Yifeng Ding

Yifeng Ding, Yuanzhe Yang

In studies of bundled modalities, we encode a complex conceptual notion into the semantics of a single modal operator and study its logic. Although there is already a substantial body of work on various concrete bundled operators, we still lack a general understanding of them. In this paper, we provide a general theory of the expressivity and axiomatization of bundled modalities. We offer a uniform way to define bisimulations for arbitrary bundled modalities and justify our definition by the corresponding Hennessy-Milner property. We also define a special class of bundled modalities called convex bundles. This class covers most bundled modalities studied in the literature, and their axiomatizations can be done with the help of convex neighborhood semantics and corresponding representation results. As case studies, we axiomatize the "someone knows" bundle $\bigvee_{a \in A} \Box_a ϕ$ over $S5$-models, the "disagreement in group" bundle $\bigvee_{a, b \in A} \Box_a ϕ\wedge \Box_b \neg ϕ$ over $KD45$-models, and the "belief without knowledge" bundle $B ϕ\wedge \neg K ϕ$ over $S4.2$-models.

Jixin Liu, Yanjing Wang, Yifeng Ding

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system K_n lacks Craig Interpolation.

Yifeng Ding

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.