Modal Knowledge and Game Semirings
Modal Knowledge and Game Semirings
复制标题
模态知识和游戏半环
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
B. Möller
中科院分区：
文献类型：
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作者：
B. Möller
代数逻辑的目的是将一般逻辑推理的一系列小步骤压缩为更大的（内）方程步骤。已证明在这方面非常有用的代数结构是模态半环和模态克林代数。我们证明，他们还可以对知识和信念逻辑以及游戏进行建模，而无需额外的努力；在这种情况下，许多标准逻辑属性都是定理而不是公理。作为第一个领域的例子，我们将讨论《智者》和《泥泞的孩子》中的经典谜题。此外，我们展示了以代数方式处理知识更新和修订的可能性。对于游戏领域，我们将游戏逻辑和动态逻辑之间众所周知的联系推广到模态半环的设置，并将其与谓词变换器语义联系起来，特别是恶魔求精代数。我们认为我们的研究提供了证据，表明模态半环能够以统一的代数方式处理各种（多）模态逻辑。
The aim of algebraic logic is to compact series of small steps of general logical inference into larger (in)equational steps. Algebraic structures that have proved very useful in this context are modal semirings and modal Kleene algebras. We show that they can also model knowledge and belief logics as well as games without additional effort; many of the standard logical properties are theorems rather than axioms in this setting. As examples of the first area, we treat the classical puzzles of the Wise Men and the Muddy Children. Moreover, we show possibilities of handling knowledge update and revision algebraically. For the area of games, we generalize the well-known connection between game logic and dynamic logic to the setting of modal semirings and link it to predicate transformer semantics, in particular to demonic refinement algebra. We think that our study provides evidence that modal semirings are capable of handling a wide variety of (multi-)modal logics in a uniform algebraic fashion.
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影响因子：
0.7
作者：
Baltag A
通讯作者：
Baltag A