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Logic Journal of IGPL 2005 13(5):561-585; doi:10.1093/jigpal/jzi042
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© The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Lukasiewicz Logic: From Proof Systems To Logic Programming

George Metcalfe1 *, Nicola Olivetti2 and Dov Gabbay3

1 Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria. E-mail: metcalfe{at}logic.at, 2 Department of Computer Science, University of Turin, Corso Svizzera 185, 10149 Turin, Italy. Email: olivetti{at}di.unito.it, 3 Department of Computer Science, King's College London, Strand, London WC2R 2LS, UK. Email: dg{at}dcs.kcl.ac.uk

We present logic programming style "goal-directed" proof methods for Lukasiewicz logic L that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of L with rational constants.

Key Words: Lukasiewicz Logics, Fuzzy Logics, Goal-Directed Methods, Logic Programming

Received 31 December 2004.


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