A complete axiomatisation for the logic of lattice effect algebras. (English) Zbl 1523.03030
Summary: In a recent work D. J. Foulis and S. Pulmannová [Stud. Log. 100, No. 6, 1291–1315 (2012; Zbl 1273.03173)] studied the logical connectives in lattice effect algebras. In this paper we extend their study and investigate further the logical calculus for which the lattice effect algebras can serve as semantic models. We shall first focus on some properties of lattice effect algebras and will then give a complete axiomatisation of this logic.
MSC:
| 03G12 | Quantum logic |
| 81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
| 06C15 | Complemented lattices, orthocomplemented lattices and posets |
Citations:
Zbl 1273.03173References:
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