Rational Pavelka Predicate Logic is a Conservative Extension of Lukasiewicz Predicate Logic
Hajek, Petr ; Paris, Jeff ; Shepherdson, John
J. Symbolic Logic, Tome 65 (2000) no. 1, p. 669-682 / Harvested from Project Euclid
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Rational Pavelka logic extends Lukasiewicz infinitely valued logic $by adding truth constants \bar{r} for rationals in [0, 1].$ We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.
Publié le : 2000-06-14
Classification:  
@article{1183746068,
     author = {Hajek, Petr and Paris, Jeff and Shepherdson, John},
     title = {Rational Pavelka Predicate Logic is a Conservative Extension of Lukasiewicz Predicate Logic},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 669-682},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746068}
}

Hajek, Petr; Paris, Jeff; Shepherdson, John. Rational Pavelka Predicate Logic is a Conservative Extension of Lukasiewicz Predicate Logic. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  669-682. http://gdmltest.u-ga.fr/item/1183746068/