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  1. J. C. Abbott (1976). Orthoimplication Algebras. Studia Logica 35 (2):173 - 177.
    Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.
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  2. V. Michele Abrusci (1990). A Comparison Between Lambek Syntactic Calculus and Intuitionistic Linear Propositional Logic. Mathematical Logic Quarterly 36 (1):11-15.
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  3. V. Michele Abrusci (1990). Non‐Commutative Intuitionistic Linear Logic. Mathematical Logic Quarterly 36 (4):297-318.
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  4. Ernest W. Adams (1986). On the Logic of High Probability. Journal of Philosophical Logic 15 (3):255 - 279.
  5. R. Adillon & Ventura Verdú (2002). On a Substructural Gentzen System, its Equivalent Variety Semantics and its External Deductive System. Bulletin of the Section of Logic 31 (3):125-134.
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  6. M. Aghaei & M. Ardeshir (2000). A Bounded Translation of Intuitionistic Propositional Logic Into Basic Propositional Logic. Mathematical Logic Quarterly 46 (2):195-206.
    In this paper we prove a bounded translation of intuitionistic propositional logic into basic propositional logic. Our new theorem, compared with the translation theorem in [1], has the advantage that it gives an effective bound on the translation, depending on the complexity of formulas.
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  7. P. Aglianò, I. M. A. Ferreirim & F. Montagna (2007). Basic Hoops: An Algebraic Study of Continuous T -Norms. Studia Logica 87 (1):73 - 98.
    A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, →, 1), where (...)
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  8. Stefano Aguzzoli & Agata Ciabattoni (2000). Finiteness in Infinite-Valued Łukasiewicz Logic. Journal of Logic, Language and Information 9 (1):5-29.
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to the same (...)
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  9. Stefano Aguzzoli & Brunella Gerla (2002). Finite-Valued Reductions of Infinite-Valued Logics. Archive for Mathematical Logic 41 (4):361-399.
    In this paper we present a method to reduce the decision problem of several infinite-valued propositional logics to their finite-valued counterparts. We apply our method to Łukasiewicz, Gödel and Product logics and to some of their combinations. As a byproduct we define sequent calculi for all these infinite-valued logics and we give an alternative proof that their tautology problems are in co-NP.
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  10. Tuomo Aho (1994). On the Interpretation of Attitude Logics. In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer. 1--11.
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  11. Seiki Akama (1996). Curry's Paradox in Contractionless Constructive Logic. Journal of Philosophical Logic 25 (2):135 - 150.
    We propose contractionless constructive logic which is obtained from Nelson's constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Curry's paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitch's and Prawitz's systems.
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  12. 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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  13. Seiki Akama, Yasunori Nagata & Chikatoshi Yamada (2008). Three-Valued Temporal Logic Q T and Future Contingents. Studia Logica 88 (2):215 - 231.
    Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of future contingents.
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  14. Galym Akishev & Robert Goldblatt (2010). Monadic Bounded Algebras. Studia Logica 96 (1):1 - 40.
    We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA's is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that can be seen as an algebraic counterpart to semantic completeness for monadic free logic. The analysis involves the representation of (...)
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  15. Natasha Alechina (2000). Functional Dependencies Between Variables. Studia Logica 66 (2):273-283.
    We consider a predicate logic Lfd where not all assignments of values to individual variables are possible. Some variables are functionally dependent on other variables. This makes sense if the models of logic are assumed to correspond to databases or states. We show that Lfd is undecidable but has a complete and sound sequent calculus formalisation.
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  16. M. Alizadeh & M. Ardeshir (2004). On the Linear Lindenbaum Algebra of Basic Propositional Logic. Mathematical Logic Quarterly 50 (1):65.
    We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra.
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  17. Majid Alizadeh & Mohammad Ardeshir (2006). Amalgamation Property for the Class of Basic Algebras and Some of its Natural Subclasses. Archive for Mathematical Logic 45 (8):913-930.
    We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property.
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  18. Majid Alizadeh & Mohammad Ardeshir (2006). On Löb Algebras. Mathematical Logic Quarterly 52 (1):95-105.
    We study the variety of Löb algebras , the algebraic structures associated with formal propositional calculus. Among other things, we prove a completeness theorem for formal propositional logic with respect to the variety of Löb algebras. We show that the variety of Löb algebras has the weak amalgamation property. Some interesting subclasses of the variety of Löb algebras, e.g. linear, faithful and strongly linear Löb algebras are introduced.
