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Jadavpur University

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Representative Papers

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

Aug 05, 2026

This study addresses the problem of finite-state reduction in finitely-valued Heyting modal logics that preserves the exact truth values of formulas. Building on relational bi-topological duality, the work proposes a minimality-preserving reduction method by constructing an observational quotient structure via evaluation maps induced by modal subalgebras, ensuring that all formulas retain their precise truth values in the reduced model. The main contributions include proving that this observational quotient is isomorphic to a finite image within its bi-topological dual; constructing tree-shaped certificates of exact truth values for any formula and state, whose depth is bounded by modal depth and whose branching depends on the height of the truth-value algebra and the number of boxed subformulas; and, for the first time, providing bounded counterexample certificates that preserve exact falsity values in cases of truth-value failure.

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Latest Papers

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

Aug 05, 2026

This study addresses the problem of finite-state reduction in finitely-valued Heyting modal logics that preserves the exact truth values of formulas. Building on relational bi-topological duality, the work proposes a minimality-preserving reduction method by constructing an observational quotient structure via evaluation maps induced by modal subalgebras, ensuring that all formulas retain their precise truth values in the reduced model. The main contributions include proving that this observational quotient is isomorphic to a finite image within its bi-topological dual; constructing tree-shaped certificates of exact truth values for any formula and state, whose depth is bounded by modal depth and whose branching depends on the height of the truth-value algebra and the number of boxed subformulas; and, for the first time, providing bounded counterexample certificates that preserve exact falsity values in cases of truth-value failure.

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