Autore: Minari, Pierluigi
Titolo: A note on Lukasiewicz's three-valued logic
Periodico: Annali del dipartimento di filosofia
Anno: 2002 - Volume: 8 - Pagina iniziale: 163 - Pagina finale: 189

It is well known that Lukasiewicz’s three-valued-logic L3 admits – unlike classical logic – the definition of two non trivial, truth-functional modal operators and ?. We address the question of finding a convenient syntactic characterization of the “modal content” of L3. To this aim, we consider Wajsberg’s axiomatization of L3 (the calculus W) and prove its equivalence with a modal calculus W_ which, essentially, includes: the BCK+double negation schemas, the characteristic modal schemas of S5 (K;T; 4;B), full contraction for boxed formulas and the “partial collapse” schema a ? (a ?a). As applications, we obtain a simple and natural completeness proof à la Lindenbaum for W, as well as a considerable simplification of Wajsberg’s original, ingenious completeness proof.




SICI: 1824-3770(2002)8<163:ANOLTL>2.0.ZU;2-C
Testo completo: http://www.fupress.net/index.php/adf/article/download/1969/1891

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