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  1. Ryszard Wójcicki. Theory of logical calculi. Basis theory of consequence operations. Synthese library, vol. 199. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1988, xviii + 473 pp. [REVIEW]Stephen L. Bloom - 1990 - Journal of Symbolic Logic 55 (3):1324-1326.
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  • An Algebraic View of Super-Belnap Logics.Hugo Albuquerque, Adam Přenosil & Umberto Rivieccio - 2017 - Studia Logica 105 (6):1051-1086.
    The Belnap–Dunn logic is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of (...)
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  • Selfextensional Logics with a Conjunction.Ramon Jansana - 2006 - Studia Logica 84 (1):63-104.
    A logic is selfextensional if its interderivability (or mutual consequence) relation is a congruence relation on the algebra of formulas. In the paper we characterize the selfextensional logics with a conjunction as the logics that can be defined using the semilattice order induced by the interpretation of the conjunction in the algebras of their algebraic counterpart. Using the charactrization we provide simpler proofs of several results on selfextensional logics with a conjunction obtained in [13] using Gentzen systems. We also obtain (...)
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  • (1 other version)Distributive Lattices with a Dual Endomorphism.H. P. Sankappanavar - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):385-392.
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  • An infinity of super-Belnap logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319-335.
    We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a single finite logical (...)
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  • Distributive lattices with a dual homomorphic operation. II.Alasdair Urquhart - 1981 - Studia Logica 40 (4):391 - 404.
    An Ockham lattice is defined to be a distributive lattice with 0 and 1 which is equipped with a dual homomorphic operation. In this paper we prove: (1) The lattice of all equational classes of Ockham lattices is isomorphic to a lattice of easily described first-order theories and is uncountable, (2) every such equational class is generated by its finite members. In the proof of (2) a characterization of orderings of with respect to which the successor function is decreasing is (...)
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  • Partiality and its dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
    This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate (...)
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  • Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
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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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  • Protoalgebraic Logics.Janusz Czelakowski - 2003 - Studia Logica 74 (1):313-342.
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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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  • Protoalgebraic Logics.Janusz Czelakowski - 2001 - Kluwer Academic Publishers.
    This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...
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  • Theory of Logical Calculi, Basic Theory of Consequence Operations.Ryszard Wójcicki - 1991 - Studia Logica 50 (3):623-629.
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  • An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
    Provability, Computability and Reflection.
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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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  • Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.
    The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...)
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  • Belnap's four-valued logic and De Morgan lattices.Josep Font - 1997 - Logic Journal of the IGPL 5 (1):1--29.
    This paper contains some contributions to the study of Belnap's four-valued logic from an algebraic point of view. We introduce a finite Hilbert-style axiomatization of this logic, along with its well-known semantical presentation, and a Gentzen calculus that slightly differs from the usual one in that it is closer to Anderson and Belnap's formalization of their “logic of first-degree entailments”. We prove several Completeness Theorems and reduce every formula to an equivalent normal form. The Hilbert-style presentation allows us to characterize (...)
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  • Distributive lattices with a dual homomorphic operation.Alasdair Urquhart - 1979 - Studia Logica 38 (2):201 - 209.
    The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.
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  • Semi-de Morgan algebras.Hanamantagouda P. Sankappanavar - 1987 - Journal of Symbolic Logic 52 (3):712-724.
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  • Nothing but the Truth.Andreas Pietz & Umberto Rivieccio - 2013 - Journal of Philosophical Logic 42 (1):125-135.
    A curious feature of Belnap’s “useful four-valued logic”, also known as first-degree entailment (FDE), is that the overdetermined value B (both true and false) is treated as a designated value. Although there are good theoretical reasons for this, it seems prima facie more plausible to have only one of the four values designated, namely T (exactly true). This paper follows this route and investigates the resulting logic, which we call Exactly True Logic.
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  • (2 other versions)Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
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  • (1 other version)Distributive lattices with a dual endomorphism.H. P. Sankappanavar - 1985 - Mathematical Logic Quarterly 31 (25‐28):385-392.
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  • (2 other versions)An Algebraic Approach to Non-Classical Logics.Anne Preller - 1977 - Journal of Symbolic Logic 42 (3):432-432.
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