Monotone operators on Gödel logic

We consider an extension of Gödel logic by a unary operator that enables the addition of non-negative reals to truth-values. Although its propositional fragment has a simple proof system, first-order validity is Π 2 -hard. We explain the close connection to Scarpellini’s result on Π 2 -hardness of Ł...

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Veröffentlicht in:	Archive for mathematical logic 2014-05, Vol.53 (3-4), p.261-284
Hauptverfasser:	Fasching, Oliver, Baaz, Matthias
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Applied mathematics Archives Fragmentation Joints Logic Mathematical analysis Mathematical logic Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operators Proving
Online-Zugang:	Volltext
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Zusammenfassung:	We consider an extension of Gödel logic by a unary operator that enables the addition of non-negative reals to truth-values. Although its propositional fragment has a simple proof system, first-order validity is Π 2 -hard. We explain the close connection to Scarpellini’s result on Π 2 -hardness of Łukasiewicz’s logic.
ISSN:	0933-5846 1432-0665
DOI:	10.1007/s00153-013-0365-4