Proper Multi-Type Display Calculi for Rough Algebras
Giuseppe Greco, Fei Liang, Krishna Manoorkar, and Alessandra, Palmigiano
TL;DR
This paper introduces proper multi-type display calculi for various types of rough algebras, ensuring soundness, completeness, and desirable proof-theoretic properties through an algebraic and multi-type approach.
Contribution
It develops a unified framework of multi-type display calculi for multiple rough algebraic structures, advancing proof-theoretic methods in this area.
Findings
Calculi are sound and complete for the targeted logics.
Calculi enjoy cut elimination and subformula property.
Framework applies to topological and pre-rough algebras.
Abstract
In the present paper, we endow the logics of topological quasi Boolean algebras, topological quasi Boolean algebras 5, intermediate algebras of types 1-3, and pre-rough algebras with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis and applies the principles of the multi-type methodology in the design of display calculi.
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