Algebraic Metods in Multivalued Logics
Algebraické metody ve vícehodnotových logikách
dizertační práce (OBHÁJENO)
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Trvalý odkaz
http://hdl.handle.net/20.500.11956/35447Identifikátory
SIS: 39761
Kolekce
- Kvalifikační práce [10690]
Autor
Vedoucí práce
Oponent práce
Navara, Mirko
Dvurečenskij, Anatolij
Fakulta / součást
Matematicko-fyzikální fakulta
Obor
Algebra, teorie čísel a matematická logika
Katedra / ústav / klinika
Katedra algebry
Datum obhajoby
23. 9. 2010
Nakladatel
Univerzita Karlova, Matematicko-fyzikální fakultaJazyk
Angličtina
Známka
Prospěl/a
In the thesis we deal with a binary operation that acts as abstract "symmetric difference". We endow orthocomplemented lattices with this operation and obtain a new class of algebras. We call these algebras orthocomplemented difference lattices (ODLs). We first see that the ODLs form a class that contains Boolean algebras and is contained in orthomodular lattices (OMLs). In the subsequent analysis we study algebraic properties of ODLs (identities valid in classes of ODLs, peculiarities connected with free ODLs, etc.) and find a characterization of set-representable ODLs. We then ask a natural question of which OML can be made (resp. can be enlarged to) an ODL. We exhibit several constructions - quite involved in places - that deepen the understanding of intrinsic properties of ODLs. As a rather surprising result in this line we find a connection with Z2-valued measures. In the end we relax the lattice condition imposed on ODLs. We obtain orthocomplemented difference posets. We then formulate and clarify several questions related to non-lattice "quantum logics".