Directed acyclic graphs (DAGs) constitute a qualitative representation for conditional independence (CI) properties of a probability distribution. It is known that every CI statement implied by the topology of a DAG is witnessed over it under a graph-theoretic criterion of d-separation. Alternatively, all such implied CI statements are derivable from the local independencies encoded by a DAG using the so-called semi-graphoid axioms. We consider Labeled Directed Acyclic Graphs (LDAGs) modeling graphically scenarios exhibiting context-specific independence (CSI). Such CSI statements are modeled (...) by labeled edges, where labels encode contexts in which the edge vanishes. We study the problem of identifying all independence statements implied by the structure and the labels of an LDAG. We show that this problem is coNP-hard for LDAGs and formulate a sound extension of the semi-graphoid axioms for the derivation of such implied independencies. Finally we connect our study to certain qualitative versions of independence ubiquitous in database theory and teams semantics. (shrink)

In this paper, we introduce a logic based on team semantics, called $\mathbf {FOT} $, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a sublogic of $\mathbf {FOT} $, called $\mathbf {FOT}^{\downarrow } $, captures exactly downward closed elementary (or first-order) team properties. We axiomatize completely the logic $\mathbf {FOT} $, and also extend the known partial axiomatization of dependence logic to dependence logic (...) enriched with the logical constants in $\mathbf {FOT}^{\downarrow } $. (shrink)

In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations (...) for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms. (shrink)