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Generalised Proof-Theory for Multi-Agent Autoepistemic Reasoning

机译:多助药自血检推理的广义证明理论

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Over the past few years, several different ap-proaches have been proposed to deal with multi-agent autoepistemic reasoning. Despite some limitations, each approach is important in its own right. While Parikh's approach allows an agent to reason nonmonotonically about other agents' knowledge, it cannot reason about other agents' nonmonotonic reasoning. Morgenstern'a logic provides a limited way to deal with the problem but unfortunately it is not constructive. Although Halpern introduces an algorithmic def-inition of multi-agent nonmonotonic reasoning, his approach cannot deal with default reason-ing even for the single-agent case. The purpose of this paper is to propose an integrated theory that deals with these problems. Using examples from speech acts theory, we demonstrate some unintuitive results against existing approaches. We then develop a simple and yet generalised proof-theoretic framework with constructive in-terpretation for multi-agent autoepistemic rea-soning. We show that this framework retains the advantages of existing approaches but does not have their peculiar results. Surprisingly, the new proof-theoretic framework can be obtained by a simple modification of Parikh's approach. Fur-thermore, the results show that our framework generalises Morgenstern's approach.
机译:在过去的几年里,已经提出了几个不同的AP-Proaches来处理多项代理人的自身血检推理。尽管有一些局限性,但每种方法都很重要。虽然Parikh的方法允许代理人对其他代理商的知识进行非语文,但它不能推理其他药剂的非单调推理。 Morgenstern'a逻辑提供了一个有限的方法来处理问题,但不幸的是它并不是建设性的。尽管HALPERN引入了多助手非单调推理的算法污染,但他的方法也无法处理默认的原因,即使是单颗粒案例也是如此。本文的目的是提出统一理论,这些理论涉及这些问题。使用语音行为理论的例子,我们展示了一些针对现有方法的不行性结果。然后,我们开发一个简单而广泛的校正理论框架,具有多种Agent Autopistem Rea-Soning的建设性in-terpretation。我们表明该框架保留了现有方法的优势,但没有其特殊的结果。令人惊讶的是,新的证明理论框架可以通过简单的Parikh方法进行简单修改来获得。毛皮恒温,结果表明,我们的框架推出了Morgenstern的方法。

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