The Doxastic Interpretation of Team Semantics

This different outlook makes Dependence Logic a most suitable framework for the formal study, in a first-order setting, of functional dependence itself; and, furthermore, this logic is readily adaptable to the analysis of other, nonfunctional notions of dependence or independence [11, 6, 8]. Like other logics of imperfect information, Dependence Logic admits both a Game Theoretic Semantics, an imperfect information variant of the one for First Order Logic, and a Team Semantics, a compositional semantics which is a natural adaptation of Hodges' Trump Semantics [15]. One striking peculiarity of the current state of the art of the research in Dependence Logic and its extensions is a willingness to take Team Semantics - and not Game Theoretic Semantics, as for the case of much IF Logic research - as the fundamental semantic framework; and this different approach is at the root of many recent technical developments in the field, such as, for example, the characterizations of team class definability of [17], [16] and [8], the hierarchy results of [4], and the study of notions of generalized quantification of [6] and [5]. This paper is a detailed account of a doxastic interpretation for Team Semantics, according to which formulas are to be interpreted as assertions about beliefs and belief updates. This is not a novel idea: as a matter of fact, it is already implicit in the equivalence proof between Trump Semantics and Game Theoretic Semantics of [15].