Epistemic Logic with Functional Dependency Operator
This work addresses a theoretical gap in epistemic logic for researchers in formal logic and AI, though it appears incremental as it extends existing operators rather than introducing a new paradigm.
The paper tackles the limitation of existing epistemic logic operators in expressing knowledge of functional dependencies between variables by introducing a new operator Kf, and it axiomatizes three resulting logics in single-agent settings and provides a unified multiagent axiomatization.
Epistemic logic with non-standard knowledge operators, especially the "knowing-value" operator, has recently gathered much attention. With the "knowing-value" operator, we can express knowledge of individual variables, but not of the relations between them in general. In this paper, we propose a new operator Kf to express knowledge of the functional dependencies between variables. The semantics of this Kf operator uses a function domain which imposes a constraint on what counts as a functional dependency relation. By adjusting this function domain, different interesting logics arise, and in this paper we axiomatize three such logics in a single agent setting. Then we show how these three logics can be unified by allowing the function domain to vary relative to different agents and possible worlds. A multiagent axiomatization is given in this case.