Axiomatizing the logic of knowing
The axiomatization and complexity of Knowing-What-Logic on model class K
[arXiv] Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether'', "knowing what'', "knowing how'' are frequently and widely used. This paper presents a axiomatization and a tableau for the modal logic of "knowing-what" operator on arbitrary Kripke models. As we are not working on S5 model class, this operator is not technically a "knowing" operator, but the inner structure is clearer in this setting.
Epistemic Logic with Functional Dependency Operator
[arXiv] 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.