Beyond Classical Set
Abstract: This work presents a novel framework for natural language semantics by augmenting the notion of the conventional set using types. Using this newly conceived set, termed “typed set”, we demonstrate the viability of this notion by showing how the meaning of non-extensional constructs can be represented and computed without resorting to metaphysically murky, psychologically unappealing and computationally expensive notions.
Set theory has established its place as de facto lingua franca not only in mathematics but in many other realms, including the analysis of natural-language (NL). In NL semantics the process is not straightforward. Because of sets’ extensional character ...