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  1.  6
    Non-distributive Relatives of ETL and NFL.Daniil Kozhemiachenko - forthcoming - Studia Logica:1-29.
    In this paper we devise non-distributive relatives of Exactly true logic by Pietz and Riveccio and its dual Non-falsity logic by Shramko, Zaitsev and Belikov. We consider two pre-orders which are algebraic counterparts of the ETL’s and NFL’s entailment relations on the de Morgan lattice 4. We generalise these pre-orders and determine which distributive properties that hold on 4 are not forced by either of the pre-orders. We then construct relatives of ETL and NFL but lack such distributive properties. For (...)
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  2.  16
    Generalisation of Proof Simulation Procedures for Frege Systems by M.L. Bonet and S.R. Buss.Daniil Kozhemiachenko - 2018 - Journal of Applied Non-Classical Logics 28 (4):389-413.
    ABSTRACTIn this paper, we present a generalisation of proof simulation procedures for Frege systems by Bonet and Buss to some logics for which the deduction theorem does not hold. In particular, we study the case of finite-valued Łukasiewicz logics. To this end, we provide proof systems and which augment Avron's Frege system HŁuk with nested and general versions of the disjunction elimination rule, respectively. For these systems, we provide upper bounds on speed-ups w.r.t. both the number of steps in proofs (...)
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