The Godel-McKinsey-Tarski embedding for infinitary intuitionistic logic and its extensions

Article Mathematics, Applied

From axioms to synthetic inference rules via focusing

Sonia Marin et al.

Summary: This paper examines the construction of synthetic inference rules using theories composed of bipolars. It explores the key step of transforming formulas into synthetic inference rules and demonstrates the flexibility of different approaches in this process.

ANNALS OF PURE AND APPLIED LOGIC (2022)

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Article Mathematics

Duality for κ-additive complete atomic modal algebras

Yoshihito Tanaka

Summary: This paper demonstrates the duality between the category of.-additive complete atomic modal algebras and the category of kappa-downward directed multi-relational Kripke frames. It discusses the relationship between these categories and presents two different proofs for the duality theorem. The proofs are based on existing duality theorems and ideas from previous researchers.

ALGEBRA UNIVERSALIS (2021)

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Article Computer Science, Theory & Methods

Neighbourhood semantics and labelled calculus for intuitionistic infinitary logic

Matteo Tesi et al.

Summary: Neighbourhood semantics for intuitionistic logic extended with countable conjunctions and disjunctions is introduced and shown equivalent to topological semantics, with an indirect completeness proof as payoff. The new semantics is used to obtain a labelled sequent calculus with good structural properties, demonstrating admissibility of weakening and contraction, invertibility with preservation of height for each rule, and cut elimination. Finally, a direct Tait-Schutte-Takeuti style form of completeness via the extraction of a countermodel from a failed proof search is proved.

JOURNAL OF LOGIC AND COMPUTATION (2021)

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Article Mathematics