This preprint was accepted January 31, 2002
Contact: O.B. Prosorov
ABSTRACT: Formal hermeneutics and Frege's principle generalized. - Various discourse interpretation procedures reveal the existence of mathematical structures which can be formulated within the framework of sheaf theory. The object of this paper is to establich the theory of discourse interpretation which we name as formal hermeneutics. For an admissible text X corresponds very naturally one category of particulars sheaves Schl(X) named in the honour of Schleiermacher. We propose the generalisation of Frege's principle of compositionality of meaning which extends it's domain from the level of individual sentence to those of discourse interpretation and provides so a basis for this correspondance. The formal hermeneutics describes semantics of a natural language in the category of textual spaces. Every particular genre of texts and discours defines there the full subcategory of formal discourse schemes. These categories and the different functors related to discourse interpretation are the principal objects of study in the formal hermeneutics as we understand it. Classification MS2000 : 03B65, 68Q55, 68T50, 91F20 Key words : formal hermeneutics, hermeneutical circle, Frege's principle of compositionality of meaning, topology phonocentric, topology logocentric, étale bundle, sheaf, category, functor, topology of Grothendieck, site, topos, textual space, formal discourse scheme.[Full text: (.ps.gz)]