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Conservative translations of four-valued logics in modal logic

Ekaterina Kubyshkina

Synthese 198 (S22):5555-5571 (2019)

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Conservative Translations Revisited.J. Ramos, J. Rasga & C. Sernadas - 2023 - Journal of Philosophical Logic 52 (3):889-913.details We provide sufficient conditions for the existence of a conservative translation from a consequence system to another one. We analyze the problem in many settings, namely when the consequence systems are generated by a deductive calculus or by a logic system including both proof-theoretic and model-theoretic components. We also discuss reflection of several metaproperties with the objective of showing that conservative translations provide an alternative to proving such properties from scratch. We discuss soundness and completeness, disjunction property and metatheorem of (...) Download Export citation Bookmark
Non-distributive Relatives of ETL and NFL.Daniil Kozhemiachenko - 2020 - Studia Logica 109 (1):137-165.details 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 (...) Download Export citation Bookmark
The Logic of Internal Rational Agent.Yaroslav Petrukhin - 2021 - Australasian Journal of Logic 18 (2).details In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent textbf{LRA} cite{LRA}. We call our logic $ bf LIRA$. In contrast to textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic cite{ZS}. This logic may be useful in a situation when according to an agent's point of (...) Download Export citation Bookmark

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