- One-step Heyting algebras and hypersequent calculi with the bounded proof property
- Journal of Logic and Computation
- Volume | Issue number
- 27 | 7
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
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 axiomatized calculi. We introduce one-step Heyting algebras and establish a semantic criterion characterizing 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 BD2.
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