The paper presents an alternative substitutional semantics for first-order modal logic which, in contrast to traditional substitutional (or truth-value) semantics, allows for a fine-grained explanation of the semantical behavior of the terms from which atomic formulae are composed. In contrast to denotational semantics, which is inherently reference-guided, this semantics supports a non-referential conception of modal truth and does not give rise to the problems which pertain to the philosophical interpretation of objectual domains (concerning, e.g., possibilia or trans-world identity). The paper (...) also proposes the notion of modality de nomine as an alternative to the denotational notion of modality de re. (shrink)

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme □∃xφ ⊃ ∃x□φ.

In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke possible world semantics. This kind of modal system characterized by finite non-deterministic matrices was originally proposed by Ju. Ivlev in the 70s. The aim of this second paper is to introduce a formal non-deterministic semantical framework for the quantified versions of some Ivlev-like non-normal modal logics. It will be shown that several well-known controversial issues of (...) quantified modal logics, relative to the identity predicate, Barcan’s formulas and de re and de dicto modalities, can be tackled from a new angle within the present framework. (shrink)