Metaphysik oder Ontologie nennt, viel allgemeiner sein sollte. Die Metaphysik untersucht das Seiende als Seiendes, und die seienden Entitäten bilden – so die These Meinongs – nur ein kleines Fragment dessen, was man unter dem Namen „Gegenstands¬theorie” untersuchen kann. Die Gegenstände als solche sind „außerseiend”, d.h. sie (...)
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  11. Roberto Cignoli (1999). Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers.
    This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as (...)
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  12. Nigel Cutland (2008). Introducing. Logic and Analysis 1 (1).
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  13. Nigel Cutland (2007). Introducing Logic and Analysis. Logic and Analysis 1 (1).
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  14. J. Dunn & A. Gupta (eds.) (1990). Truth or Consequences. Kluwer.
    This collection of essays was compiled for the occasion of Nuel Belnap's 60th birthday.
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  15. D. J. Foulis & C. H. Randall (1974). Empirical Logic and Quantum Mechanics. Synthese 29 (1-4):81 - 111.
  16. Harold T. Hodes (1984). The Modal Theory of Pure Identity and Some Related Decision Problems. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (26‐29):415-423.
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  17. Renling Jin (2007). Inverse Problem for Cuts. Logic and Analysis 1 (1):61-89.
    Let U be an initial segment of $^*{\mathbb N}$ closed under addition (such U is called a cut) with uncountable cofinality and A be a subset of U, which is the intersection of U and an internal subset of $^*{\mathbb N}$ . Suppose A has lower U-density α strictly between 0 and 3/5. We show that either there exists a standard real $\epsilon$ > 0 and there are sufficiently large x in A such that | (A+A) ∩ [0, 2x]| > (...)
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  18. Tom Lindstrøm (2008). Nonlinear Stochastic Integrals for Hyperfinite Lévy Processes. Logic and Analysis 1 (2):91-129.
    I develop a notion of nonlinear stochastic integrals for hyperfinite Lévy processes and use it to find exact formulas for expressions which are intuitively of the form $\sum_{s=0}^t\phi(\omega,dl_{s},s)$ and $\prod_{s=0}^t\psi(\omega,dl_{s},s)$ , where l is a Lévy process. These formulas are then applied to geometric Lévy processes, infinitesimal transformations of hyperfinite Lévy processes, and to minimal martingale measures. Some of the central concepts and results are closely related to those found in S. Cohen’s work on stochastic calculus for processes with jumps (...)
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  19. Robert S. Lubarsky & Michael Rathjen (2008). On the Constructive Dedekind Reals. Logic and Analysis 1 (2):131-152.
    In order to build the collection of Cauchy reals as a set in constructive set theory, the only power set-like principle needed is exponentiation. In contrast, the proof that the Dedekind reals form a set has seemed to require more than that. The main purpose here is to show that exponentiation alone does not suffice for the latter, by furnishing a Kripke model of constructive set theory, Constructive Zermelo–Fraenkel set theory with subset collection replaced by exponentiation, in which the Cauchy (...)
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  20. Ewa Orlowska & Joanna Golinska-Pilarek (2011). Dual Tableaux: Foundations, Methodology, Case Studies. Springer.
    The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that the corresponding dual tableaux are built in a (...)
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  21. A. Prestel (2011). Mathematical Logic and Model Theory: A Brief Introduction. Springer.
    Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic ...
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  22. M. Rathjen & R. S. Lubarsky (2008). On the Constructive Dedekind Reals. Logic and Analysis 1 (1):131-152.
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  23. Tamara Servi (2008). Noetherian Varieties in Definably Complete Structures. Logic and Analysis 1 (3-4):187-204.
    We prove that the zero-set of a C ∞ function belonging to a noetherian differential ring M can be written as a finite union of C ∞ manifolds which are definable by functions from the same ring. These manifolds can be taken to be connected under the additional assumption that every zero-dimensional regular zero-set of functions in M consists of finitely many points. These results hold not only for C ∞ functions over the reals, but more generally for definable C (...)
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  24. Stefan Themerson (1974). Logic, Labels, and Flesh. [London]Gaberbocchus.
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  25. Todor D. Todorov & Hans Vernaeve (2008). Full Algebra of Generalized Functions and Non-Standard Asymptotic Analysis. Logic and Analysis 1 (3-4):205-234.
    We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between (...)
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  26. Imme P. van den Berg (2008). Asymptotics of Families of Solutions of Nonlinear Difference Equations. Logic and Analysis 1 (2):153-185.
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  27. Itaï Ben Yaacov (2008). Topometric Spaces and Perturbations of Metric Structures. Logic and Analysis 1 (3-4):235-272.
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Classical Logic
  1. J. L. Bell (1993). Hilbert's Ɛ-Operator and Classical Logic. Journal of Philosophical Logic 22 (1):1 - 18.
  2. Jaroslav Peregrin, Is Propositional Calculus Categorical?
    According to the standard definition, a first-order theory is categorical if all its models are isomorphic. The idea behind this definition obviously is that of capturing semantic notions in axiomatic terms: to be categorical is to be, in this respect, successful. Thus, for example, we may want to axiomatically delimit the concept of natural number, as it is given by the pre-theoretic semantic intuitions and reconstructed by the standard model. The well-known results state that this cannot be done within first-order (...)
