An axiom system for orthomodular quantum logic
Studia Logica 40 (1):1 - 12 (1981)
| Abstract | Logical matrices for orthomodular logic are introduced. The underlying algebraic structures are orthomodular lattices, where the conditional connective is the Sasaki arrow. An axiomatic calculusOMC is proposed for the orthomodular-valid formulas.OMC is based on two primitive connectives — the conditional, and the falsity constant. Of the five axiom schemata and two rules, only one pertains to the falsity constant. Soundness is routine. Completeness is demonstrated using standard algebraic techniques. The Lindenbaum-Tarski algebra ofOMC is constructed, and it is shown to be an orthomodular lattice whose unit element is the equivalence class of theses ofOMC. | |||||||||
| 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 articlesRichard Holzer (2004). On Subdirectly Irreducible OMAs. Studia Logica 78 (1-2):261 - 277.
L. Herman, E. L. Marsden & R. Piziak (1975). Implication Connectives in Orthomodular Lattices. Notre Dame Journal of Formal Logic 16 (3):305-328.
Roger M. Cooke & Michiel Lambalgen (1983). The Representation of Takeuti's *20c ||_ -Operator. Studia Logica 42 (4):407 - 415.
Gary M. Hardegree (1981). Material Implication in Orthomodular (and Boolean) Lattices. Notre Dame Journal of Formal Logic 22 (2):163-182.
Roberto Giuntini (1987). Quantum Logics and Lindenbaum Property. Studia Logica 46 (1):17 - 35.
Yuichiro Kitajima (2008). Reichenbach’s Common Cause in an Atomless and Complete Orthomodular Lattice. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 47 (2):511-519.
G. N. Georgacarakos (1980). Equationally Definable Implication Algebras for Orthomodular Lattices. Studia Logica 39 (1):5 - 18.
J. C. Abbott (1976). Orthoimplication Algebras. Studia Logica 35 (2):173 - 177.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads20 ( #61,589 of 549,551 )Recent downloads (6 months)1 ( #63,397 of 549,551 )How can I increase my downloads? |
My notes
Discussion
