Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/proof-analysis-in-intermediate-logics-gbyGlNimfB
References (48)
-
Saul Kripke (1959)
A completeness theorem in modal logicJournal of Symbolic Logic, 24
-
M. Dummett, E. Lemmon, Iwao Nishimura, D. Makinson (1967)
Modal Logics Between S4 and S5 -
A. Avellone, Mauro Ferrari, P. Miglioli (1999)
Duplication-Free Tableau Calculi and Related Cut-Free Sequent Calculi for the Interpolable Propositional Intermediate LogicsLog. J. IGPL, 7
-
S. Negri, J. Plato (2011)
Proof Analysis -
D. Gabbay (1996)
Labelled Deductive Systems. Oxford Logic Guides, vol. 33 -
(1986)
Eine Interpretation des intuitionistischen Aussagenkalküls -
V. Jankov (1968)
The Calculus of the Weak "law of Excluded Middle"Mathematics of The Ussr-izvestiya, 2
-
Sara Negri (2003)
Contraction-free sequent calculi for geometric theories with an application to Barr's theoremArchive for Mathematical Logic, 42
-
Sara Negri (2010)
Kripke completeness revisited -
(1966)
Tree proofs in modal logic (abstract) -
N. Olivetti, G. Pozzato, C. Schwind (2004)
A Sequent Calculus and Theorem Prover for Standard Conditional Logics -
Sara Negri (2005)
Proof Analysis in Modal LogicJournal of Philosophical Logic, 34
-
(1967)
An invertible sequential version of the constructive predicate calculus -
(1933)
English tr -
K. Brünnler, A. Guglielmi (2004)
First-Order Logic Revisited -
Mauro Ferrari, P. Miglioli (1993)
Counting the maximal intermediate constructive logicsJournal of Symbolic Logic, 58
-
Sara Negri, J. Plato (1998)
Cut Elimination in the Presence of AxiomsBulletin of Symbolic Logic, 4
-
M. Baaz, Rosalie Iemhoff (2008)
On Skolemization in constructive theoriesJournal of Symbolic Logic, 73
-
A. Simpson (1994)
The proof theory and semantics of intuitionistic modal logic -
G. Holmström-Hintikka, Sten Lindström, R. Sliwinski (2001)
Provability in Logic -
A cut-free sequent system for Grzegorczyk logic, with an application to the provability interpretation of intuitionistic logic -
Sara Negri, J. Plato (2004)
Proof systems for lattice theoryMathematical Structures in Computer Science, 14
-
(1944)
Untersuchungen zum Prädikatenkalkül -
Sara Negri (2011)
Proof Theory for Modal LogicPhilosophy Compass, 6
-
R. Dyckhoff (1999)
A Deterministic Terminating Sequent Calculus for Gödel-Dummett logicLog. J. IGPL, 7
-
Sara Negri, J. Plato (2001)
Structural proof theory -
M. Fitting (1983)
Proof Methods for Modal and Intuitionistic Logics -
(1998)
Handbook of Tableaux Methods -
Sara Negri, J. Plato, T. Coquand (2004)
Proof-theoretical analysis of order relationsArchive for Mathematical Logic, 43
-
P. Blackburn, M. Rijke, Y. Venema (2001)
Modal Logic, 53
-
H. Wansing (1998)
Displaying Modal Logic -
Kai Bruennler, Alessio Guglielmi (2004)
A First Order System with Finite Choice of Premises -
II. Mathematisches (1996)
Power and Weakness of the Modal Display Calculus -
R. Dyckhoff, Sara Negri (2006)
Decision methods for linearly ordered Heyting algebrasArchive for Mathematical Logic, 45
-
A. Ciabattoni, Lutz Straßburger, K. Terui (2009)
Expanding the Realm of Systematic Proof Theory -
L. Wallen (1990)
Automated Deduction in Non-classical Logic -
L. Maksimova (1979)
Interpolation properties of superintuitionistic logicsStudia Logica, 38
-
Rosalie Iemhoff (2006)
On the rules of intermediate logicsArchive for Mathematical Logic, 45
-
G. Mints (2000)
A Short Introduction to Intuitionistic Logic -
A. Troelstra, H. Schwichtenberg (1996)
Basic proof theory, 43
-
J. McKinsey, A. Tarski (1948)
Some theorems about the sentential calculi of Lewis and HeytingThe Journal of Symbolic Logic, 13
-
L. Pinto, Tarmo Uustalu (2009)
Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents -
L. Viganò (2000)
Labelled non-classical logics -
R. Goré (1999)
Tableau Methods for Modal and Temporal Logics -
M. Fitting (1998)
Proof Methods for Modal and Intuitionistic Logics. Synthese Library, vol. 169 -
S. Negri (2009)
Acts of Knowledge—History, Philosophy and Logic -
Saul Kripke (1965)
Semantical Analysis of Intuitionistic Logic IStudies in logic and the foundations of mathematics, 40
-
A. Ciabattoni, Nikolaos Galatos, K. Terui (2008)
From Axioms to Analytic Rules in Nonclassical Logics2008 23rd Annual IEEE Symposium on Logic in Computer Science
- Publisher
- Springer Journals
- Copyright
- Copyright © 2011 by Springer-Verlag
- Subject
- Mathematics; Algebra; Mathematical Logic and Foundations; Mathematics, general
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-011-0254-7
- Publisher site
- See Article on Publisher Site
Abstract
Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the explanation of the rules.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Nov 20, 2011