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  1. De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics.Paul Égré, Lorenzo Rossi & Jan Sprenger - 2021 - Journal of Philosophical Logic 50 (2):215-247.
    In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for (...)
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  • Proof Theory of Finite-valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...)
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  • Conservatively extending classical logic with transparent truth.David Ripley - 2012 - Review of Symbolic Logic 5 (2):354-378.
    This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the (...)
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  • Labeled calculi and finite-valued logics.Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach - 1998 - Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...)
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  • LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Arazim Pavel & Lávička Tomáš (eds.), The Logica Yearbook 2016. College Publications.
    Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.
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  • Multiple-conclusion lp and default classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.
    Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of . With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.
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  • On All Strong Kleene Generalizations of Classical Logic.Stefan Wintein - 2016 - Studia Logica 104 (3):503-545.
    By using the notions of exact truth and exact falsity, one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the Strong Kleene schema. Besides familiar logics such as Strong Kleene logic, the Logic of Paradox and First Degree Entailment, the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar (...)
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  • Ewa Orlowska and Joanna Golinska-Pilarek, Dual Tableaux: Foundations, Methodology, Case Studies, Springer, Series: Trends in Logic, Vol. 33, 2011, pp. xvi+523, 113 illus. ISBN: 978-94-007-0004-8 EURO 181,85, 978-94-007-0005-5 EURO 159,99. [REVIEW]Walter Carnielli - 2013 - Studia Logica 101 (1):229-232.
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