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  1. Erik Aarts (1994). Proving Theorems of the Second Order Lambek Calculus in Polynomial Time. 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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  2. Parosh Aziz Abdulla (2010). Well (and Better) Quasi-Ordered Transition Systems. Bulletin of Symbolic Logic 16 (4):457-515.
    In this paper, we give a step by step introduction to the theory of well quasi-ordered transition systems. The framework combines two concepts, namely (i) transition systems which are monotonic wrt. a well-quasi ordering ; and (ii) a scheme for symbolic backward reachability analysis. We describe several models with infinite-state spaces, which can be analyzed within the framework, e.g., Petri nets, lossy channel systems, timed automata, timed Petri nets, and multiset rewriting systems. We will also present better quasi-ordered transition systems (...)
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  3. Andrew Aberdein (2001). Classical Recapture. In V. Fano, M. Stanzione & G. Tarozzi (eds.), Prospettive Della Logica E Della Filosofia Della Scienza. Rubettino. 11-18.
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  4. M. Abraham, D. M. Gabbay & U. Schild (2011). Obligations and Prohibitions in Talmudic Deontic Logic. Artificial Intelligence and Law 19 (2-3):117-148.
    This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg (...)
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  5. V. Michele Abrusci (2002). Classical Conservative Extensions of Lambek Calculus. Studia Logica 71 (3):277 - 314.
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  6. V. Michele Abrusci, Jean-Yves Girard & Jacques Van De Wiele (1990). Some Uses of Dilators in Combinatorial Problems. II. Journal of Symbolic Logic 55 (1):32-40.
    We study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with "+ 1" instead of "- 1"). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator (...)
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  7. Wilhelm Ackermann (1950). Widerspruchsfreier Aufbau der Logik I: Typenfreies System Ohne Tertium Non Datur. Journal of Symbolic Logic 15 (1):33-57.
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  8. Ernest W. Adams (1986). On the Logic of High Probability. Journal of Philosophical Logic 15 (3):255 - 279.
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  9. Melvin Joseph Adler (1980). A Pragmatic Logic for Commands. J. Benjamins.
    The purpose of this essay is to both discuss commands as a species of speech act and to discuss commands within the broader framework of how they are used and ...
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  10. Diederik Aerts, Sonja Smets & Jean P. Van Bendegem (2010). The Contributions of Logic to the Foundations of Physics: Foreword. [REVIEW] Studia Logica 95 (1-2):1-3.
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  11. Thomas Ågotnes, Wiebe van der Hoek & Michael Wooldridge (2008). Quantified Coalition Logic. 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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  12. Stefano Aguzzoli & Brunella Gerla (2010). Probability Measures in the Logic of Nilpotent Minimum. Studia Logica 94 (2):151 - 176.
    We axiomatize the notion of state over finitely generated free NM-algebras, the Lindenbaum algebras of pure Nilpotent Minimum logic. We show that states over the free n -generated NM-algebra exactly correspond to integrals of elements of with respect to Borel probability measures.
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  13. Tarek Sayed Ahmed (2005). Algebraic Logic, Where Does It Stand Today? Bulletin of Symbolic Logic 11 (4):465-516.
    This is a survey article on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing, finite combinatorics, and Gödel's incompleteness results. We focus on cylindric algebras. Relation algebras and polyadic algebras are mostly covered only insofar as they relate to cylindric algebras, and even there we have not told the whole story. (...)
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  14. Tarek Sayed Ahmed & Istvan Németi (2001). On Neat Reducts of Algebras of Logic. Studia Logica 68 (2):229-262.
    SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if (...)
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  15. Kazimierz Ajdukiewicz (1960). The Axiomatic Systems From the Methodological Point of View. Studia Logica 9 (1):205 - 220.
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  16. Seiki Akama (1991). The Gentzen-Kripke Construction of the Intermediate Logic LQ. Notre Dame Journal of Formal Logic 33 (1):148-153.
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  17. Seiki Akama (1990). Subformula Semantics for Strong Negation Systems. Journal of Philosophical Logic 19 (2):217 - 226.
    We present a semantics for strong negation systems on the basis of the subformula property of the sequent calculus. The new models, called subformula models, are constructed as a special class of canonical Kripke models for providing the way from the cut-elimination theorem to model-theoretic results. This semantics is more intuitive than the standard Kripke semantics for strong negation systems.
