An implicational logic for orthomodular lattices
Orthomodular lattices were introduced to get an algebraic description of the propositional logic of quantum mechanics. In this paper, we set up axiomatization of this logic as a Hilbert style implicational logical system L, i.e., we present a set of axioms and derivation rules formulated in the sign...
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| Dokumentumtípus: | Cikk |
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Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 3-4 |
| Kulcsszavak: | Ortomoduláris rács, Algebrai logika, Derivációs szabály, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-813-6 |
| Online Access: | http://acta.bibl.u-szeged.hu/46317 |
| Tartalmi kivonat: | Orthomodular lattices were introduced to get an algebraic description of the propositional logic of quantum mechanics. In this paper, we set up axiomatization of this logic as a Hilbert style implicational logical system L, i.e., we present a set of axioms and derivation rules formulated in the signature {—> ,0}. The other logical operations V, A, are expressed in terms of implication (which is the so-called Dishkant implication) and falsum. We further show that the system L is algebraizable in the sense of Blok and Pigozzi, and that orthomodular lattices provide an equivalent algebraic semantics for it. |
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| Terjedelem/Fizikai jellemzők: | 383-394 |
| ISBN: | 0001-6969 |