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arXiv cs/0405038cs.AIcs.LO
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演绎数学知识

Deductive Algorithmic Knowledge

Riccardo Pucella

摘要:

算法知识的框架假设代理使用算法来计算他们明确知道的事实。在许多感兴趣的情况下,演绎系统,而不是一个特定的算法,捕获了代理用来计算他们明确知道的东西的形式推理。我们引入了一个逻辑推理的隐式和显式的知识与后者定义的演绎系统正式的逻辑理论的代理。演绎系统的高度结构化的性质导致了在任何固定的演绎系统上解释时所产生的逻辑的非常自然的公理化。逻辑的决策问题,在一个单一的代理人的存在,是NP-完全的一般,没有比命题逻辑更难。当我们确定一个在非确定多项式时间内可判定的演绎系统时,它仍然是NP完全的。这些结果以一种简单的方式扩展到多个代理。

英文摘要:

The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by the agents to compute what they explicitly know. We introduce a logic for reasoning about both implicit and explicit knowledge with the latter defined with respect to a deductive system formalizing a logical theory for agents. The highly structured nature of deductive systems leads to very natural axiomatizations of the resulting logic when interpreted over any fixed deductive system. The decision problem for the logic, in the presence of a single agent, is NP-complete in general, no harder than propositional logic. It remains NP-complete when we fix a deductive system that is decidable in nondeterministic polynomial time. These results extend in a straightforward way to multiple agents.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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