A representation theorem for tense n × m -valued Łukasiewicz-Moisil algebras

Aldo Victorio Figallo; Gustavo Pelaitay

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 3, page 345-360
  • ISSN: 0862-7959

Abstract

top
In 2000, Figallo and Sanza introduced n × m -valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of n -valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM n × m of tense n × m -valued Łukasiewicz-Moisil algebras (or tense LM n × m -algebras), namely n × m -valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM n -algebras). Our most important result is a representation theorem for tense LM n × m -algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM n -algebras.

How to cite

top

Figallo, Aldo Victorio, and Pelaitay, Gustavo. "A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras." Mathematica Bohemica 140.3 (2015): 345-360. <http://eudml.org/doc/271573>.

@article{Figallo2015,
abstract = {In 2000, Figallo and Sanza introduced $n\times m$-valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$-valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM$_\{n\times m\}$ of tense $n\times m$-valued Łukasiewicz-Moisil algebras (or tense LM$_\{n\times m\}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM$_\{n\}$-algebras). Our most important result is a representation theorem for tense LM$_\{n\times m\}$-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM$_\{n\}$-algebras.},
author = {Figallo, Aldo Victorio, Pelaitay, Gustavo},
journal = {Mathematica Bohemica},
keywords = {$n$-valued Łukasiewicz-Moisil algebra; tense $n$-valued Łukasiewicz-Moisil algebra; $n\times m$-valued Łukasiewicz-Moisil algebra},
language = {eng},
number = {3},
pages = {345-360},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras},
url = {http://eudml.org/doc/271573},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Figallo, Aldo Victorio
AU - Pelaitay, Gustavo
TI - A representation theorem for tense $n\times m$-valued Łukasiewicz-Moisil algebras
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 3
SP - 345
EP - 360
AB - In 2000, Figallo and Sanza introduced $n\times m$-valued Łukasiewicz-Moisil algebras which are both particular cases of matrix Łukasiewicz algebras and a generalization of $n$-valued Łukasiewicz-Moisil algebras. Here we initiate an investigation into the class tLM$_{n\times m}$ of tense $n\times m$-valued Łukasiewicz-Moisil algebras (or tense LM$_{n\times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with two unary operations called tense operators. These algebras constitute a generalization of tense Łukasiewicz-Moisil algebras (or tense LM$_{n}$-algebras). Our most important result is a representation theorem for tense LM$_{n\times m}$-algebras. Also, as a corollary of this theorem, we obtain the representation theorem given by Georgescu and Diaconescu in 2007, for tense LM$_{n}$-algebras.
LA - eng
KW - $n$-valued Łukasiewicz-Moisil algebra; tense $n$-valued Łukasiewicz-Moisil algebra; $n\times m$-valued Łukasiewicz-Moisil algebra
UR - http://eudml.org/doc/271573
ER -

