An extension of the probability logic $LPP_2$

Abstract

In this paper we present a probability logic which allows Boolean combinations of formulas of the form of a1w(φ1) +···+akw(φk)≥c, where φ1, . . . , φk are propositional formulas, a1, . . . , ak, care rational numbers. The logic with such syntax was introduced in [1]. We present axiomatic system along with the ideas from [2, 3] and prove extended completeness, instead of simple completeness shown in [1].