The hide and seek game, as described in [3], models interactions between agents in pursuit-evasion scenarios. Interestingly, there is a natural counterpart in modal logic, particularly the logic of the hide and seek game. In this chapter, we extend the logic with formulas from hybrid logics and explore the properties of the resulting logic. Such an extension is beneficial in various aspects. For instance, it expands the potential applications of the system and makes the logic itself a tool linking research from different areas. Moreover, it is useful in improving our understanding of the basic logic of the hide and seek game itself: for instance, when the latter shows that equality sometime can drastically increase the computational complexity of a logic, our hybrid extension determines when equality becomes problematic. Finally, the extension improves the technical properties of the logical system, including the expressiveness. We will present complete Hilbert-style proof system for the resulting logic.

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The Hide and Seek Game: Perspectives from Hybrid Logic

  • Katsuhiko Sano,
  • Fenrong Liu,
  • Dazhu Li

摘要

The hide and seek game, as described in [3], models interactions between agents in pursuit-evasion scenarios. Interestingly, there is a natural counterpart in modal logic, particularly the logic of the hide and seek game. In this chapter, we extend the logic with formulas from hybrid logics and explore the properties of the resulting logic. Such an extension is beneficial in various aspects. For instance, it expands the potential applications of the system and makes the logic itself a tool linking research from different areas. Moreover, it is useful in improving our understanding of the basic logic of the hide and seek game itself: for instance, when the latter shows that equality sometime can drastically increase the computational complexity of a logic, our hybrid extension determines when equality becomes problematic. Finally, the extension improves the technical properties of the logical system, including the expressiveness. We will present complete Hilbert-style proof system for the resulting logic.