SMALL INFINITARY EPISTEMIC LOGICS
SMALL INFINITARY EPISTEMIC LOGICS
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小无限认知逻辑
DOI：
10.1017/s1755020319000029
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
SUZUKI NOBU-YUKI
中科院分区：
文献类型：
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作者：
HU TAI-WEI;KANEKO MAMORU;SUZUKI NOBU-YUKI
我们开发了一系列小的无穷认知逻辑研究演绎推理涉及内部/人际信仰/知识，如共同知识，共同信念，和信仰的无限回归。具体地说，我们给出了命题认知逻辑GL（Lα），其中α到给定的αo（αo ≥ ω），使得GL（L 0）是有限的KDn，有n个主体，并且GL（Lα）（α ≥ 1）允许某些可数无穷公式的合取. GL（Lα）是小的，因为语言是可数的，并且可以是构造性的。公式集Lα一直增加到α = ω，但在ω处停止。我们给出了GL（Lα）的Kripke-完备性，对每个α ≤ ω，利用Rasiowa-Sikorski引理和Tanaka-Ono引理证明了这一结论。GL（Lα）有足够的表达能力来讨论无限长的内部/人际信念。作为应用，我们讨论了GL（Lα）中公理T（真性）、公理4（正内省）、公理5（负内省）和常识的显式可定义性。我们估计这些讨论在级数GL（Lα），α ≤ ω中的何处进行。
We develop a series of small infinitary epistemic logics to study deductive inference involving intra-/interpersonal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL (Lα) are presented for ordinal α up to a given αo (αo ≥ ω) so that GL(L0) is finitary KDn with n agents and GL(Lα) (α ≥ 1) allows conjunctions of certain countably infinite formulae. GL(Lα) is small in that the language is countable and can be constructive. The set of formulae Lα is increasing up to α = ω but stops at ω We present Kripke-completeness for GL(Lα) for each α ≤ ω, which is proved using the Rasiowa–Sikorski lemma and Tanaka–Ono lemma. GL(Lα) has a sufficient expressive power to discuss intra-/interpersonal beliefs with infinite lengths. As applications, we discuss the explicit definability of Axioms T (truthfulness), 4 (positive introspection), 5 (negative introspection), and of common knowledge in GL(Lα) Also, we discuss the rationalizability concept in game theory in our framework. We evaluate where these discussions are done in the series GL(Lα), α ≤ ω.