Product logic and probabilistic Ulam games

Authors:
Franco Montagna;Claudio Marini;Giulia Simi
Affiliations:
Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy;Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy;Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

There is a well-known game semantics for Lukasiewicz logic, introduced by Daniele Mundici, namely the Renyi-Ulam game. Records in a Reny-Ulam game are coded by functions, which constitute an MV-algebra, and it is possible to prove a completeness theorem with respect to this semantics. In this paper we investigate some probabilistic variants of the Renyi-Ulam game, and we prove that some of them constitute a complete game semantics for product logic, whilst some other constitute a game semantics for a logic between @PMTL and product logic.