Abstract
Predicates that preserve their values on a larger (extended) body of data are called equitone. An algebra of such predicates is constructed, a system of its generators is specified, and a complete system of transformations of identities is defined. The results obtained are used for construction and investigation of complete classes of compositions of various types and levels of abstractions that are used in logics of partial predicates.
Similar content being viewed by others
REFERENCES
N. S. Nikitchenko and S. S. Shkilńyak, “Neoclassical logics of predicates,” Probl. Progr., No. 3-4, 3-17 (2000).
N. S. Nikitchenko, “Propositional compositions of partial predicates,” Kibern. Sist. Anal., No. 2, 3-19 (2000).
N. S. Nikitchenko, “Applicative compositions of partial predicates,” Kibern. Sist. Anal., No. 2, 14-33 (2001).
N. S. Nikitchenko, “Predicate composite-nominative systems,” Probl. Progr., No. 2, 3-19 (1999).
N. S. Nikitchenko, “Compositions of programs inducing monotone functions of a special form,” Programmirovanie, No. 1, 3-17 (1987).
M. Ryan and M. Sadler, “Valuation systems and consequence relations,” in:. S. Abramsky, Dov. M. Gabbay, and T. S. E. Maibaum (eds.), Handbook of Logic in Computer Science, 1, Clarendon Press, Oxford (1992), pp. 1-79.
B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge (1990).
G. Birkhoff, Lattice Theory [Russian translation], Nauka, Moscow (1984).
P. Cohn, Universal Algebra [Russian translation], Mir, Moscow (1968).
S. Kleene, Introduction to Metamathematics [Russian translation], IL, Moscow (1957).
E. Mendelson, Introduction to Mathematical Logic [Russian translation], Nauka, Moscow (1971).
J. Kalman, “Lattices with involution,” Trans. Am. Math. Soc., 87, 150-155 (1958).
N. I. Kondakov, Dictionary and Reference Book of Logic [in Russian], Nauka, Moscow (1975).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nikitchenko, N.S. Equitone Predicate Algebras and Their Applications. Cybernetics and Systems Analysis 39, 97–112 (2003). https://doi.org/10.1023/A:1023829327704
Issue Date:
DOI: https://doi.org/10.1023/A:1023829327704