Natural Density and the Quantifier “Most”

Abstract

This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form "Most A are B ", where A and B are plural nouns and the interpretations of A and B are infinite subsets of N. There are two widely used semantics for Most A are B : (i) C(A ∩ B) > C(A \ B) and (ii) C(A ∩ B) > C(A) 2 , where C(X) denotes the cardinality of a Mathematics Subject Classification (2010). 03B65, 03C80, 11B05.

Most-Intersection of Countable Sets

“…Now let us consider the infinite case. For this purpose we define some notions given in our earlier work [8]. Definition 2.…”

“…We define a special form of the binary predicate Most in the following manner (see [8] for the general case). Let U be countably infinite universe and let A ⊆ U be a set.…”

“…The operator relies on the relative natural density comparison of two infinite sets via the 'most' quantifier. We cover some of our previous work [8] to which the reader can refer for further details. Though for completeness, we will give the necessary background knowledge.…”