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  19. Patrick Allo (2013). Noisy Vs. Merely Equivocal Logics. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. 57--79.
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  20. E. H. Alves & J. A. D. Guerzoni (1990). Extending Montague's System: A Three Valued Intensional Logic. Studia Logica 49 (1):127 - 132.
    In this note we present a three-valued intensional logic, which is an extension of both Montague's intensional logic and ukasiewicz three-valued logic. Our system is obtained by adapting Gallin's version of intensional logic (see Gallin, D., Intensional and Higher-order Modal Logic). Here we give only the necessary modifications to the latter. An acquaintance with Gallin's work is pressuposed.
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  21. E. H. Alves & A. M. Sette (1996). On the Equivalence Between Some Systems of Non-Classical Logic. Bulletin of the Section of Logic 25:68-72.
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  22. Giambattista Amati, Luigia Carlucci-Aiello & Fiora Pirri (1997). Intuitionistic Autoepistemic Logic. Studia Logica 59 (1):103-120.
    In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.
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  23. H. Andréka, T. Gergely & I. Németi (1977). On Universal Algebraic Constructions of Logics. Studia Logica 36 (1-2):9 - 47.
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  24. Irving H. Anellis (2009). Russell and His Sources for Non-Classical Logics. Logica Universalis 3 (2):153-218.
    My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that (...)
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  25. G. Aldo Antonelli (2000). Book Review To Appear in the Bulletin of Symbolic Logic. [REVIEW] Bulletin of Symbolic Logic 6 (4):480-84.
    The emergence, over the last twenty years or so, of so-called “non-monotonic” logics represents one of the most significant developments both in logic and artificial intelligence. These logics were devised in order to represent defeasible reasoning, i.e., that kind of inference in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further evidence.
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  26. G. Aldo Antonelli (1999). A Directly Cautious Theory of Defeasible Consequence for Default Logic Via the Notion of General Extension. Artificial Intelligence 109 (1-2):71-109.
    This paper introduces a generalization of Reiter’s notion of “extension” for default logic. The main difference from the original version mainly lies in the way conflicts among defaults are handled: in particular, this notion of “general extension” allows defaults not explicitly triggered to pre-empt other defaults. A consequence of the adoption of such a notion of extension is that the collection of all the general extensions of a default theory turns out to have a nontrivial algebraic structure. This fact has (...)
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  27. G. Aldo Antonelli (1992). Revision Rules: An Investigation Into Non-Monotonic Inductive Definitions. Dissertation, University of Pittsburgh
    Many different modes of definition have been proposed over time, but none of them allows for circular definitions, since, according to the prevalent view, the term defined would then be lacking a precise signification. I argue that although circular definitions may at times fail uniquely to pick out a concept or an object, sense still can be made of them by using a rule of revision in the style adopted by Anil Gupta and Nuel Belnap in the theory of truth.
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  28. Michael A. Arbib & Ernest G. Manes (1975). A Category-Theoretic Approach to Systems in a Fuzzy World. Synthese 30 (3-4):381 - 406.
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  29. Mohammad Ardeshir & S. Mojtaba Mojtahedi (2014). Completeness of Intermediate Logics with Doubly Negated Axioms. Mathematical Logic Quarterly 60 (1-2):6-11.
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  30. Ofer Arieli & Arnon Avron (1996). Reasoning with Logical Bilattices. Journal of Logic, Language and Information 5 (1):25--63.
    The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. (...)
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  31. Ofer Arieli, Arnon Avron & Anna Zamansky (2011). Maximal and Premaximal Paraconsistency in the Framework of Three-Valued Semantics. Studia Logica 97 (1):31 - 60.
    Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued (...)
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  32. A. Arruda & E. Alves (1979). Semantical Study of Some Systems of Vagueness Logic. Bulletin of the Section of Logic 8 (3):139-144.
    In [1] we have characterized four types vagueness related to negation, and constructed the corresponding propositional calculi adequate to formalize each type of vagueness. The calculi obtained were named V0; V1; V2 and C1 . The relations among these calculi and the classical propositional calculus C0 can be represented in the following diagram, where the arrows indicate that a system is a proper subsystem of the other V0 V1 C0 V2 C1 6 1 PP PP PP PiP 1 PP PP (...)
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  33. Ayda I. Arruda, R. Chuaqui & Newton C. A. Costa (eds.) (1980). Mathematical Logic in Latin America: Proceedings of the IV Latin American Symposium on Mathematical Logic Held in Santiago, December 1978. Sole Distributors for the U.S.A. And Canada, Elsevier North-Holland.
