arXiv subjects

Prakash Chandra Mali

Publications and source records attributed to Prakash Chandra Mali.

3 recordsLinked to original sources

arXiv2026

A Bitopological Approach to Finite Reduction and Bounded Exact-Value Certificates for Fitting's Finite Heyting-valued Modal Logic

Fitting's finite Heyting-valued modal logic interprets modal formulas over a finite Heyting algebra. We use a relational bitopological representation to obtain a finite-state reduction. For a finite model and a finite vocabulary, the modal subalgebra generated by the atomic valuations determines a state-evaluation map. We prove that the observational quotient is isomorphic to its finite image in the bitopological dual and that the quotient relation is the restriction of the canonical dual relation. Hence every formula over the vocabulary preserves its exact truth value, and the quotient is minimal among surjective reductions through which all generated observations factor. In addition, for any formula and state, we construct a finite tree-like exact-value certificate whose depth is bounded by modal depth and whose branching depends only on the height of the truth-value algebra and the number of boxed subformulas. Failed formulas therefore admit bounded reduced counterexamples preserving their precise failure values.

cs.LO↗

arXiv2025

Duality for Fitting's Multi-valued Modal logic via bitopology and biVietoris coalgebra

Fitting's Heyting-valued logic and Heyting-valued modal logic have already been studied from an algebraic viewpoint. In addition to algebraic axiomatizations with the completeness of Fitting's Heyting-valued logic and Heyting-valued modal logic, both topological and coalgebraic dualities have also been developed for algebras of Fitting's Heyting-valued modal logic. Bitopological methods have recently been employed to investigate duality for Fitting's Heyting-valued logic. However, the concepts of bitopology and bi-Vietoris coalgebras are conspicuously absent from the development of dualities for Fitting's many-valued modal logic. With this study, we try to bridge that gap. The main results are bitopological and coalgebraic duality for Fitting's many-valued modal logic. We develop a bitopological duality for algebras of Fitting's Heyting-valued modal logic by extending known bitopological duality for Fitting's non-modal logic. To develop coalgebraic duality, we adapt Lauridsen's bi-Vietoris construction from the category of pairwise Stone spaces to the category $PBS_{\mathcal{L}}$ of $\mathcal{L}$-valued (with $\mathcal{L}$ a bounded finite distributive lattice, i.e., a Heyting algebra) pairwise Boolean spaces by incorporating a structure map, and from this obtain the $\mathcal{L}$-biVietoris functor. Finally, we establish dual equivalence between coalgebras for the $\mathcal{L}$-biVietoris functor and algebras of Fitting's $\mathcal{L}$-valued modal logic. As a result, we conclude that Fitting's Heyting-valued modal logic is sound and complete with respect to the coalgebras of the $\mathcal{L}$-biVietoris functor. We also apply this coalgebraic approach to the bitopological duality to show the existence of cofree and final coalgebras and to establish a Hennessy-Milner property.

cs.LO↗

arXiv2022

Coalgebraic Fuzzy geometric logic

The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric logic. To define the modal operators, we introduce a notion of fuzzy-open predicate lifting. Based on coalgebras for an endofunctor $T$ on the category $\textbf{Fuzzy-Top}$ of fuzzy topological spaces and fuzzy continuous maps, we build models for the coalgebraic fuzzy geometric logic. Bisimulations for the defined models are discussed in this work.

cs.LO↗