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A non-distributive logic for semiconcepts of a context and its modal extension with semantics based on Kripke contexts
Prosenjit Howlader, Mohua Banerjee
A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure doubl…
Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems
Prosenjit Howlader, Mohua Banerjee
The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M…
Topological Representation of Double Boolean Algebras
Prosenjit Howlader, Mohua Banerjee
In formal concept analysis, the collection of protoconcepts of any context forms a double Boolean algebra (dBa) which is fully contextual. Semiconcepts of a context form a pure dBa…
Contrapositionally Complemented Pseudo-Boolean Algebras and Intuitionistic Logic with Minimal Negation
Anuj Kumar More, Mohua Banerjee
The article is a study of two algebraic structures, the `contrapositionally complemented pseudo-Boolean algebra' (ccpBa) and `contrapositionally complemented pseudo-Boolean…
Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-valued, Rough and Perp Semantics
Arun Kumar, Mohua Banerjee
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with t…