scholarly journals Admissibility and refutation: some characterisations of intermediate logics

2014 ◽  
Vol 53 (7-8) ◽  
pp. 779-808 ◽  
Author(s):  
Jeroen P. Goudsmit
Keyword(s):  
Intermediate Logics

Intermediate Logics

2000 ◽  
pp. 93-115
Author(s):  
Dov M. Gabbay ◽  
Nicola Olivetti
Keyword(s):  
Intermediate Logics

Proof analysis in intermediate logics

2011 ◽  
Vol 51 (1-2) ◽  
pp. 71-92 ◽  
Author(s):  
Roy Dyckhoff ◽  
Sara Negri
Keyword(s):  
Intermediate Logics ◽  
Proof Analysis

HEREDITARILY STRUCTURALLY COMPLETE POSITIVE LOGICS

2019 ◽  
Vol 13 (3) ◽  
pp. 483-502 ◽  
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.

On finite approximability of ?-intermediate logics

Studia Logica ◽  
1982 ◽  
Vol 41 (1) ◽  
pp. 67-73
Author(s):  
Wies?aw Dziobiak
Keyword(s):  
Intermediate Logics ◽  
Finite Approximability

scholarly journals UNIFICATION IN INTERMEDIATE LOGICS

2015 ◽  
Vol 80 (3) ◽  
pp. 713-729 ◽  
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.

scholarly journals GEOMETRISATION OF FIRST-ORDER LOGIC

2015 ◽  
Vol 21 (2) ◽  
pp. 123-163 ◽  
Author(s):  
ROY DYCKHOFF ◽  
SARA NEGRI
Keyword(s):  
Proof Theory ◽  
Normal Forms ◽  
Order Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Conservative Extension ◽  
First Order ◽  
First Order Theory ◽  
Intermediate Logics ◽  
Normal Form Theorem

AbstractThat every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms.

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