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• W3094740951 abstract "The article is a study of two algebraic structures, the `contrapositionally complemented pseudo-Boolean algebra' (ccpBa) and `contrapositionally $vee$ complemented pseudo-Boolean algebra' (c$vee$cpBa). The algebras have recently been obtained from a topos-theoretic study of categories of rough sets. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. We study properties of these algebras, give examples, and compare them with relevant existing algebras. `Intuitionistic Logic with Minimal Negation (ILM)' corresponding to ccpBas and its extension ILM-${vee}$ for c$vee$cpBas, are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce's logic. With a focus on properties of the two negations, two kinds of relational semantics for ILM and ILM-${vee}$ are obtained, and an inter-translation between the two semantics is provided. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn's logical framework for the purpose, two logics $K_{im}$ and $K_{im-{vee}}$ are presented, where the language does not include implication. $K_{im}$-algebras are reducts of ccpBas. The negations in the algebras are shown to occupy distinct positions in an enhanced form of Dunn's Kite of negations. Relational semantics for $K_{im}$ and $K_{im-{vee}}$ are given, based on Dunn's compatibility frames. Finally, relationships are established between the different algebraic and relational semantics for the logics defined in the work." @default.
• W3094740951 created "2020-11-09" @default.
• W3094740951 creator A5042323062 @default.
• W3094740951 creator A5046102840 @default.
• W3094740951 date "2020-10-29" @default.
• W3094740951 modified "2023-09-25" @default.
• W3094740951 title "Contrapositionally Complemented Pseudo-Boolean Algebras and Intuitionistic Logic with Minimal Negation" @default.
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• W3094740951 hasPublicationYear "2020" @default.
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