Łukasiewicz logic and weighted logics over MV-semirings

Authors:
Sibylle Schwarz
Affiliations:
Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany
Venue:
Journal of Automata, Languages and Combinatorics
Year:
2007

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Abstract

We connect Łukasiewicz logic, a well-established many-valued logic, with weighted logics, recently introduced by Droste and Gastin. We use this connection to show that for formal power series with coefficients in semirings derived from standard MV-algebras, recognizability and definability in a fragment of second order Łukasiewicz logic coincide. This implies decidability properties for these fragments of Łukasiewicz logic.