We investigate proof-theoretic properties of hypersequent calculi for intermediate logics using algebraic methods. More precisely, we consider a new weakly analytic subformula property (the bounded proof property) of such calculi. Despite being strictly weaker than both cut-elimination and the subformula property this property is sufficient to ensure decidability of finitely axiomatised calculi. We introduce one-step Heyting algebras and establish a semantic criterion characterising calculi for intermediate logics with the bounded proof property and the finite model property in terms of one-step Heyting algebras. Finally, we show how this semantic criterion can be applied to a number of calculi for well-known intermediate logics such as LC, KC and BD_2 .
One-Step Heyting Algebras and Hypersequent Calculi with the Bounded Proof Property / N. Bezhanishvili, S. Ghilardi, F. Moellestrom Lauridsen. - In: JOURNAL OF LOGIC AND COMPUTATION. - ISSN 0955-792X. - (2016). [Epub ahead of print] [10.1093/logcom/exw029]
One-Step Heyting Algebras and Hypersequent Calculi with the Bounded Proof Property
S. GhilardiSecondo
;
2016
Abstract
We investigate proof-theoretic properties of hypersequent calculi for intermediate logics using algebraic methods. More precisely, we consider a new weakly analytic subformula property (the bounded proof property) of such calculi. Despite being strictly weaker than both cut-elimination and the subformula property this property is sufficient to ensure decidability of finitely axiomatised calculi. We introduce one-step Heyting algebras and establish a semantic criterion characterising calculi for intermediate logics with the bounded proof property and the finite model property in terms of one-step Heyting algebras. Finally, we show how this semantic criterion can be applied to a number of calculi for well-known intermediate logics such as LC, KC and BD_2 .File | Dimensione | Formato | |
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