Quasilinear QMV Algebras

Roberto Giuntini

doi:10.1007/bf00676251

Quasilinear QMV Algebras

International Journal of Theoretical Physics ◽

10.1007/bf00676251 ◽

1995 ◽

Vol 34 (8) ◽

pp. 1397-1407 ◽

Cited By ~ 9

Author(s):

Roberto Giuntini

Keyword(s):

Qmv Algebras

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MEANDERS IN ORTHOPOSETS AND QMV ALGEBRAS

Demonstratio Mathematica ◽

10.1515/dema-2001-0102 ◽

2001 ◽

Vol 34 (1) ◽

pp. 1-12

Author(s):

A. Dvurečenskij ◽

S. Pulmannová ◽

S. Salvati

Keyword(s):

Qmv Algebras

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A direct product decomposition of QMV algebras

Science China Mathematics ◽

10.1007/s11425-011-4310-x ◽

2012 ◽

Vol 55 (4) ◽

pp. 841-850

Author(s):

Xian Lu ◽

Yun Shang ◽

RuQian Lu

Keyword(s):

Direct Product ◽

Product Decomposition ◽

Direct Product Decomposition ◽

Qmv Algebras

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Automata theory based on unsharp quantum logic

Mathematical Structures in Computer Science ◽

10.1017/s0960129509007701 ◽

2009 ◽

Vol 19 (4) ◽

pp. 737-756 ◽

Cited By ~ 5

Author(s):

YUN SHANG ◽

XIAN LU ◽

RUQIAN LU

Keyword(s):

Quantum Logic ◽

Finite Automata ◽

Automata Theory ◽

Quantum Structures ◽

Closure Properties ◽

Mv Algebra ◽

Quantum Finite Automata ◽

Distributive Law ◽

Qmv Algebras ◽

Mv Algebras

By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and only if a certain kind of distributive law holds for the sum operation. We introduce the notions of (quantum) finite automata based on these two unsharp quantum structures, and discuss closure properties of languages and the subset construction of automata. We show that the universal validity of some important properties (such as sum, concatenation and subset constructions) depend heavily on the above distributive law. These generalise results about automata theory based on sharp quantum logic.

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