Soundness and completeness results for LEA and probability semantics

Abstract

Abstract In Artemov (2020, J. Logic Comput., 30, 61–76), a logical system called the logic of evidence aggregation (LEA) was introduced, along with an intended semantics for it called probability semantics. The goal was to describe probabilistic evidence aggregation in the setting of formal logic. However, as noted in that paper, LEA is not complete with respect to probability semantics. This leaves the tasks open to find sound and complete semantics for LEA and a proper axiomatization for probability semantics. In this paper, we do both. We define a class of basic models called deductive basic models. We show LEA is sound and complete with respect to the class of deductive basic models. We also define an axiomatic system LEA$_+$ extending LEA and show it is sound and complete with respect to probability semantics. Along the way, we develop an intermediate system LEA$_-$ which, it turns out, is equivalent to propositional lax logic with a classical logic base. Sequent systems and decidability results for LEA$_-$ and LEA$_+$ are also presented.