Search results for "Distributivity"
showing 3 items of 3 documents
Spaces of typen on partially ordered sets
1989
This paper contains a generalized approach to incidence geometry on partially ordered sets. A difference to the usual geometrical concepts is that points may have different size. Our main result states that a large class of spaces allows lattice theoretic characterizations. Especially, a generalized version of the Veblen-Young axiom of projective geometry has a lattice theoretic equivalent, called then-generation property (which is a generalization of the ‘Verbindungssatz’). Modularity and distributivity of a lattice of subspaces are reflected in the underlying space. Finally we give specializations and examples.
Two integrals and some modified versions — Critical remarks
1986
The aim of this paper is to discuss different constructions of integrals (Sections 3 and 4) based on @?-decomposable measures (Section 1). According to the classification of the continuous t-conorms @? in essentially two types namely v and Archimedean t-conorms, there exist mainly two types of integrals namely the constructions of Sugeno (Section 3) and of Weber (Section 4). Further constructions corresponding to the Archimedean case result to be special cases or not well defined (Section 4). In all cases a crucial property is some restricted distribution law for the pair (@?, ) with an appropriate operation(Section 2). Some applications shall illustrate the use of the two integrals (Sectio…
Algebraic aspects and coherence conditions for conjoined and disjoined conditionals
2019
We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula and we prove a …