Conditioning of events and related topics

The author presents a lattice ordered semigroup approach for the foundation of conditional events which covers the special situations where the underlying unconditional events are Boolean or fuzzy, respectively. The structure of a lattice with an additional semigroup operation interpreted as an intersection is considered. An additional axiom (MV), transforming that type of lattice into a MV-algebra, makes possible the construction of conditional events in this approach, and of two types of connectives as well as quite general uncertainty measures for conditional events.<>