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  18. Seiki Akama (1987). Constructive Predicate Logic with Strong Negation and Model Theory. Notre Dame Journal of Formal Logic 29 (1):18-27.
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  19. M. J. Alban (1943). Independence of the Primitive Symbols of Lewis's Calculi of Propositions. Journal of Symbolic Logic 8 (1):25-26.
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  20. Carlos E. Alchourrón & David Makinson (1986). Maps Between Some Different Kinds of Contraction Function: The Finite Case. Studia Logica 45 (2):187 - 198.
    In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose (...)
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  21. Natasha Alechina & Brian Logan (2010). Belief Ascription Under Bounded Resources. Synthese 173 (2):179 - 197.
    There exists a considerable body of work on epistemic logics for resource-bounded reasoners. In this paper, we concentrate on a less studied aspect of resource-bounded reasoning, namely, on the ascription of beliefs and inference rules by the agents to each other. We present a formal model of a system of bounded reasoners which reason about each other’s beliefs, and investigate the problem of belief ascription in a resource-bounded setting. We show that for agents whose computational resources and memory are bounded, (...)
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  22. Robert A. Alps & Robert C. Neveln (1981). A Predicate Logic Based on Indefinite Description and Two Notions of Identity. Notre Dame Journal of Formal Logic 22 (3):251-263.
  23. J. E. J. Altham (1971). The Logic of Plurality. London,Methuen.
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  24. Alan Ross Anderson (1957). Independent Axiom Schemata for Von Wright's M. Journal of Symbolic Logic 22 (3):241-244.
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  25. Alan Ross Anderson (1956). Independent Axiom Schemata for S. Journal of Symbolic Logic 21 (3):255-256.
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  26. J. G. Anderson (1974). A Note on Finite Intermediate Logics. Notre Dame Journal of Formal Logic 15 (1):149-155.
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  27. James H. Andrews (2007). An Untyped Higher Order Logic with Y Combinator. Journal of Symbolic Logic 72 (4):1385 - 1404.
    We define a higher order logic which has only a notion of sort rather than a notion of type, and which permits all terms of the untyped lambda calculus and allows the use of the Y combinator in writing recursive predicates. The consistency of the logic is maintained by a distinction between use and mention, as in Gilmore's logics. We give a consistent model theory, a proof system which is sound with respect to the model theory, and a cut-elimination proof (...)
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  28. Peter B. Andrews (1971). Resolution in Type Theory. Journal of Symbolic Logic 36 (3):414-432.
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  29. R. B. Angell (1960). The Sentential Calculus Using Rule of Inference Re. Journal of Symbolic Logic 25 (2):143 -.
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  30. Richard B. Angell (2002). A-Logic. University Press of America.
    A-LOGIC is a full-length book (600+ pg). It functions as a system of logic designed to: 1) solve the standard paradoxes and major problems of standard mathematical logic; 2) minimize that logic's anomalies with respect to ordinary language, yet; 3) prove that all theorems in mathematical logic are tautologies. It covers lst order logic the logic of the words "and", "or", "not", "all" and "some". But it also has a non truth functional "if...then" and differs in its definition of validity, (...)
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  31. O. Anshakov & S. Rychkov (1995). On Finite-Valued Propositional Logical Calculi. Notre Dame Journal of Formal Logic 36 (4):606-629.
    In this paper we describe, in a purely algebraic language, truth-complete finite-valued propositional logical calculi extending the classical Boolean calculus. We also give a new proof of the Completeness Theorem for such calculi. We investigate the quasi-varieties of algebras playing an analogous role in the theory of these finite-valued logics to the role played by the variety of Boolean algebras in classical logic.
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  32. G. Aldo Antonelli (2000). Proto-Semantics for Positive Free Logic. Journal of Philosophical Logic 29 (3):277-294.
    This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non (...)
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  33. Lennart Åqvist (1975). A New Approach to the Logical Theory of Interrogatives: Analysis and Formalization. Tbl Verlag G. Narr.
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  34. Carlos Areces, Patrick Blackburn & Maarten Marx (2001). Hybrid Logics: Characterization, Interpolation and Complexity. Journal of Symbolic Logic 66 (3):977-1010.
