Product logic and probabilistic Ulam games

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 Pi MTL and product logic. (C) 2006 Elsevier B.V. All rights reserved.