2,294 research outputs found
Epistemic Logic with Partial Dependency Operator
In this paper, we introduce dependency modality
into epistemic logic so as to reason about
dependency relationship in Kripke models. The resulted dependence epistemic
logic possesses decent expressivity and beautiful properties. Several
interesting examples are provided, which highlight this logic's practical
usage. The logic's bisimulation is then discussed, and we give a sound and
strongly complete axiomatization for a sub-language of the logic
Independence Logic and Abstract Independence Relations
We continue the work on the relations between independence logic and the
model-theoretic analysis of independence, generalizing the results of [15] and
[16] to the framework of abstract independence relations for an arbitrary AEC.
We give a model-theoretic interpretation of the independence atom and
characterize under which conditions we can prove a completeness result with
respect to the deductive system that axiomatizes independence in team semantics
and statistics
Reasoning about embedded dependencies using inclusion dependencies
The implication problem for the class of embedded dependencies is
undecidable. However, this does not imply lackness of a proof procedure as
exemplified by the chase algorithm. In this paper we present a complete
axiomatization of embedded dependencies that is based on the chase and uses
inclusion dependencies and implicit existential quantification in the
intermediate steps of deductions
Structural completeness in propositional logics of dependence
In this paper we prove that three of the main propositional logics of
dependence (including propositional dependence logic and inquisitive logic),
none of which is structural, are structurally complete with respect to a class
of substitutions under which the logics are closed. We obtain an analogues
result with respect to stable substitutions, for the negative variants of some
well-known intermediate logics, which are intermediate theories that are
closely related to inquisitive logic
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