    Hybrid languages are expansions of propositional modal languages which can refer to (or even quantify over) worlds. The use of strong hybrid languages dates back to at least [Pri67], but recent work (for example [BS98, BT98a, BT99]) has focussed on a more constrained system called $\mathscr{H}(\downarrow, @)$ . We show in detail that $\mathscr{H}(\downarrow, @)$ is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Fraisse game, and an enriched notion of (...)
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  35. Horacio Arló-Costa & Richmond H. Thomason (2001). Iterative Probability Kinematics. Journal of Philosophical Logic 30 (5):479-524.
    Following the pioneer work of Bruno De Finetti [12], conditional probability spaces (allowing for conditioning with events of measure zero) have been studied since (at least) the 1950's. Perhaps the most salient axiomatizations are Karl Popper's in [31], and Alfred Renyi's in [33]. Nonstandard probability spaces [34] are a well know alternative to this approach. Vann McGee proposed in [30] a result relating both approaches by showing that the standard values of infinitesimal probability functions are representable as Popper functions, and (...)
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  36. Charles Ashbacher (2002). Introduction to Neutrosophic Logic. American Research Press.
    Neutrosophic Logic was created by Florentin Smarandache (1995) and is an extension / combination of the fuzzy logic, intuitionistic logic, paraconsistent logic, ...
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  37. Alessandro Avellone, Camillo Fiorentini, Paolo Mantovani & Pierangelo Miglioli (1996). On Maximal Intermediate Predicate Constructive Logics. Studia Logica 57 (2-3):373 - 408.
    We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.
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  38. Arnon Avron, A Simple Proof of Completeness and Cut-Elimination for Propositional G¨ Odel Logic.
    We provide a constructive, direct, and simple proof of the completeness of the cut-free part of the hypersequential calculus for G¨odel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). We then extend the results and proofs to derivations from assumptions, showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions.
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  39. Matthias Baaz, Petr Hájek, David Švejda & Jan Krajíček (1998). Embedding Logics Into Product Logic. Studia Logica 61 (1):35-47.
    We construct a faithful interpretation of ukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable.We prove a completeness theorem for product logic extended by a unary connective of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic.
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  40. Matthias Baaz & Rosalie Iemhoff (2008). On Skolemization in Constructive Theories. Journal of Symbolic Logic 73 (3):969-998.
    In this paper a method for the replacement, in formulas, of strong quantifiers by functions is introduced that can be considered as an alternative to Skolemization in the setting of constructive theories. A constructive extension of intuitionistic predicate logic that captures the notions of preorder and existence is introduced and the method, orderization, is shown to be sound and complete with respect to this logic. This implies an analogue of Herbrand's theorem for intuitionistic logic. The orderization method is applied to (...)
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  41. John Bacon (1982). First-Order Logic Based on Inclusion and Abstraction. Journal of Symbolic Logic 47 (4):793-808.
  42. A. J. Baker (1972). Syllogistic with Complex Terms. Notre Dame Journal of Formal Logic 13 (1):69-87.
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  43. A. J. Baker (1966). Non-Empty Complex Terms. Notre Dame Journal of Formal Logic 7 (1):48-56.
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  44. Philippe Balbiani, Andreas Herzig & Nicolas Troquard (2008). Alternative Axiomatics and Complexity of Deliberative Stit Theories. Journal of Philosophical Logic 37 (4):387 - 406.
    We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...)
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  45. Jorge Baralt-Torrijos, Lucio Chiaraviglio & William Grosky (1975). The Programmatic Semantics of Binary Predicator Calculi. Notre Dame Journal of Formal Logic 16 (4):591-596.
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  46. Juan Barba (1993). A Modal Reduction for Partial Logic. Journal of Philosophical Logic 22 (4):429 - 435.
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  47. Ruth C. Barcan (1946). The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication. Journal of Symbolic Logic 11 (4):115-118.
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  48. Ruth C. Barcan (1946). A Functional Calculus of First Order Based on Strict Implication. Journal of Symbolic Logic 11 (1):1-16.
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  49. H. P. Barendregt (1984). The Lambda Calculus: Its Syntax and Semantics. Sole Distributors for the U.S.A. And Canada, Elsevier Science Pub. Co..
    The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
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  50. Henk Barendregt (1997). The Impact of the Lambda Calculus in Logic and Computer Science. Bulletin of Symbolic Logic 3 (2):181-215.
    One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand.
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