Supervenience, Dependence, Disjunction

A Simple Logic of Functional Dependence

“…Now, it is easy to prove by induction that the map F sending the two assignments s and u in M to s in M, and the assignment t in M to t in M has the following property. For any LFD formula ϕ and any assignment 51 But, conditional dependence sees a difference here: the formula D Epistemically, each model in U can be seen as a candidate for the true structure of the world, and the dependence universe then represents a 'space of inquiry'. But a dependence universe might also be a family of available processes one can switch between.…”

“…For any LFD formula ϕ and any assignment v, M ′ , v |= ϕ iff M, F (v) |= ϕ. 51 But, conditional dependence sees a difference here: the formula D P xy x y is true at s in the model M (the restriction leaves only the assignment s), but not in M ′ , since both s, u remain after the restriction. So D P xy x y cannot be definable in terms of LFD formulas.…”

“…This happens, e.g., when analyzing two correlated variables by introducing a new variable on which both depend. 51 The general fact here is that F is a modal 'p-morphism', cf. [22], in a sense appropriate to dependence models.…”

“…. In addition, studies of dependence with a classical logic base are found in[38],[51].67 This is just one option. See[53] for an alternative way of reducing the complexity of DL.…”

Logics for Propositional Determinacy and Independence

“…The first one of them is [9] which develops a formal modal logic of supervenience and also addresses some research questions raised in [14] and reiterated here in §8. The other one is [29] which explores, inter alia, connections between supervenience and dependence and discusses in detail some aspects of [14].…”