It is shown that the decomposition coefficients provide a direct and systematic means to carry out modal classification and quantification.
Kripke's semantics for modal logic allows quantification over possible worlds only in the metalanguage (see the entry modal logic), for example.
In "Modalities and Quantification" (1946) and in Meaning and Necessity (1947), Carnap interprets the object language operator of necessity as expressing at the object level the semantic notion of logical truth: "[T]he guiding idea in our constructions of systems of modal logic is this: a proposition p is logically necessary if and only if a sentence expressing p is logically true.
Outside of negation, both classes of items display the properties of anti-episodicity (aversion to episodic environments) and quantificational variability (a modal form of universal quantification which favors distributive over collective readings) (Giannakidou 2001).
Aside from the fact that Kripke's treatment of the quantifiers arguably yields an intuitively more correct semantics of quantification in modal contexts, formally, unlike a fixed domain semantics, it prevents certain controversial modal principles — most notably, the so-called Barcan Formula ⌈◇∃νφ → ∃ν◇φ⌉ (Barcan 1946) — from being logical truths.
The modal might introduces existential quantification over possible situations that are accessible from the evaluation situation s (see the entry modal logic).
This is a book, which includes an extensive discussion of important differences in the behavior of plural and second-order quantification in modal contexts.
They outlined a formal system of modal logic with propositional quantification, which they used to formulate an Existence Postulate designed to guarantee the existence of at least two propositions that are consistent and independent from each other.
Our rationale for doing as much is that one will get the technical details, and the particular philosophical issues that motivated them, from looking at specific logics—specific theories of logical consequence (e.g., relevant logics, substructural logics, non-monotonic logics, dynamic logics, modal logics, theories of quantification, and so on).
The experimental quantification of the modal parameter variability of nominally identical electric guitars in an industrial context is the aim of this article.
