| Paper Abstract and Keywords |
| Presentation |
2008-12-05 12:40
A comparison of implications in orthomodular quantum logic
-- Morphological analysis of quantum logic --
Mitsuhiko Fujio (Kyushu Inst. of Tech.) |
| Abstract |
(in Japanese) |
(See Japanese page) |
| (in English) |
Morphological operators are generalized to lattices as adjunction pairs. In particular, Morphology for set lattices is applied to analyze logics through Kripke semantics. For example, a pair of Morphological operators as an adjunction gives rise to a temporalization of normal modal logic. Also, constructions of models for intuitionistic logic or linear logics can be described in terms of Morphological interior and/or closure operators. This shows that Morphological analysis can be applied to various non-classical logics.
On the other hand, quantum logics are algebraically formalized as orhomodular or modular ortho-complemented lattices, and shown to allow Kripke semantics. This suggest the possibility of Morphological analysis for quantum logics.
In this article, we consider the implication problem in quantum logics to show an efficiency of Morphological analysis for quantum logic. We will give a comparison of the 5 polynomial implication connectives available in quantum logics. |
| Keyword |
(in Japanese) |
(See Japanese page) |
| (in English) |
Mathematical Morphology / Kripke semantics / non-classical logic / quantum logic / implication connective / / / |
| Reference Info. |
IEICE Tech. Rep., vol. 108, no. 334, SIS2008-61, pp. 109-112, Dec. 2008. |
| Paper # |
SIS2008-61 |
| Date of Issue |
2008-11-27 (SIS) |
| ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
| Download PDF |
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| Conference Information |
| Committee |
SIS |
| Conference Date |
2008-12-04 - 2008-12-05 |
| Place (in Japanese) |
(See Japanese page) |
| Place (in English) |
Kansai Univ. |
| Topics (in Japanese) |
(See Japanese page) |
| Topics (in English) |
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| Paper Information |
| Registration To |
SIS |
| Conference Code |
2008-12-SIS |
| Language |
Japanese |
| Title (in Japanese) |
(See Japanese page) |
| Sub Title (in Japanese) |
(See Japanese page) |
| Title (in English) |
A comparison of implications in orthomodular quantum logic |
| Sub Title (in English) |
Morphological analysis of quantum logic |
| Keyword(1) |
Mathematical Morphology |
| Keyword(2) |
Kripke semantics |
| Keyword(3) |
non-classical logic |
| Keyword(4) |
quantum logic |
| Keyword(5) |
implication connective |
| Keyword(6) |
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| Keyword(7) |
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| 1st Author's Name |
Mitsuhiko Fujio |
| 1st Author's Affiliation |
Kyushu Institute of Technology (Kyushu Inst. of Tech.) |
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| Speaker |
Author-1 |
| Date Time |
2008-12-05 12:40:00 |
| Presentation Time |
30 minutes |
| Registration for |
SIS |
| Paper # |
SIS2008-61 |
| Volume (vol) |
vol.108 |
| Number (no) |
no.334 |
| Page |
pp.109-112 |
| #Pages |
4 |
| Date of Issue |
2008-11-27 (SIS) |
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