As shown in Fan, there are some similarities/resemblances between contingency and accident. Given this, one may naturally ask if we can unify the two operators to manifest all of their similarities/resemblances. In this article, instead of looking at the interactions between the two operators like in Fan, we turn our attention to the resemblances between the two operators. We extend the unification method in Fan to the current setting. The main results include some model-theoretical ones, such as expressivity, frame definability, (...) bisimulation, and some axiomatization ones. (shrink)

In Fan's 2019 article, “Symmetric Contingency Logic with Unlimitedly Many Modalities”, it is left as an open question in Fan (2019b) how to (completely) axiomatize contingency logic over the class of symmetric and transitive frames, and conjectured that is the desired axiomatization. In the current article, we show that the conjecture is false, and then propose a desired axiomatization, thereby answering the open question. Beyond these results, we also present a family of axiomatizations of contingency logic over Kripke frames.

The result of an interaction is influenced by its epistemic state, and several epistemic notions are related to multiagent situations. Strong belief-disagreement on a certain proposition between agents means that one agent believes the proposition and the other believes its negation. This paper presents a logical system describing strong belief-disagreement between agents and demonstrates its soundness and completeness. The notion of belief-disagreement as well as belief-agreement can facilitate gaining a clearer understanding of the acts of trade and speech.

Hilbert-style axiomatic systems are presented for versions of the modal logics K, where {D, 4, 5}, with noncontingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the noncontingency logic of any logic containing the seriality axiom is proved to be nonserial. It is also shown that any class of frames definable (...) in the noncontingency language contains the class of functional frames, and dually, there exists a greatest consistent normal noncontingency logic. (shrink)

I discuss the question of when knowledge of higher order ignorance is possible and show in particular that, under quite plausible assumptions, knowledge of second order ignorance is impossible.