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An order-theoretic analysis of interpretations among propositional deductive systems
Annals of Pure and Applied Logic 164 (2):112-130 (2013)
Abstract
In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have different underlying languagesLinks
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Citations of this work
Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras.Ciro Russo - 2022 - Logica Universalis 16 (1):355-380.
An Abstract Approach to Consequence Relations.Petr Cintula, José Gil-férez, Tommaso Moraschini & Francesco Paoli - 2019 - Review of Symbolic Logic 12 (2):331-371.
The semantic isomorphism theorem in abstract algebraic logic.Tommaso Moraschini - 2016 - Annals of Pure and Applied Logic 167 (12):1298-1331.
A categorical equivalence between logical quantale modules and quantum B‐modules.Xianglong Ruan & Xiaochuan Liu - forthcoming - Mathematical Logic Quarterly.
Corrigendum to “An order-theoretic analysis of interpretations among propositional deductive systems” [Ann. Pure Appl. Logic 164 (2) (2013) 112–130]. [REVIEW]Ciro Russo - 2016 - Annals of Pure and Applied Logic 167 (3):392-394.
References found in this work
Equivalence of Consequence Operations.W. J. Blok & Bjarni Jónsson - 2006 - Studia Logica 83 (1-3):91-110.
Correspondences between Gentzen and Hilbert Systems.J. G. Raftery - 2006 - Journal of Symbolic Logic 71 (3):903 - 957.
Definitional equivalence and algebraizability of generalized logical systems.Alexej P. Pynko - 1999 - Annals of Pure and Applied Logic 98 (1-3):1-68.
Equivalence of consequence relations: an order-theoretic and categorical perspective.Nikolaos Galatos & Constantine Tsinakis - 2009 - Journal of Symbolic Logic 74 (3):780-810.
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