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Representative Papers

Multimodal Logic Programming with Full Formulas

Aug 14, 2026

This study addresses the limitation of existing multimodal logic programming systems restricted to Horn clauses by proposing MMLP, a system supporting arbitrary formulas as both programs and queries. Grounded in nested proof calculus and a permission set unification algorithm, the approach integrates finite syntactic certificates with focused search strategies to achieve cut-free completeness and termination under Hilbert semantics. Experimental results demonstrate that MMLP produces correct answers with complete solution coverage. While equivalent to KDI4s5-MPROLOG on common fragments, MMLP significantly overcomes prior syntactic constraints, offering enhanced expressiveness and theoretical completeness for multimodal logic programming.

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Component Modalities of Quantum Logic

Jul 16, 2026

This study investigates the structural and proof-theoretic issues arising from forcing conditions in relational quantum modal logic, with a focus on the coherence of modal transitions across compatible worlds. By introducing a notion of compatibility component structures, the work establishes, for the first time, a connection between such structures and central propositional approximations, characterizing upper and lower approximations of stable propositions within superselection models. Leveraging relational semantics, Boolean algebras, and local validity semantics—combined with connectedness constructions and maximal consistent pair techniques—the authors build a canonical model and formulate a unified logical system. The paper proves that the multi-conclusion sequent calculi extended with axioms T, 4, and B are complete with respect to component frames, equivalence frames, and connected compatibility frames, thereby establishing a comprehensive proof theory for component modal logics.

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Decidability of Quantum Modal Logic

Mar 18, 2026

This study addresses the decidability problem in quantum modal logic—specifically, whether there exists an effective algorithm to determine if an arbitrary formula is a theorem. To this end, the paper introduces Harrop’s lemma into this logical framework for the first time, combining formal reasoning techniques with decidability analysis to rigorously establish the decidability of quantum modal logic. This result not only fills a critical gap in the proof-theoretic understanding of the system but also provides a solid theoretical foundation for future work on automated reasoning and algorithmic implementation within this logic.

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Latest Papers

Multimodal Logic Programming with Full Formulas

Aug 14, 2026

This study addresses the limitation of existing multimodal logic programming systems restricted to Horn clauses by proposing MMLP, a system supporting arbitrary formulas as both programs and queries. Grounded in nested proof calculus and a permission set unification algorithm, the approach integrates finite syntactic certificates with focused search strategies to achieve cut-free completeness and termination under Hilbert semantics. Experimental results demonstrate that MMLP produces correct answers with complete solution coverage. While equivalent to KDI4s5-MPROLOG on common fragments, MMLP significantly overcomes prior syntactic constraints, offering enhanced expressiveness and theoretical completeness for multimodal logic programming.

0 citationsRead paper

Component Modalities of Quantum Logic

Jul 16, 2026

This study investigates the structural and proof-theoretic issues arising from forcing conditions in relational quantum modal logic, with a focus on the coherence of modal transitions across compatible worlds. By introducing a notion of compatibility component structures, the work establishes, for the first time, a connection between such structures and central propositional approximations, characterizing upper and lower approximations of stable propositions within superselection models. Leveraging relational semantics, Boolean algebras, and local validity semantics—combined with connectedness constructions and maximal consistent pair techniques—the authors build a canonical model and formulate a unified logical system. The paper proves that the multi-conclusion sequent calculi extended with axioms T, 4, and B are complete with respect to component frames, equivalence frames, and connected compatibility frames, thereby establishing a comprehensive proof theory for component modal logics.

0 citationsRead paper

Decidability of Quantum Modal Logic

Mar 18, 2026

This study addresses the decidability problem in quantum modal logic—specifically, whether there exists an effective algorithm to determine if an arbitrary formula is a theorem. To this end, the paper introduces Harrop’s lemma into this logical framework for the first time, combining formal reasoning techniques with decidability analysis to rigorously establish the decidability of quantum modal logic. This result not only fills a critical gap in the proof-theoretic understanding of the system but also provides a solid theoretical foundation for future work on automated reasoning and algorithmic implementation within this logic.

0 citationsRead paper