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  3. Henry Bradford Smith (1938). A First Book in Logic. New York, F.S. Crofts & Co..
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Aristotelian Logic
  1. Jason Aleksander (2004). Modern Paradoxes of Aristotle's Logic. Epoché: A Journal for the History of Philosophy 9 (1):79-99.
    This paper intends to explain key differences between Aristotle’s understanding of the relationships between nous, epistêmê, and the art of syllogistic reasoning(both analytic and dialectical) and the corresponding modern conceptions of intuition, knowledge, and reason. By uncovering paradoxa that Aristotle’s understanding of syllogistic reasoning presents in relation to modern philosophical conceptions of logic and science, I highlight problems of a shift in modern philosophy—a shift that occurs most dramatically in the seventeenth century—toward a project of construction, a pervasive desire for (...)
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  2. 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 the same properties (...)
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  3. Edgar Andrade-Lotero & Catarina Dutilh Novaes (2012). Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW] Journal of Philosophical Logic 41 (2):387-418.
    We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...)
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  4. Ignacio Angelelli (1978). Analytica Priora I, $38$ and Reduplication. [REVIEW] Notre Dame Journal of Formal Logic 19 (2):295-296.
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  5. R. B. Angell (1986). Truth-Functional Conditionals and Modern Vs. Traditional Syllogistic. Mind 95 (378):210-223.
  6. E. J. Ashworth (1970). Some Notes on Syllogistic in the Sixteenth and Seventeenth Centuries. Notre Dame Journal of Formal Logic 11 (1):17-33.
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  7. Allan Bäck (1995). Aristotelian Necessities. History and Philosophy of Logic 16 (1):89-106.
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  8. Allan Bäck (1982). Syllogisms with Reduplication in Aristotle. Notre Dame Journal of Formal Logic 23 (4):453-458.
  9. John Bacon (1967). Syllogistic Without Existence. Notre Dame Journal of Formal Logic 8 (3):195-219.
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  10. A. J. Baker (1972). Syllogistic with Complex Terms. Notre Dame Journal of Formal Logic 13 (1):69-87.
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  11. A. J. Baker (1966). Non-Empty Complex Terms. Notre Dame Journal of Formal Logic 7 (1):48-56.
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  12. P. Banks (2010). O Filosofické Interpretaci Logiky Aristotelský Dialog. Studia Neoaristotelica 7 (2):197-210.
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  13. Evelyn M. Barker (1984). Unneeded Surgery on Aristotle's Prior Analytics. Notre Dame Journal of Formal Logic 25 (4):323-331.
  14. Jonathan Barnes & Susanne Bobzien (1991). Alexander of Aphrodisias' on Aristotle's Prior Analytics 1.1-7. Duckworth.
    ABSTRACT: English translation of the 2nd/3rd century Peripatetic Philosopher's Alexander of Aphrodisias commentary on Aristotle's non-modal syllogistic, i.e. on one of the most influential logical texts of all times. -/- Volume includes introduction on Alexander of Aphrodisias and the early commentators, translation with notes and comments, appendices with a new translation of Aristotle's text, a summary of Aristotle's non-modal syllogistic and textual notes.
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  15. Susanne Bobzien (2011). The Combinatorics of Stoic Conjunction. Oxford Studies in Ancient Philosophy 40 (1):157-188.
    ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...)
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  16. Susanne Bobzien (2007). Aristotle's De Interpretatione 8 is About Ambiguity. In D. Scott (ed.), Maieusis: Essays in Ancient Philosophy. Oxford University Press. 301.
    ABSTRACT: In this paper I show that, contrary to the prevalent view, in his De Interpretatione chapter 8, Aristotle is concerned with a kind of ambiguity, i.e. with homonymy; more precisely, with homonymy of linguistic expressions as it may occur in dialectical argument. The paper has two parts. In the first part, I argue that in the Sophistici Elenchi 175b39-176a5 Aristotle indubitably deals with homonymy in dialectical argument; that De Interpretatione 8 is a parallel to Sophistici Elenchi 175b39-176a5; that De (...)
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  17. Susanne Bobzien (2006). Ancient Logic. In Stanford Encyclopedia of Philosophy.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...)
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  18. Susanne Bobzien (2006). Logic, History Of: Ancient Logic. In Donald M. Borchert (ed.), Encyclopedia of Philosophy. Thomson Gale.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with a focus on issues that may be of interest to contemporary logicians and covering important topics in Post-Aristotelian logic that are frequently neglected (such as Peripatetic hypothetical syllogistic, the Stoic axiomatic system of propositional logic and various later ancient developments).
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  19. Susanne Bobzien (2006). Ancient Logic. Stanford Encyclopedia of Philosophy.
    ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians.
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  20. Susanne Bobzien (2006). The Stoics on Fallacies of Equivocation. In D. Frede & B. Inwood (eds.), Language and Learning, Proceedings of the 9th Symposium Hellenisticum. Cambridge University Press.
    ABSTRACT: This paper discusses the Stoic treatment of fallacies that are based on lexical ambiguities. It provides a detailed analysis of the relevant passages, lays bare textual and interpretative difficulties, explores what the Stoic view on the matter implies for their theory of language, and compares their view with Aristotle’s. In the paper I aim to show that, for the Stoics, fallacies of ambiguity are complexes of propositions and sentences and thus straddle the realms of meaning (which is the domain (...)
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