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Journal Neurocomputers №10 for 2014 г.
Article in number:
About an approximate solution of a production-logical equation on a Boolean lattice
Keywords: boolean lattice production-logical relation canonical relation structural layering of a relation production-logical equation
Authors:
I.Yu. Ivanov - Magistrand, Applied and System Software Department, Voronezh State University. E-mail: hour1scorp@gmail.com
Abstract:
A boolean lattice with a production-logical relation defined on it (LP-structure) is an effective mathematical model which allows to study intelligent production systems at an abstract level. In this paper the class of production logical equations on a finite LP-strucutre is introduced and examined. These equations may be used to optimize backward inference in systems that use a full set of logical connections of a propositional language in its productions. The concepts of a canonical relation on a boolean lattice and a structural layering of such relation are introduced to represent an initial lattice relation as a set of directed graphs. The method of an approximate solution finding of a production-logical equation based on relation layer directed graph nodes traversal is proposed.
Pages: 53-63
References

  1. Rasyeva Ye. Matematika metamatematiki: per. s angl. / Ye. Rasyeva, R. Sikorski. M.: Nauka, 1972. 591 s.
  2. Chechkin A. V. Matematicheskaya informatika. M.: Nauka, gl. red. fiz.-mat. lit. 1991. 416 s.
  3. Makhortov S.D. LP-struktury na reshetkakh tipov i nekotorye zadachi refaktoringa / S. D. Makhortov // Programmirovanie. 2009. № 4. S. 5 - 14.
  4. Teyz A., Gribomon P. i dr. Logicheskiy podkhod k iskusstvennomu intellektu: ot klassicheskoy logiki k logicheskomu programmirovaniyu: per. s frants. M.: Mir. 1990. 432 s.
  5. Makhortov S. D. Matematicheskie osnovy iskusstvennogo intellekta: teoriya LP-struktur dlya postroeniya i issledovaniya modeley znaniy produktsionnogo tipa / pod red. V. A. Vasenina. M.: MTsNMO, 2009. 304 s.
  6. Makhortov S. D. Logicheskie uravneniya na reshetkakh / S. D. Makhortov // Vestnik VGU. Seriya «Fizika, matematika». Voronezh: 2004, № 2. S. 170 - 178.
  7. Birkgof G. Teoriya reshyetok: per. s angl. / G. Birkgof. M.: Nauka. Glav. red. fiz.-mat. lit., 1984. 568 s.
  8. Grettser G. Obshchaya teoriya reshyetok: per. s angl. / G. Grettser. Pod red. D. M. Smirnova. M.: Mir, 1981. 456 s.
  9. Artamonov V. A., Saliy V. N., Skornyakov L. A. i dr. Obshchaya algebra. T. 2. / Pod obshch. red. L. A. Skornyakova. M.: Nauka. Gl. red. fiz.-mat. lit., 1991. 480 s.
  10. Bolotova S. Yu., Makhortov S. D. Algoritmy relevantnogo obratnogo vyvoda, osnovannye na reshenii produktsionno-logicheskikh uravneniy // Iskusstvennyy intellekt i prinyatie resheniy. 2011. № 2. S. 40 - 50.
  11. Makhortov S. D. Osnovannyy na reshetkakh podkhod k issledovaniyu i optimizatsii mnozhestva pravil uslovnoy sistemy perepisyvaniya termov // Intellektual'nye sistemy. 2009. T. 13. Vyp. 1-4. S. 51 - 68.
  12. Chechkin A. V. Neyrokomp'yuternaya paradigma informatiki // Neyrokomp'yutery: razrabotka, primenenie. 2011. № 7. S. 3 - 9.