References

top
  1. Boicescu, V., Filipoiu, A., Georgescu, G., Rudeanu, S., Łukasiewicz-Moisil Algebras, Annals of Discrete Mathematics 49 North-Holland, Amsterdam (1991). (1991) Zbl0726.06007MR1112790
  2. Botur, M., Chajda, I., Halaš, R., Kolařík, M., 10.1007/s10773-011-0748-4, Int. J. Theor. Phys. 50 (2011), 3737-3749. (2011) Zbl1246.81014MR2860032DOI10.1007/s10773-011-0748-4
  3. Botur, M., Paseka, J., On tense {MV}-algebras, Fuzzy Sets and Systems 259 (2015), 111-125. (2015) Zbl1335.03069MR3278748
  4. Burgess, J. P., Basic tense logic, Handbook of Philosophical Logic. Vol. II: Extensions of Classical Logic Synthese Lib. 165 D. Reidel Publishing, Dordrecht (1984), 89-133 D. Gabbay et al. (1984) Zbl0875.03046MR0844597
  5. Chajda, I., Kolařík, M., 10.2478/s12175-012-0015-z, Math. Slovaca 62 (2012), 379-388. (2012) Zbl1324.03026MR2915603DOI10.2478/s12175-012-0015-z
  6. Chajda, I., Paseka, J., 10.1007/s00500-012-0857-x, Soft Comput. 16 (2012), 1733-1741. (2012) Zbl1318.03059DOI10.1007/s00500-012-0857-x
  7. Chiriţă, C., 10.1007/s00500-011-0796-y, Soft Comput. 16 (2012), 979-987. (2012) Zbl1277.03067MR2760964DOI10.1007/s00500-011-0796-y
  8. Chiriţă, C., Tense θ -valued Łukasiewicz-Moisil algebras, J. Mult.-Val. Log. Soft Comput. 17 (2011), 1-24. (2011) Zbl1236.03046MR2760964
  9. Chiriţă, C., 10.15837/ijccc.2010.5.2220, Int. J. of Computers, Communications and Control 5 (2010), 642-653. (2010) DOI10.15837/ijccc.2010.5.2220
  10. Diaconescu, D., Georgescu, G., Tense operators on {MV}-algebras and Łukasiewicz-Moisil algebras, Fundam. Inform. 81 (2007), 379-408. (2007) Zbl1136.03045MR2372716
  11. Figallo, A. V., Pelaitay, G., 10.3233/FI-2015-1160, Fund. Inform. 136 (2015), 317-329. (2015) Zbl1350.03047MR3320018DOI10.3233/FI-2015-1160
  12. Figallo, A. V., Pelaitay, G., 10.1093/jigpal/jzt024, Log. J. IGPL 22 (2014), 255-267. (2014) Zbl1347.06012MR3188082DOI10.1093/jigpal/jzt024
  13. Figallo, A. V., Pelaitay, G., Note on tense SH n -algebras, An. Univ. Craiova Ser. Mat. Inform. 38 (2011), 24-32. (2011) MR2874020
  14. Figallo, A. V., Pelaitay, G., Tense operators on SH n -algebras, Pioneer J. Algebra Number Theory Appl. 1 (2011), 33-41. (2011) MR3029804
  15. Figallo, A. V., Sanza, C., Monadic n × m -valued Łukasiewicz-Moisil algebras, Math. Bohem. 137 (2012), 425-447. (2012) Zbl1274.03104MR3058274
  16. Figallo, A. V., Sanza, C. A., The 𝒩 S n × m -propositional calculus, Bull. Sect. Log., Univ. Łód'z, Dep. Log. 37 (2008), 67-79. (2008) Zbl1286.03182MR2460596
  17. Figallo, A. V., Sanza, C., Álgebras de Łukasiewicz n × m -valuadas con negación, Noticiero Unión Mat. Argent. 93 (2000), 93-94. (2000) 
  18. Kowalski, T., Varieties of tense algebras, Rep. Math. Logic 32 (1998), 53-95. (1998) Zbl0941.03066MR1735173
  19. Moisil, G. C., Essais sur les logiques non chrysippiennes, Éditions de l'Académie de la République Socialiste de Roumanie Bucharest French (1972). (1972) Zbl0241.02006MR0398774
  20. Paseka, J., 10.1016/j.fss.2013.02.010, Fuzzy Sets and Systems 232 (2013), 62-73. (2013) Zbl1314.06016MR3118535DOI10.1016/j.fss.2013.02.010
  21. Sanza, C. A., 10.2478/s11533-008-0035-7, Cent. Eur. J. Math. 6 (2008), 372-383. (2008) Zbl1155.06009MR2424999DOI10.2478/s11533-008-0035-7
  22. Sanza, C. A., n × m -valued Łukasiewicz algebras with negation, Rep. Math. Logic 40 (2006), 83-106. (2006) Zbl1096.03076MR2207304
  23. Sanza, C., Álgebras de Łukasiewicz n × m -valuadas con negación, Doctoral Thesis Universidad Nacional del Sur, Bahía Blanca, Argentina (2005). (2005) 
  24. Sanza, C., 10.1093/jigpal/12.6.499, Log. J. IGPL 12 (2004), 499-507. (2004) Zbl1062.06018MR2117684DOI10.1093/jigpal/12.6.499
  25. Suchoń, W., Matrix Łukasiewicz algebras, Rep. Math. Logic 4 (1975), 91-104. (1975) Zbl0348.02021

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.