Quantum logical calculi and lattice structures
Journal of Philosophical Logic 7 (1):347 - 386 (1978)
| Abstract | In a preceding paper [1] it was shown that quantum logic, given by the tableaux-calculus T eff, is complete and consistent with respect to the dialogic foundation of logics. Since in formal dialogs the special property of the value-definiteness of propositions is not postulated, the calculus T eff represents a calculus of effective (intuitionistic) quantum logic.Beginning with the tableaux-calculus the equivalence of T eff to calculi which use more familiar figures such as sequents and implications can be investigated. In this paper we present a sequents-calculus of Gentzen-type and a propositional calculus of Brouwer-type which are shown to be equivalent to T eff. The effective propositional calculus provides an interpretation for a lattice structure, called quasi-implicative lattice. If, in addition, the value-definiteness of quantum mechanical propositions is postulated, a propositional calculus is obtained which provides an interpretation for a quasi-modular orthocomplemented lattice which, as is well-known, has as a model the lattice of subspaces of a Hilbert space. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,709 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesOthman Qasim Malhas (1987). Quantum Logic and the Classical Propositional Calculus. Journal of Symbolic Logic 52 (3):834-841.
Andrzej Wiśniewski (2004). Socratic Proofs. Journal of Philosophical Logic 33 (3):299-326.
Alexej P. Pynko (2009). Distributive-Lattice Semantics of Sequent Calculi with Structural Rules. Logica Universalis 3 (1).
Lars Hansen (2005). On an Algebra of Lattice-Valued Logic. Journal of Symbolic Logic 70 (1):282 - 318.
A. V. Kuznetsov & A. Yu Muravitsky (1986). On Superintuitionistic Logics as Fragments of Proof Logic Extensions. Studia Logica 45 (1):77 - 99.
Othman Qasim Malhas (1994). Abacus Logic: The Lattice of Quantum Propositions as the Poset of a Theory. Journal of Symbolic Logic 59 (2):501-515.
P. Mittelstaedt & E. -W. Stachow (1978). The Principle of Excluded Middle in Quantum Logic. Journal of Philosophical Logic 7 (1):181 - 208.
E. -W. Stachow (1976). Completeness of Quantum Logic. Journal of Philosophical Logic 5 (2):237 - 280.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads3 ( #202,107 of 549,681 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
