Generalizing the Real Interval Arithmetic

R. CALLEJAS-BEDREGAL, B.R.C. BEDREGAL, R.H.N. SANTIAGO

Abstract


In this work we propose a generalized real interval arithmetic. Since the real interval arithmetic is constructed from the real arithmetic, it is reasonable to extend it to intervals on any domain which has some algebraic structure, such as field, ring or group structure. This extension is based on the local equality theory of Santiago [11, 12] and on an interval constructor which mappes bistrongly consistently complete dcpos into bifinitely consistently complete dcpos.

References


[1] B.M. Acióly, “Uma Fundamentação Computacional da Matemática Intervalar”, Ph.D. thesis, CPGCC da UFRGS, Porto Alegre, RS, 1991.

R. Callejas-Bedregal and B. R. Callejas Bedregal, Intervals as a domain constructor, in “Seletas do XXIII CNMAC”, Tendências em Matemática Aplicada e Computacional, 2 (2001), 43-52.

R. Callejas-Bedregal and B. R. Callejas Bedregal, BiScott dcpos as cartesian closed category, in “Pre-proceeding of the Second International Symposium on Domain Theory, Chengdu-China, pp. 22-26, october, 2001.

R. Callejas-Bedregal and B. R. Callejas Bedregal, Interval as a categorical constructor, in “IV Workshop on Formal Methods, Rio de Janeiro, 01-02 October, pages 139-150, 2001.

G.P. Dimuro, A.C.R. Costa and D.M. Claudio. A bi-structured coherence space for a global representation of the system IR of real intervals, in “CIT’99: Trends in Information Technology”, (Proceedings of the International Conference on Information Technology, Bubhaneswar, December 20-22, 1999), Tata McGraw-Hill, pp. 173-178, 2000.

G. Gr¨atzer, “General Lattice Theory”, Academic Press, New York, 1978.

R.B. Kearfott, “Rigorous Global Search: Continuous Problems”, Kluwer Academic Publishers, Dordrecht, 1996.

S.M. Markov. On the extended interval arithmetic, Computes Rendus de L’Acad`emie Bulgare des Sciences, 2, No. 31 (1978), 163-166.

R.E. Moore, “Interval Analysis”, Prentice Hall, New Jersey, 1966.

R.E. Moore, “Methods and Applications for Interval Analysis”, SIAM, Philadelphia.

R.H.N. Santiago, “The Theory of Interval Local Equations”, Ph.D.thesis, Federal University of Pernambuco, PE, Brazil, 1999.

R.H.N. Santiago, Interval local theory: toward a model for real type, in “IV Workshop on Formal Methods”, Rio de Janeiro, 01-02 October, pp. 108-114, 2001.

D.S. Scott, Outline of a mathematical theory of computation, in “4th Annual Princeton Conference on Information Sciences and Systems”, p. 169-176, 1970.

D.S. Scott, Identity and existency in intuitionistic logic, in Fourman, M. et al., editors, in “Lecture Notes in Mathematics” (Fourman, M. et al., eds.), 753, pp 660-696, Springer-Verlag, Durham, 1977.

XSC-Languages, http://www.math.uni-wuppertal.de/org/WRST/xsc-sprachen. html, Access in may of 2002.




DOI: https://doi.org/10.5540/tema.2002.03.01.0061

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia