Algebraic lattices and nonassociative structures

Algebraic Properties of Intuitionistic Fuzzy Residuated Lattices

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

Epistemic closure and commutative, nonassociative residuated structures

K–axiom–based epistemic closure for explicit knowledge is rejected for even the most trivial cases of deductive inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation. The recognition that deductive inference concerns interaction as much as it concerns consequence allows for perspectives from logics of multi–agent information flow t...

Algebraic Lattices

Let L be a non empty reflexive relational structure. The functor CompactSublatt(L) yields a strict full relational substructure of L and is defined as follows: (Def. 1) For every element x of L holds x ∈ the carrier of CompactSublatt(L) iff x is compact. Let L be a lower-bounded non empty reflexive antisymmetric relational structure. Observe that CompactSublatt(L) is non empty. Next we state th...

Constructions of algebraic lattices

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices 3n , for n = 2, 3, 4, 6, 8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, ...

Algebraic Aspects of Orthomodular Lattices