Formalizations of certain intermediate logics Part I

On Implicational Intermediate Logics Axiomatizable by Formulas Minimal in Classical Logic: A Counter-Example to the Komori–Kashima Problem

Studia Logica ◽

10.1007/s11225-021-09955-0 ◽

2021 ◽

Author(s):

Yoshiki Nakamura ◽

Naosuke Matsuda

Keyword(s):

Classical Logic ◽

Counter Example ◽

Intermediate Logics

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Intermediate logics preserving admissible inference rules of heyting calculus

Mathematical Logic Quarterly ◽

10.1002/malq.19930390144 ◽

1993 ◽

Vol 39 (1) ◽

pp. 403-415 ◽

Cited By ~ 3

Author(s):

Vladimir V. Rybakov

Keyword(s):

Inference Rules ◽

Intermediate Logics ◽

Admissible Inference Rules

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Intermediate Logics

Applied Logic Series - Goal-Directed Proof Theory ◽

10.1007/978-94-017-1713-7_3 ◽

2000 ◽

pp. 93-115

Author(s):

Dov M. Gabbay ◽

Nicola Olivetti

Keyword(s):

Intermediate Logics

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Hypertableau and Path-Hypertableau Calculi for some Families of Intermediate Logics

Lecture Notes in Computer Science - Automated Reasoning with Analytic Tableaux and Related Methods ◽

10.1007/10722086_15 ◽

2000 ◽

pp. 160-174 ◽

Cited By ~ 3

Author(s):

Agata Ciabattoni ◽

Mauro Ferrari

Keyword(s):

Intermediate Logics

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Proof analysis in intermediate logics

Archive for Mathematical Logic ◽

10.1007/s00153-011-0254-7 ◽

2011 ◽

Vol 51 (1-2) ◽

pp. 71-92 ◽

Cited By ~ 39

Author(s):

Roy Dyckhoff ◽

Sara Negri

Keyword(s):

Intermediate Logics ◽

Proof Analysis

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HEREDITARILY STRUCTURALLY COMPLETE POSITIVE LOGICS

The Review of Symbolic Logic ◽

10.1017/s1755020319000169 ◽

2019 ◽

Vol 13 (3) ◽

pp. 483-502 ◽

Cited By ~ 1

Author(s):

ALEX CITKIN

Keyword(s):

Intermediate Logics ◽

Positive Logic ◽

Image Position

AbstractPositive logics are $\{ \wedge , \vee , \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.

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On finite approximability of ?-intermediate logics

Studia Logica ◽

10.1007/bf00373493 ◽

1982 ◽

Vol 41 (1) ◽

pp. 67-73

Author(s):

Wies?aw Dziobiak

Keyword(s):

Intermediate Logics ◽

Finite Approximability

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Tsutomu Hosoi. On intermediate logics. Journal of the Faculty of Science, University of Tokyo, section I, vol. 14 (1967), pp. 293–312, and vol. 16 (1969), pp. 1–12.

Journal of Symbolic Logic ◽

10.2307/2270285 ◽

1971 ◽

Vol 36 (2) ◽

pp. 329-330

Author(s):

A. S. Troelstra

Keyword(s):

Intermediate Logics

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Admissibility and refutation: some characterisations of intermediate logics

Archive for Mathematical Logic ◽

10.1007/s00153-014-0388-5 ◽

2014 ◽

Vol 53 (7-8) ◽

pp. 779-808 ◽

Cited By ~ 3

Author(s):

Jeroen P. Goudsmit

Keyword(s):

Intermediate Logics

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UNIFICATION IN INTERMEDIATE LOGICS

Journal of Symbolic Logic ◽

10.1017/jsl.2015.5 ◽

2015 ◽

Vol 80 (3) ◽

pp. 713-729 ◽

Cited By ~ 1

Author(s):

ROSALIE IEMHOFF ◽

PAUL ROZIÈRE

Keyword(s):

Intermediate Logics ◽

Unification Type

AbstractThis paper contains a proof–theoretic account of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments, the connection between valuations and most general unifiers is clarified, and it is shown how from the closure of a formula under the Visser rules a proof of the formula under a projective unifier can be obtained. This implies that in the logics considered, for the n-unification type to be finitary it suffices that the m-th Visser rule is admissible for a sufficiently large m. At the end of the paper it is shown how these results imply several well-known results from the literature.

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