There is a well-known game semantics for Lukasiewicz logic, introduced by Daniele Mundici, namely the Rényi–Ulam game. Records in a Rény–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 Rényi–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 MTL and product logic.
Montagna, F., Marini, C., Simi, G. (2007). Product logic and probabilistic Ulam games. FUZZY SETS AND SYSTEMS, 158(6), 639-651 [10.1016/j.fss.2006.11.007].
Product logic and probabilistic Ulam games
MONTAGNA, FRANCO;SIMI, GIULIA
2007-01-01
Abstract
There is a well-known game semantics for Lukasiewicz logic, introduced by Daniele Mundici, namely the Rényi–Ulam game. Records in a Rény–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 Rényi–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 MTL and product logic.
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https://hdl.handle.net/11365/8269
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