Complete Game Logic with Sabotage
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909217001046016 |
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| author | Wafa, Noah Abou El Platzer, André |
| author_facet | Wafa, Noah Abou El Platzer, André |
| contents | Game Logic with sabotage ($\mathsf{GL_s}$) is introduced as a simple and natural extension of Parikh's game logic with a single additional primitive, which allows players to lay traps for the opponent. $\mathsf{GL_s}$ can be used to model infinite sabotage games, in which players can change the rules during game play. In contrast to game logic, which is strictly less expressive, $\mathsf{GL_s}$ is exactly as expressive as the modal $μ$-calculus. This reveals a close connection between the entangled nested recursion inherent in modal fixpoint logics and adversarial dynamic rule changes characteristic for sabotage games. A natural Hilbert-style proof calculus for $\mathsf{GL_s}$ is presented and proved complete using syntactic equiexpressiveness reductions. The completeness of a simple extension of Parikh's calculus for game logic follows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete Game Logic with Sabotage Wafa, Noah Abou El Platzer, André Logic in Computer Science Computer Science and Game Theory Logic 03B70 (Primary) 03B45, 68Q60, 91A44, 91A05, 91A25 (Secondary) F.3.1; F.4.1; F.3.3 Game Logic with sabotage ($\mathsf{GL_s}$) is introduced as a simple and natural extension of Parikh's game logic with a single additional primitive, which allows players to lay traps for the opponent. $\mathsf{GL_s}$ can be used to model infinite sabotage games, in which players can change the rules during game play. In contrast to game logic, which is strictly less expressive, $\mathsf{GL_s}$ is exactly as expressive as the modal $μ$-calculus. This reveals a close connection between the entangled nested recursion inherent in modal fixpoint logics and adversarial dynamic rule changes characteristic for sabotage games. A natural Hilbert-style proof calculus for $\mathsf{GL_s}$ is presented and proved complete using syntactic equiexpressiveness reductions. The completeness of a simple extension of Parikh's calculus for game logic follows. |
| title | Complete Game Logic with Sabotage |
| topic | Logic in Computer Science Computer Science and Game Theory Logic 03B70 (Primary) 03B45, 68Q60, 91A44, 91A05, 91A25 (Secondary) F.3.1; F.4.1; F.3.3 |
| url | https://arxiv.org/abs/2404.09873 |