2025/07/08 by Matteo De Berardinis, De Berardinis, Matteo, Silvio Ghilardi +1 · 2 citations
Computer Science · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2507.06007
In a previous paper, we showed that profinite L-algebras (where L is a variety of modal algebras generated by its finite members) are monadic over Set. This monadicity result suggests that profinite L-algebras could be presented as Lindenbaum algebras for propositional theories in infinitary versions of propositional modal calculi. In this paper we identify such calculi as modal enrichments of Maehara-Takeuti's infinitary extension of the sequent calculus LK. We also investigate correspondences between syntactic properties of the calculi and regularity/exactness properties of the opposite category of profinite L-algebras.