The distinction between the essential and the accidental characteristics of a thing should be understood not in modal terms (the received view) nor in definitional terms (Fine’s recent proposal) but as follows: an essential characteristic of a thing is one that is not explained by any other of that thing’s characteristics, and an accidental characteristic of a thing is one that is so explained. Various versions of this proposal can be formulated.

Kit Fine; XIV*—Ontological Dependence, Proceedings of the Aristotelian Society, Volume 95, Issue 1, 1 June 1995, Pages 269–290, https://doi.org/10.1093/aristote.

This paper provides a possible worlds semantics for the system of the author's previous paper 'The Logic of Essence '. The basic idea behind the semantics is that a statement should be taken to be true in virtue of the nature of certain objects just in case it is true in any possible world compatible with the nature of those objects. It is shown that a slight variant of the original system is sound and complete under the proposed semantics.

Standard possible world semantics for propositional modal languages ignore truth-value gaps. However, simple considerations suggest that it should not be so. In Section 1, I identify what I take to be a correct truth-clause for necessity under the assumption that some possible worlds are incomplete (i.e., "at" which some propositions lack a truth-value). In Section 2, I build a world semantics, the semantics of TV-models, for standard modal propositional languages, which agrees with the truth-clause for necessity previously identified. Sections 3–5 (...) are devoted to systematic concerns. In particular, in Section 4, Prior’s system Q (propositional version) is given a TV-models semantics and proved adequate (i.e., sound and complete) with respect to it. (shrink)

We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.

This paper presents a propositional version of Kit Fine's (quantified) logic for essentialist statements, provides it with a semantics, and proves the former adequate (i.e. sound and complete) with respect to the latter.