Switch to: Citations

References in:

Finite Frames Fail: How Infinity Works Its Way into the Semantics of Admissibility

Jeroen P. Goudsmit

Studia Logica 104 (6):1191-1204 (2016)

Add references

You must login to add references.

Admissibility and refutation: some characterisations of intermediate logics.Jeroen P. Goudsmit - 2014 - Archive for Mathematical Logic 53 (7-8):779-808.details Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to construct refutation systems, employing techniques from the study of admissible rules. Concretely, we provide a refutation system for the intermediate logics of bounded branching, known as the Gabbay–de Jongh logics. We show that this gives a characterisation of these logics (...) Download Export citation Bookmark 3 citations
One hundred and two problems in mathematical logic.Harvey Friedman - 1975 - Journal of Symbolic Logic 40 (2):113-129.details Download Export citation Bookmark 62 citations
On Finite Model Property for Admissible Rules.Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner - 1999 - Mathematical Logic Quarterly 45 (4):505-520.details Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...) Download Export citation Bookmark 8 citations
Intermediate Logics and Visser's Rules.Rosalie Iemhoff - 2005 - Notre Dame Journal of Formal Logic 46 (1):65-81.details Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of Visser's rules. We apply these results to some specific intermediate logics and (...) Download Export citation Bookmark 25 citations
On the admissible rules of intuitionistic propositional logic.Rosalie Iemhoff - 2001 - Journal of Symbolic Logic 66 (1):281-294.details We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility. Download Export citation Bookmark 58 citations
Unification in intuitionistic logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.details We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras. Download Export citation Bookmark 65 citations
Unification, finite duality and projectivity in varieties of Heyting algebras.Silvio Ghilardi - 2004 - Annals of Pure and Applied Logic 127 (1-3):99-115.details We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object. Download Export citation Bookmark 18 citations

1