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2011 | 9 | 5 | 1185-1191
Tytuł artykułu

Algebraic axiomatization of tense intuitionistic logic

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EN
Abstrakty
EN
We introduce two unary operators G and H on a relatively pseudocomplemented lattice which form an algebraic axiomatization of the tense quantifiers “it is always going to be the case that” and “it has always been the case that”. Their axiomatization is an extended version for the classical logic and it is in accordance with these operators on many-valued Łukasiewicz logic. Finally, we get a general construction of these tense operators on complete relatively pseudocomplemented lattice which is a power lattice via the so-called frame.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1185-1191
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-07-26
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autor
Bibliografia
  • [1] Birkhoff G., Lattice Theory, Amer. Math. Soc. Colloq. Publ., 3rd ed., 25, American Mathematical Society, Providence, 1967
  • [2] Botur M., Chajda I., Halaš R., Kolařík M., Tense operators on basic algebras, Internat. J. Theoret. Phys. (in press), DOI: 10.1007/s10773-011-0748-4
  • [3] Brouwer L.E.J., Intuitionism and formalism, Bull. Amer. Math. Soc., 1913, 20(2), 81–96 http://dx.doi.org/10.1090/S0002-9904-1913-02440-6
  • [4] Burgess J.P., Basic tense logic, In: Handbook of Philosophical Logic II, Synthese Lib., 165, Reidel, Dordrecht, 1984, 89–133
  • [5] Chajda I., Halaš R., Kühr J., Semilattice Structures, Res. Exp. Math., 30, Heldermann, Lemgo, 2007
  • [6] Chajda I., Kolařík M., Dynamic effect algebras, Math. Slovaca (in press)
  • [7] Chiriţă C., Tense ϑ-valued Moisil propositional logic, International Journal of Computers, Communications & Control, 2010, 5(5), 642–653
  • [8] Chiriţă C., Tense ϑ-valued Łukasiewicz-Moisil algebras, J. Mult.-Valued Logic Soft Comput., 2011, 17(1), 1–24
  • [9] Diaconescu D., Georgescu G., Tense operators on MV-algebras and Łukasiewicz-Moisil algebras, Fund. Inform., 2007, 81(4), 379–408
  • [10] Ewald W.B., Intuitionistic tense and modal logic, J. Symbolic Logic, 1986, 51(1), 166–179 http://dx.doi.org/10.2307/2273953
  • [11] Heyting A., Intuitionism. An Introduction, North-Holland, Amsterdam, 1956
  • [12] Rasiowa H., Sikorski R., The Mathematics of Metamathematics, Monogr. Mat., 41, PWN, Warszawa, 1963
  • [13] Turunen E., Mathematics Behind Fuzzy Logic, Adv. Soft Comput., Physica-Verlag, Heidelberg, 1999
  • [14] Wijesekera D., Constructive modal logics. I, Ann. Pure Appl. Logic, 1990, 50(3), 271–301 http://dx.doi.org/10.1016/0168-0072(90)90059-B
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-011-0063-6
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