First-Order Conditional Logic and Neighborhood-Sheaf Semantics for Analysis of Conditional Sentences

In this study, we define the neighborhood-sheaf semantics (NSS) of V C, a firstorder conditional logic system [10, Chaps. 5 and 19]. NSS was proposed in [5]. Additionally, we prove that the traditional Kripke semantics of V C can be constructed in terms of NSS. Neighborhood semantics is more general than Kripke semantics because it allows a family of sets of possible worlds “near” a certain world to have more than two members. On the other hand, Kripke semantics of conditional logic uses special Kripke frames in which accessibility relations of a world vary depending on formula. This special frame is properly represented by NSS. Sections 2 and 3 provide an overview of NSS and first-order conditional logic. In Sect. 4 we define NSS of V C and prove the equivalence between NSS and Kripke semantics of V C.