On the Sentence Valuations in a Semiring

Abstract

This paper proposes an algebraic way of sentence valuations in a semiring. Actually, throughout the paper only valuations in the ring of integers with usual addition and multiplication are considered. These valuations take into consideration both words and their positions within the sentences. Two synonymy relations, with respect to a given valuation, are introduced. All sentences that are synonymous form a synonymy class. Some basic problems regarding the synonymy classes, which are actually formal languages, are formulated and studied. Some of them are completely solved whereas partial answers are provided for others. TUCS Research Group Theory Group: Mathematical Structures in Computer Science