Formal Hermeneutics Based on Frege Duality

Abstract

We outline a sheaf-theoretical framework for the discourse interpretation theory called formal hermeneutics in our previous works (1997, 2001, 2002, 2003, 2004). This approach will provide a common categorical paradigm to generalize the classic Frege’s compositionality and contextuality principles at each semantic level (text, sentence, word). So revised, these principles are reconciled in a natural dual equivalence between two key categories, called Frege duality, that gives rise to some important functional representations of fragmentary meanings. As its application, we develop an inductive meaning theory formalizing the creative process of text understanding. Based on Frege duality, our formal hermeneutics intends to reveal the mathematical structures that underlie the natural language understanding process.