Logic with Probabilistic Operators
Natasha Alechina · 1995
this paper we study languages which contain operators P r : "the probability of : : : is equal to r", where r is a rational number. Depending on the semantics we choose, the logic of such operators is a generalization of the modal logic KD (KD45). Namely, P 1 is a KD-modality (KD45-modality). In Abadi & Halpern (1989), Bacchus (1991), Fagin, Halpern & Megiddo (1988), Halpern (1990), Voorbraak (1993) some richer languages are investigated. Corresponding logics are complete when probabilistic modalities are added to a propositional language and are proved to be non-axiomatizable in the first-order case. The latter result (cf. Abadi & Halpern (1989) or Halpern (1990)) suggests considering a less expressive language. The present investigation is closely related to the work of Fattorosi-Barnaba & Amati (1987) and van der Hoek (1992). They studied a logic with operators P