Relative Necessity Operators and the Subjunctive Conditional

Abstract

This chapter studies mainly binary intensional operators of the form A ⇒ B. We begin with recalling the properties of binary operators that are complete for (types of) neighborhood interpretation (Definition 2.4, Remark 2.6). We then narrow down the meaning of ⇒ to that of some sort of a relative necessity, i.e. a necessity operator for B which depends on A, that is, L_AB. Then we study n-ry necessity operators and n-ry entailment operators. Our next step is to give an example of applying these operators and suggest an analysis of the subjunctive conditional in terms of a ternary operator.