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Information Sciences
Volume 151, May 2003, Pages 107-124
 
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doi:10.1016/S0020-0255(02)00301-8    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2002 Elsevier Science Inc. All rights reserved.

On the sentence valuation in a semiring

A. AtanasiuE-mail The Corresponding Author, a, C. Martín-VideE-mail The Corresponding Author, b and Victor MitranaCorresponding Author Contact Information, E-mail The Corresponding Author, a

a Faculty of Mathematics, University of Bucharest, Str. Academiei No. 14, 70109, Bucharest, Romania b Research Group in Mathematical Linguistics, Rovira i Virgili University, Pça. Imperial Tàrraco 1, 43005, Tarragona, Spain

Received 22 March 2000; 
revised 3 November 2001; 
accepted 28 January 2002. ;
Available online 19 March 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.

Author Keywords: Valuation; Synonymy; Strong synonymy; Synonymy class; Decidability

Article Outline

1. Introduction
2. Definitions and examples
3. The polynomial case
3.1. The constant polynomial
3.2. The linear polynomial
4. The exponential case an
5. Final remarks
Acknowledgements
Appendix A
References

Information Sciences
Volume 151, May 2003, Pages 107-124
 
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