On standard completeness and finite model property for a probabilistic logic on Łukasiewicz events

The probabilistic logic FP(Ł,Ł) was axiomatized with the aim of presenting a formal setting for reasoning about probability infinite-valued Łukasiewicz events. Besides several attempts, proving that axiomatic system to be complete respect class standard models, remained an open problem since first paper on published in 2007. In this article we give solution it. particular introduce two semantics system: one based states and second regular Borel measures prove is both these classes models. Further, will show finite model property holds FP(Ł,Ł).