Algebraic structures in the vicinity of pre-rough algebra and their logics

Proper Multi-Type Display Calculi for Rough Algebras

“…Very recently, sequent calculi with cut elimination and a non-standard version of subformula property have been introduced in [20] for some of these logics, but not for the logic of the so-called intermediate algebras of type 3 (cf. [23], Definition 2.11). In these calculi, the subformula property is non-standard because each logical connective has four introduction rules, two of which are non-standard and introduce the given logical connective under the scope of negation.…”

Logics for Rough Concept Analysis

“…This paper continues a line of investigation started in [9] and aimed at introducing sequent calculi for the logics of varieties of 'rough algebras', introduced and discussed in [1,19]. The 'rough algebras' considered in the present paper are nondistributive (i.e.…”

“…Conditions (17) define the'Kent algebra' counterparts of topological quasi Boolean algebras 5 (tqBa5) [19]. In the next definition, we introduce 'Kent algebra' counterparts of some other varieties considered in [19], and also varieties characterized by interaction axioms between lax and strict connectives which follow the pattern of the 5-axioms in rough algebras.…”

Rough concepts

“…The links between rough set theory and proof theory are mainly mediated by the theory of the varieties of algebras introduced in connection with approximation spaces. In [68], sequent calculi which are sound and complete but without cut elimination are defined for the logics naturally associated with the classes of algebras discussed in [67]. Sequent calculi with cut elimination and a non-standard version of subformula property have been introduced in [54] for some but not all of these logics.…”