On the sentence valuation in a semiring

Authors:
A. Atanasiu;C. Martín-Vide;Victor Mitrana
Affiliations:
Faculty of Mathematics, University of Bucharest, Str. Academiei No. 14, 70109 Bucharest, Romania;Research Group in Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tàrraco 1, 43005 Tarragona, Spain;Faculty of Mathematics, University of Bucharest, Str. Academiei No. 14, 70109 Bucharest, Romania
Venue:
Information Sciences—Informatics and Computer Science: An International Journal
Year:
2003

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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 which is actually a formal language. Some basic problems regarding the synonymy classes are formulated in the general setting but the results presented concern only very special valuations.