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INTERVAL SHEFFER STROKE BASIC ALGEBRAS

Year 2019, Volume: 9 Issue: 1, 134 - 141, 01.03.2019

Abstract

In this paper we deal with She er stroke basic algebras A = A; j , and we de ne the operations ja, jb, jb a for any elements a; b 2 A in such a way that [a; 1]; ja , [0; b]; jb , [a; b]; jb a become also She er Stroke basic algebras, respectively. Subsequeutly, we show that these interval She er Stroke basic algebras on a given She er Stroke basic algebra A = A; j verify the patchwork condition.

References

  • I. Chajda, (2015), Basic algebras, logics, trends and applications, Asian-European Journal of Mathe- matics 8.03, 1550040.
  • I. Chajda, (2005), Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Fac- ultas Rerum Naturalium, Mathematica, 44.1, 19-23.
  • I. Chajda, R. Halaˇs, and J. K¨uhr, (2007), Semilattice structures, Vol. 30, Heldermann Verlag, Lemgo, Germany.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Independence of the axiomatic system of basic algebras, Soft Computing 13, 41-43.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Interval Basic Algebras, NOVI SAD J. MATH., Vol. 39-2.
  • I. Chajda, and J. K¨uhr, (2006), A note on interval MV-algebras, Math. Slovaca, 56, 47-52.
  • I. Chajda, and J. K¨uhr, (2006), GMV-algebras and meet-semilattices with sectionally antitone permu- tations, Math. Slovaca, 56, 275-288
  • A. Dvureˇcenskij, and M. Hyˇc ko, (2006), Algebras on subintervals of BL-algebras, pseudo BL-algebras and bounded residuated l-monoids, Math. Slovaca, 56, 125-144.
  • J. Jakubik, (2006), On intervals and the dual of pseudo MV-algebras, Math. Slovaca, 56, 213-221.
  • H. M. Sheffer, (1913), A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4), 481-488.
  • Oner T., Senturk I., (2017), The Sheffer Stroke Operation Reducts of Basic Algebras, Open Math., 15, 926-935.
  • McCune, William, et al., (2002), Short single axioms for Boolean algebra, Journal of Automated Reasoning, 29.1, 1-16.
  • Abbott J. C., (1967), Implicational algebras, Bulletin math´ematique de la Soci´et´e des Sciences Math´ematiques de la R´epublique Socialiste de Roumanie, 11.1, 3-23.
Year 2019, Volume: 9 Issue: 1, 134 - 141, 01.03.2019

Abstract

References

  • I. Chajda, (2015), Basic algebras, logics, trends and applications, Asian-European Journal of Mathe- matics 8.03, 1550040.
  • I. Chajda, (2005), Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Fac- ultas Rerum Naturalium, Mathematica, 44.1, 19-23.
  • I. Chajda, R. Halaˇs, and J. K¨uhr, (2007), Semilattice structures, Vol. 30, Heldermann Verlag, Lemgo, Germany.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Independence of the axiomatic system of basic algebras, Soft Computing 13, 41-43.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Interval Basic Algebras, NOVI SAD J. MATH., Vol. 39-2.
  • I. Chajda, and J. K¨uhr, (2006), A note on interval MV-algebras, Math. Slovaca, 56, 47-52.
  • I. Chajda, and J. K¨uhr, (2006), GMV-algebras and meet-semilattices with sectionally antitone permu- tations, Math. Slovaca, 56, 275-288
  • A. Dvureˇcenskij, and M. Hyˇc ko, (2006), Algebras on subintervals of BL-algebras, pseudo BL-algebras and bounded residuated l-monoids, Math. Slovaca, 56, 125-144.
  • J. Jakubik, (2006), On intervals and the dual of pseudo MV-algebras, Math. Slovaca, 56, 213-221.
  • H. M. Sheffer, (1913), A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4), 481-488.
  • Oner T., Senturk I., (2017), The Sheffer Stroke Operation Reducts of Basic Algebras, Open Math., 15, 926-935.
  • McCune, William, et al., (2002), Short single axioms for Boolean algebra, Journal of Automated Reasoning, 29.1, 1-16.
  • Abbott J. C., (1967), Implicational algebras, Bulletin math´ematique de la Soci´et´e des Sciences Math´ematiques de la R´epublique Socialiste de Roumanie, 11.1, 3-23.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

T. Oner This is me

T. Katıcan This is me

A. Ülker This is me

Publication Date March 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 1

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