TY - GEN
T1 - A note on extensions
T2 - International Symposium on Logical Foundations of Computer Science, LFCS 2013
AU - Goudsmit, Jeroen
PY - 2013/12/1
Y1 - 2013/12/1
N2 - Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.
AB - Any intermediate logic with the disjunction property admits the Visser rules if and only if it has the extension property. This equivalence restricts nicely to the extension property up to n. In this paper we demonstrate that the same goes even when omitting the rule ex falso quod libet, that is, working over minimal rather than intuitionistic logic. We lay the groundwork for providing a basis of admissibility for minimal logic, and tie the admissibility of the Mints-Skura rule to the extension property in a stratified manner.
KW - Admissible rules
KW - Disjunction property
KW - Extensions of Kripke models
KW - Minimal logic
UR - http://www.scopus.com/inward/record.url?scp=84892934733&partnerID=8YFLogxK
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U2 - 10.1007/978-3-642-35722-0_15
DO - 10.1007/978-3-642-35722-0_15
M3 - Conference contribution
AN - SCOPUS:84892934733
SN - 9783642357213
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 206
EP - 218
BT - Logical Foundations of Computer Science - International Symposium, LFCS 2013, Proceedings
Y2 - 6 January 2013 through 8 January 2013
ER -