DocumentCode :
3081194
Title :
A note on triangulation of PostAlgebras and ≪leibnizian≫ lattices
Author :
Serfati, Michel
Author_Institution :
Inst. de Recherche sur l´´Enseignement des Mathematiques, Paris VII Univ., France
fYear :
2005
fDate :
19-21 May 2005
Firstpage :
221
Lastpage :
226
Abstract :
One first defines the triangles of a lattice T, that is, the lattices Δs(T) of all decreasing sequences of s elements of T, and study some basic properties (modularity, distributivity, boundedness, atomisticity, inf-pseudo complementation, monotonic representations) of Δs(T). An important result is: if T is a Boolean algebra, then Δs(T) is a Post algebra (of order (s+1)); one specially discusses the case when T is the powerset P(Ω):Δs(T) is then isomorphic to the postian lattice Ps+1(Ω) of the (s+1)-ordered partitions of Q, which is a multivalued genereralization of the powerset. Afterwards, one studies some cases where T is, in turn, a Post algebra, specially T=Pr(Ω). One then exhibits some typical finite distributive lattices called leibnizians, denoted s-1> and also defines, with the help of triangulation, the lattices Ps, r(Ω) which are called the postians of type (s, r) of a set Ω. Actually both structures (leibnizians as well as postians) turn out to be important algebraic condensations of Post multivalued logical conceptions.
Keywords :
Boolean algebra; multivalued logic; set theory; Boolean algebra; Post algebra triangulation; finite distributive lattices; leibnizian lattices; multivalued logical conception; set theory; Boolean algebra; Lattices;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Multiple-Valued Logic, 2005. Proceedings. 35th International Symposium on
ISSN :
0195-623X
Print_ISBN :
0-7695-2336-6
Type :
conf
DOI :
10.1109/ISMVL.2005.4
Filename :
1423185
Link To Document :
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