Why can I tell you that I ran for five minutes but not that I *ran all the way to the store for five minutes? Why can you say that there are five pounds of books in this package if it contains several books, but not *five pounds of book if it contains only one? What keeps you from using *sixty degrees of water to tell me the temperature of the water in your pool when you can use sixty inches of water to tell me its height? And what goes wrong when I complain that *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. This work provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above. This provides a starting point from which various linguistic applications of mereology are developed and explored. The main foundational issues, relevant data, and choice points are introduced in an accessible format.
Algebraic Semantics of Proto-Transitive Rough Sets
