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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. Jair Abe (1987). A Note On Curry Algebras. Bulletin of the Section of Logic 16 (4):151-156.
    In one of its possible formulations, the principle of the excluded middle says that, from two propositions A and ¬A , one is true. A paracomplete logic is a logic which can be the basis of theories in which there are propositions A such that A and ¬A are both false. So, we may assert that in a paracomplete logic the law of the excluded middle fails. For a discussion of such kind of logic, as well as for the study (...)
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  3. 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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  4. V. Michele Abrusci (1990). Non‐Commutative Intuitionistic Linear Logic. Mathematical Logic Quarterly 36 (4):297-318.
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  5. W. Ackermann (1959). Umezawa Toshio. On Intermediate Many-Valued Logics. Journal of the Mathematical Society of Japan, Bd. 11 Heft 2 , S. 116–128. [REVIEW] Journal of Symbolic Logic 24 (3):250.
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  6. Wilhelm Ackermann (1956). Stanley Robert. An Extended Procedure in Quantificational Logic. Journal of Symbolic Logic 21 (2):197.
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  7. Wilhelm Ackermann (1956). Sampei Yoemon. On the Orthogonal Expansion of the Boolean Polynomial and its Applications I. Journal of the Faculty of Science, Hokkaido University, Series I, Bd. 11 Heft 3 , S. 113–125.Sampei Yoemon. On the Orthogonal Expansion of the Boolean Polynomial and its Applications II. Commentarii Mathematici Universitatis Sancti Pauli, Bd. 1 Heft 2 , S. 51–57. [REVIEW] Journal of Symbolic Logic 21 (4):401-402.
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  8. Wilhelm Ackermann (1950). Dienes Paul. On Ternary Logic. Journal of Symbolic Logic 15 (3):225.
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  9. A. Adam & U. I. Zuravlev (1970). Set-Theoretical Methods in the Algebra of Logic. Journal of Symbolic Logic 35 (1):162.
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  10. Ernest W. Adams (1986). On the Logic of High Probability. Journal of Philosophical Logic 15 (3):255 - 279.
  11. J. Agassi (1985). Two Valued Logic in Ordinary Circumstances. International Logic Review 32:83.
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  12. 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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  13. P. Aglianò, I. M. A. Ferreirim & F. Montagna (2007). Basic Hoops: An Algebraic Study of Continuous T-Norms. Studia Logica 87 (1):73-98.
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  14. Juan C. Agudelo-Agudelo, Carlos A. Agudelo-González & Oscar E. García-Quintero (2016). On Polynomial Semantics for Propositional Logics. Journal of Applied Non-Classical Logics 26 (2):103-125.
    Some properties and an algorithm for solving systems of multivariate polynomial equations over finite fields are presented. It is then shown how formulas of propositional logics can be translated into polynomials over finite fields in such a way that several logic problems are expressed in terms of algebraic problems. Consequently, algebraic properties and algorithms can be used to solve the algebraically-represented logic problems. The methods described herein combine and generalise those of various previous works.
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  15. 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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  16. Tuomo Aho (1994). On the Interpretation of Attitude Logics. In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer Academic Publishers. pp. 1--11.
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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, 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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  19. 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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  20. 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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  21. A. Aliseda & L. Leonides (2013). Hypotheses Testing in Adaptive Logics: An Application to Medical Diagnosis. Logic Journal of the IGPL 21 (6):915-930.
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  22. 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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  23. 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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  24. 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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  25. Agostinho Almeida (2009). Canonical Extensions and Relational Representations of Lattices with Negation. Studia Logica 91 (2):171-199.
    This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation or (...)
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  26. 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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  27. 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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  28. 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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  29. Alan Ross Anderson (1957). Prior A. N.. Many-Valued and Modal Systems: An Intuitive Approach. The Philosophical Review, Vol, 64 , Pp. 626–630. Journal of Symbolic Logic 22 (3):328-329.
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  30. Alan Ross Anderson (1957). Turquette Atwell R.. Many-Valued Logics and Systems of Strict Implication. The Philosophical Review, Vol. 63 , Pp. 365–379. [REVIEW] Journal of Symbolic Logic 22 (3):328.
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  31. Alan Ross Anderson, A. N. Prior & Boleslaw Sobocinski (1966). The Theory of Implication.The Theory of Implication: Two Corrections.A Note on Prior's Systems in "The Theory of Deduction.". [REVIEW] Journal of Symbolic Logic 31 (4):665.
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  32. H. Andréka, T. Gergely & I. Németi (1977). On Universal Algebraic Constructions of Logics. Studia Logica 36 (1-2):9 - 47.
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  33. 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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  34. R. B. Angell (1970). Iséki Kiyoshi. An Algebra Related with a Propositional Calculus. Proceedings of the Japan Academy, Vol. 42 , Pp. 26–29.Arai Yoshinari, Iséki Kiyoshi, and Tanaka Shôtarô. Characterizations of BCI, BCK-Algebras. Proceedings of the Japan Academy, Vol. 42 , Pp. 105–107.Iséki Kiyoshi. Algebraic Formulation of Propositional Calculi with General Detachment Rule. Proceedings of the Japan Academy, Vol. 43 , Pp. 31–34. [REVIEW] Journal of Symbolic Logic 35 (3):465-466.
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  35. 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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  36. 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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  37. 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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  38. 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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  39. M. Ardeshir & V. Vaezian (2012). A Unification of the Basic Logics of Sambin and Visser. Logic Journal of the IGPL 20 (6):1202-1213.
  40. 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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  41. J. R. B. Arenhart (2014). Semantic Analysis of Non-Reflexive Logics. Logic Journal of the IGPL 22 (4):565-584.
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  42. O. Arieli & A. Avron (2000). General Patterns for Nonmonotonic Reasoning: From Basic Entailments to Plausible Relations. Logic Journal of the IGPL 8 (2):119-148.
    This paper has two goals. First, we develop frameworks for logical systems which are able to reflect not only non-monotonic patterns of reasoning, but also paraconsistent reasoning. Our second goal is to have a better understanding of the conditions that a useful relation for nonmonotonic reasoning should satisfy. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. These generalizations allow the use of monotonic nonclassical logics as the underlying logic upon (...)
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  43. 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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  44. 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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  45. 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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  46. 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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  47. 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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  48. 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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  49. Miloš Arsenijević (2003). Generalized Concepts of Syntactically and Semantically Trivial Differences and Instant-Based and Period-Based Time Ontologies. Journal of Applied Logic 1 (1-2):1-12.
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  50. 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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