Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [6] developed an algorithm to enumerate, up to isomorphism, all nite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. ...

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in O(e) elementary arithmetic operations, where e denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorit...

in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

In this paper we discuss the nature of independence of sources in the theory of evidence from an algebraic point of view, starting from an analogy with projective geometries. Independence in Dempster’s rule is equivalent to independence of frames as Boolean algebras. Collection of frames, in turn, can be given several algebraic interpretations in terms of semimodular lattices, matroids, and geo...

Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [6] developed an algorithm to enumerate, up to isomorphism, all nite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. ...