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  1. Louis Osgood Kattsoff. Modality and probability. The philosophical review, vol. 46 (1937), pp. 78–85.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-44.
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  • A few more useful 8-valued logics for reasoning with tetralattice eight.Dmitry Zaitsev - 2009 - Studia Logica 92 (2):265 - 280.
    In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN 3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is (...)
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  • How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
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  • The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
    It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.This landmark work offers both ...
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  • Intuitive semantics for first-degree entailments and 'coupled trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
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  • Basic logic: Reflection, symmetry, visibility.Giovanni Sambin, Giulia Battilotti & Claudia Faggian - 2000 - Journal of Symbolic Logic 65 (3):979-1013.
    We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with (...)
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  • Intuitionistic logic with strong negation.Yuri Gurevich - 1977 - Studia Logica 36 (1-2):49 - 59.
    This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension of (...)
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  • Some Useful 16-Valued Logics: How a Computer Network Should Think.Yaroslav Shramko & Heinrich Wansing - 2005 - Journal of Philosophical Logic 34 (2):121-153.
    In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = ������(2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᵍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an (...)
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  • Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - 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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  • A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
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  • Three uses of the herbrand-Gentzen theorem in relating model theory and proof theory.William Craig - 1957 - Journal of Symbolic Logic 22 (3):269-285.
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  • Lattice Logic, Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems.Norihiro Kamide - 2021 - Journal of Philosophical Logic 50 (4):781-811.
    Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect (...)
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  • A Few More Useful 8-valued Logics for Reasoning with Tetralattice EIGHT 4.Dmitry Zaitsev - 2009 - Studia Logica 92 (2):265-280.
    In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, (...)
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  • (1 other version)Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
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  • Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.
    Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is (...)
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  • (1 other version)Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2003 - Bulletin of Symbolic Logic 9 (2):231-234.
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  • Four-valued Logic.Katalin Bimbó & J. Michael Dunn - 2001 - Notre Dame Journal of Formal Logic 42 (3):171-192.
    Four-valued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction and its residuals can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier semantics for this system (...)
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  • Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
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  • Paraconsistent quantum logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1989 - Foundations of Physics 19 (7):891-904.
    Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue.
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  • The Geometry of Non-Distributive Logics.Greg Restall & Francesco Paoli - 2005 - Journal of Symbolic Logic 70 (4):1108 - 1126.
    In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems (...)
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  • The Fmla-Fmla Axiomatizations of the Exactly True and Non-falsity Logics and Some of Their Cousins.Yaroslav Shramko, Dmitry Zaitsev & Alexander Belikov - 2019 - Journal of Philosophical Logic 48 (5):787-808.
    In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...)
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  • (1 other version)Constructible Falsity.David Nelson - 1950 - Journal of Symbolic Logic 15 (3):228-228.
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  • Order- dual realational semantics for non-distributive propositional logics.Chrysafis Hartonas - 2016 - Logic Journal of the IGPL 25 (2):145-182.
    This article addresses and resolves some issues of relational, Kripke-style, semantics for the logics of bounded lattice expansions with operators of well-defined distribution types, focusing on the case where the underlying lattice is not assumed to be distributive. It therefore falls within the scope of the theory of Generalized Galois Logics, introduced by Dunn, and it contributes to its extension. We introduce order-dual relational semantics and present a semantic analysis and completeness theorems for non-distributive lattice logic with n -ary additive (...)
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  • The value of the four values.Ofer Arieli & Arnon Avron - 1998 - Artificial Intelligence 102 (1):97-141.
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  • Modal and temporal extensions of non-distributive propositional logics.Chrysafis Hartonas - 2016 - Logic Journal of the IGPL 24 (2):156-185.
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  • (1 other version)Klassische und nichtklassische Aussagenlogik.Wolfgang Rautenberg - 1982 - Studia Logica 41 (4):431-431.
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  • Extending paraconsistent quantum logic: a single-antecedent/succedent system approach.Norihiro Kamide - 2018 - Mathematical Logic Quarterly 64 (4-5):371-386.
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  • The trilaticce of constructive truth values.Yaroslav Shramko, J. Michael Dunn & Tatsutoshi Takenaka - 2001 - Journal of Logic and Computation 11 (1):761--788.
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