This paper uses an "admissible set semantics" to treat quantification in quantified modal logics. The truth condition for the universal quantifier states that a universally quantified statement (x)A(x) is true at a world w if and only if there is some proposition true at that world that entails every instance of A(x). It is shown that, for any canonical propositional modal logic the corresponding admissible set semantics characterises the quantified version of that modal logic.

We introduce an operator to represent the simple notion of being wrong. Read Wp to mean: the agent is wrong about p . Being wrong about p means believing p though p is false. We add this operator to the language of propositional logic and study it. We introduce a canonical model for logics of being wrong, show completeness for the minimal logic of being wrong and various other systems. En route we examine the expressiveness of the language. In conclusion, (...) we discuss an open question regarding K4. (shrink)

We present and show topological completeness for LB, the logic of the topological border. LB is also a logic of epistemic ignorance. Also, we present and show completeness for LUT, the logic of unknown truths. A simple topological completeness proof for S4 is also presented using a T1 space.

We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of essence (...) and accident is highlighted and illustrated, both with respect to the definability of the more usual modal operators as well as with respect to the characterizability of classes of frames. Several interesting problems and directions are left open for exploration. (shrink)