206 citations
- University of HelsinkiFI96 papers
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8 papers · 1 filter
Axiomatizing modal inclusion logic and its variants
Aleksi Anttila, Matilda Häggblom, Fan Yang
We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal for…
Esakia Duals of Regular Heyting Algebras
Gianluca Grilletti, Davide Emilio Quadrellaro
We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we give a characterisation of Esakia spaces dual to regular Heyting algebras and…
Sort logic and foundations of mathematics
Jouko Väänänen
I have argued elsewhere that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and…
Compactness in Team Semantics
Joni Puljujärvi, Davide Emilio Quadrellaro
We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon Lück's ultraproduct construction for team semanti…
Inner Models from Extended Logics: Part 2
Juliette Kennedy, Menachem Magidor, Jouko Väänänen
We introduce a new inner model arising from stationary logic. We show that assuming a proper class of Woodin cardinals, or alternatively , the regular uncountable…
Dependence Logic with Generalized Quantifiers: Axiomatizations
Fredrik Engström, Juha Kontinen, Jouko Väänänen
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpret…