SHEAF-THEORETIC FORMAL SEMANTICS
Oleg Prosorov · Trames Journal of the Humanities and Social Sciences · 2006
We outline a sheaf-theoretical framework for a discourse interpretation theory developed in our previous works on formal semantics.This theory applies rigorous mathematical methods in studying the process of interpretation of a natural language text written with good grace and intended for a human understanding.We propose the generalization of Frege's principle of compositionality of meaning which extends its domain from the level of isolated sentence to that of a whole text and takes into account the multiplicity of senses and meanings of words, sentences and texts.The present sheaf-theoretical formal semantics provides a mathematical model of the text interpretation process while rejecting the attempts to codify interpretative practice as a kind of calculus.