Semantisches Browsen
Aus International Center for Computational Logic
Every modal logic L gives rise to the cons … Every modal logic L gives rise to the consequence relation that relates formulas phi and psi iff psi is true in a world of an L-model whenever phi is true in that world. We consider the following algorithmic problem for L. Given two modal formulas phi1 and phi2, decide whether their conjunction is a conservative extension of phi1 in the sense that whenever psi is a consequence of the conjunction of phi1 and phi2 and psi does not contain propositional variables not occurring in phi1, then psi is already a consequence of phi1.. We first prove that the conservativeness problem is co-NExpTime-hard for all modal logics of unbounded width (which have rooted frames with more than N successors of the root, for any N smaller than omega. Then we show that this problem is (i) co-NExpTime-complete for S5 and K, (ii) in ExpSpace for S4 and (iii) ExpSpace-complete for GL.3 (the logic of finite strict linear orders). The proofs for S5 and K use the fact that these logics have uniform interpolants of exponential size. uniform interpolants of exponential size. +
@inproceedings{ GhiLuWoZa-06,
author = {S. {Ghilardi} and C. {Lutz} and F. {Wolter} and M. {Zakharyaschev}},
booktitle = {Advances in Modal Logics Volume 6},
editor = {Guido {Governatori} and Ian {Hodkinson} and Yde {Venema}},
pages = {187--207},
publisher = {College Publications},
title = {Conservative Extensions in Modal Logics},
year = {2006},
}
author = {S. {Ghilardi} and C. {Lutz} and F. {Wolter} and M. {Zakharyaschev}},
booktitle = {Advances in Modal Logics Volume 6},
editor = {Guido {Governatori} and Ian {Hodkinson} and Yde {Venema}},
pages = {187--207},
publisher = {College Publications},
title = {Conservative Extensions in Modal Logics},
year = {2006},
}
Ghilardi +
S. Ghilardi, Carsten Lutz, Frank Wolter, M … S. Ghilardi, Carsten Lutz, Frank Wolter, M. Zakharyaschev<br/> '''[[LATPub338|<b>Conservative Extensions in Modal Logics</b>]]''' <br/>__NOTOC__In Guido Governatori and Ian Hodkinson and Yde Venema, eds., <i>Advances in Modal Logics Volume 6</i>, 187-207, 2006. College Publications<br/><span class="fas fa-chevron-right" style="font-size: 85%;" ></span> [[LATPub338|Details]] <span class="fas fa-chevron-right" style="font-size: 85%; margin-left: 2ex; "></span> [[Media:GhiLuWoZa-AiML06.pdf|Download]]GhiLuWoZa-AiML06.pdf|Download]] +
S. Ghilardi, Carsten Lutz, Frank Wolter, M … S. Ghilardi, Carsten Lutz, Frank Wolter, M. Zakharyaschev<br/> '''[[LATPub338/en|<b>Conservative Extensions in Modal Logics</b>]]''' <br/>__NOTOC__In Guido Governatori and Ian Hodkinson and Yde Venema, eds., <i>Advances in Modal Logics Volume 6</i>, 187-207, 2006. College Publications<br/><span class="fas fa-chevron-right" style="font-size: 85%;" ></span> [[LATPub338|Details]] <span class="fas fa-chevron-right" style="font-size: 85%; margin-left: 2ex;" ></span> [[Media:GhiLuWoZa-AiML06.pdf|Download]]GhiLuWoZa-AiML06.pdf|Download]] +
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Conservative Extensions in Modal Logics +
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25. März 2015, 14:34:05 +
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