David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Non-determined game logic is the logic of two player board games where the game may end in a draw: unlike the case with determined games, a loss of one player does not necessarily constitute of a win of the other player. A calculus for non-determined game logic is given in  and shown to be complete. The calculus adds a new rule for the treatment of greatest fixpoints, and a new unfolding axiom for iterations of the universal player. The technique of the completeness proof is inspired by the canonical model construction for propositional dynamic logic (PDL). In this paper, this is extended to the logic of determined games. It is proved that the calculus for nondetermined game logic, together with the axiom of determinacy, is complete for determined game logic. Next, it is shown that the axioms and rules of the new calculus can all be derived from the calculus proposed by Parikh in , for which the completeness was still open. This proves Parikh’s conjecture that his calculus is complete for determined games.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Shier Ju & Xuefeng Wen (2008). An N -Player Semantic Game for an N + 1-Valued Logic. Studia Logica 90 (1):17 - 23.
Johan Van Benthem (2003). Logic Games Are Complete for Game Logics. Studia Logica 75 (2):183 - 203.
Johan van Benthem (2003). Logic Games Are Complete for Game Logics. Studia Logica 75 (2):183-203.
Chris Freiling (1984). Banach Games. Journal of Symbolic Logic 49 (2):343-375.
Johan Van Benthem, Sujata Ghosh & Fenrong Liu (2008). Modelling Simultaneous Games in Dynamic Logic. Synthese 165 (2):247 - 268.
Johan van Benthem, Sujata Ghosh & Fenrong Liu (2008). Modelling Simultaneous Games in Dynamic Logic. Synthese 165 (2):247-268.
Dietmar Berwanger (2003). Game Logic is Strong Enough for Parity Games. Studia Logica 75 (2):205 - 219.
E. -W. Stachow (1976). Completeness of Quantum Logic. Journal of Philosophical Logic 5 (2):237 - 280.
Marc Pauly & Rohit Parikh (2003). Game Logic - an Overview. Studia Logica 75 (2):165 - 182.
Added to index2009-01-28
Total downloads13 ( #174,287 of 1,696,808 )
Recent downloads (6 months)7 ( #81,860 of 1,696,808 )
How can I increase my downloads?