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Abstract: . We study how a logic C+J conbining classical logic C and intuitionistic logic J can be defined. We show that its Hilbert axiomatization cannot be attained by simply extending the union of the axiomatizations of C and J by so called interaction axioms. Such a logic would collapse into classical logic. 1. Introduction In this short note we study how a logic C+J containing classical logic C as well as intuitionistic logic J can be defined. Precisely, we shall study intuitionistic implication... (Update)
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.... proof theoretic level it is possible to avoid the collapse by constraining the use of the axiom ( 1 ( 2 1 ) as proposed in [dCH96]. But at the model theoretic level it is an open problem how to avoid the collapse. It should be noted that it is necessary to be able to...
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BibTeX entry: (Update)
L. F. del Cerro and A. Herzig. Combining classical and intuitionistic logic. In F. Baader and K. Schulz, editors, Frontiers of Combining Systems, pages 93--102. Kluwer Academic Publishers, 1996. http://citeseer.ist.psu.edu/cerro96combining.html More
@inproceedings{ cerro96combining,
author = "Luis Fari{\~{n}}as del Cerro and Andreas Herzig",
title = "Combining Classical and Intuitionistic Logic, or: Intuitionistic Implication as a Conditional",
booktitle = "Frontiers of Combining Systems: Proceedings of the 1st International Workshop, Munich (Germany)",
publisher = "Kluwer Academic Publishers",
editor = "F.~Baader and K. U.~Schulz",
pages = "93--102",
year = "1996",
url = "citeseer.ist.psu.edu/cerro96combining.html" }
Citations (may not include all citations):134 Labelled Deductive Systems (context) - Gabbay - 1996
130 The computational complexity of provability in systems of mo.. (context) - Ladner - 1977
48 Semantical analysis of intuitionistic logic (context) - Kripke - 1965
25 Intuitionistic propositional logic is polynomial-space compl.. (context) - Statman - 1979
19 Normal multimodal logics (context) - Catach - 1988
13 How completeness and correspondence theory got married (context) - Kracht - 1993
10 Interval semantics for tense logic: some remarks (context) - Humberstone - 1979
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