    (or not oveA-complete.) . Let * be a unary operator defined on the set F of formulas of the language £ (ie, if A is a formula of £, then *A is also a ...
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  34. Ayda I. Arruda & Newton C. A. Costa (1984). On the Relevant Systemsp Andp* and Some Related Systems. Studia Logica 43 (1-2):33 - 49.
    In this paper we study the systemsP andP * (see Arruda and da Costa,O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemtica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories havingP andP * as their underlying logics are non-trivial.
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  35. Ayda I. Arruda & Newton C. A. da Costa (1984). On the Relevant Systems P and P* and Some Related Systems. Studia Logica 43 (1/2):33 - 49.
    In this paper we study the systems P and $P^{\ast}$ (see Arruda and da Costa, O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemātica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories having P and $P^{\ast}$ as their underlying logics are non-trivial.
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  36. Richard T. W. Arthur (2011). Natural Deduction: An Introduction to Logic with Real Arguments, a Little History and Some Humour. Broadview Press.
    Richard Arthur's Natural Deduction provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern "informal logic" with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.
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  37. 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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  38. E. J. Ashworth (1973). Are There Really Two Logics? Dialogue 12 (01):100-109.
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  39. Arnon Avron, Four-Valued Diagnoses for Strati Ed Knowledge-Bases.
    We present a four-valued approach for recovering consistent data from inconsistent set of assertions. For a common family of knowledge-bases we also provide an e cient algorithm for doing so automaticly. This method is particularly useful for making model-based diagnoses.
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  40. Arnon Avron, Logical Non-Determinism as a Tool for Logical Modularity: An Introduction.
    It is well known that every propositional logic which satisfies certain very natural conditions can be characterized semantically using a multi-valued matrix ([Los and Suszko, 1958; W´ ojcicki, 1988; Urquhart, 2001]). However, there are many important decidable logics whose characteristic matrices necessarily consist of an infinite number of truth values. In such a case it might be quite difficult to find any of these matrices, or to use one when it is found. Even in case a logic does have a (...)
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  41. Arnon Avron, Non-Deterministic Matrices and Modular Semantics of Rules.
    We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straightforward way. Our main tool for this task is the use of finite Nmatrices, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set (...)
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  42. Arnon Avron, On Negation, Completeness and Consistency.
    We have avoided here the term \false", since we do not want to commit ourselves to the view that A is false precisely when it is not true. Our formulation of the intuition is therefore obviously circular, but this is unavoidable in intuitive informal characterizations of basic connectives and quanti ers.
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  43. Arnon Avron, The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics.
    Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers (...)
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  44. Arnon Avron (2014). Paraconsistency, Paracompleteness, Gentzen Systems, and Trivalent Semantics. Journal of Applied Non-Classical Logics 24 (1-2):12-34.
    A quasi-canonical Gentzen-type system is a Gentzen-type system in which each logical rule introduces either a formula of the form , or of the form , and all the active formulas of its premises belong to the set . In this paper we investigate quasi-canonical systems in which exactly one of the two classical rules for negation is included, turning the induced logic into either a paraconsistent logic or a paracomplete logic, but not both. We provide a constructive coherence criterion (...)
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  45. Arnon Avron (1991). Natural 3-Valued Logics--Characterization and Proof Theory. Journal of Symbolic Logic 56 (1):276-294.
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  46. Arnon Avron, The Semantics and Proof Theory of Linear Logic.
    Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we shall investigate (...)
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  47. 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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  48. Alexandru Baltag (1999). Interpolation and Preservation for Pebble Logics. Journal of Symbolic Logic 64 (2):846-858.
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  49. Stefano Baratella & Andrea Masini (2013). A Natural Deduction System for Bundled Branching Time Logic. Journal of Applied Non-Classical Logics 23 (3):268 - 283.
    We introduce a natural deduction system for the until-free subsystem of the branching time logic Although we work with labelled formulas, our system differs conceptually from the usual labelled deduction systems because we have no relational formulas. Moreover, no deduction rule embodies semantic features such as properties of accessibility relation or similar algebraic properties. We provide a suitable semantics for our system and prove that it is sound and weakly complete with respect to such semantics.
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  50. H. P. Barendregt (1992). Typed Lambda Calculi. S. Abramsky Et AL. In S. Abramsky, D. Gabbay & T. Maibaurn (eds.), Handbook of Logic in Computer Science. Oxford University Press. 117--309.
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