Epistemic logics model how agents reason about their beliefs and the beliefs
of other agents. Existing logics typically assume the ability of agents to
reason perfectly about propositions of unbounded modal depth. We present DBEL,
an extension of S5 that models agents that can reason about epistemic formulas
only up to a specific modal depth. To support explicit reasoning about agent
depths, DBEL includes depth atoms Ead (agent a has depth exactly d) and Pad
(agent a has depth at least d). We provide a sound and complete axiomatization
of DBEL.
We extend DBEL to support public announcements for bounded depth agents and
show how the resulting DPAL logic generalizes standard axioms from public
announcement logic. We present two alternate extensions and identify two
undesirable properties, amnesia and knowledge leakage, that these extensions
have but DPAL does not. We provide axiomatizations of these logics as well as
complexity results for satisfiability and model checking.
Finally, we use these logics to illustrate how agents with bounded modal
depth reason in the classical muddy children problem, including upper and lower
bounds on the depth knowledge necessary for agents to successfully solve the
problem.

DBEL 是 S5 的扩展，用来模拟深度有限的代理人进行关于知识公式的推理，同时添加了深度原子 Ead 和 Pad，扩展了公开声明逻辑的公理，解决了遗忘和知识泄漏等问题，并用这些逻辑来解决经典的泥泞孩子问题。

深度有限的认知逻辑

Depth-bounded Epistemic Logic

The tension between deduction and induction is perhaps the most fundamental
issue in areas such as philosophy, cognition and artificial intelligence. In an
influential paper, Valiant recognised that the challenge of learning should be
integrated with deduction. In particular, he proposed a semantics to capture
the quality possessed by the output of Probably Approximately Correct (PAC)
learning algorithms when formulated in a logic. Although weaker than classical
entailment, it allows for a powerful model-theoretic framework for answering
queries. In this paper, we provide a new technical foundation to demonstrate
PAC learning with multi-agent epistemic logics. To circumvent the negative
results in the literature on the difficulty of robust learning with the PAC
semantics, we consider so-called implicit learning where we are able to
incorporate observations to the background theory in service of deciding the
entailment of an epistemic query. We prove correctness of the learning
procedure and discuss results on the sample complexity, that is how many
observations we will need to provably assert that the query is entailed given a
user-specified error bound. Finally, we investigate under what circumstances
this algorithm can be made efficient. On the last point, given that reasoning
in epistemic logics especially in multi-agent epistemic logics is
PSPACE-complete, it might seem like there is no hope for this problem. We
leverage some recent results on the so-called Representation Theorem explored
for single-agent and multi-agent epistemic logics with the only knowing
operator to reduce modal reasoning to propositional reasoning.

此文介绍了使用多智能体认知逻辑演示 PAC 学习的技术基础，涉及逻辑和弱推理，以提供强大的模型理论框架来回答查询，并研究了该算法的正确性、样本复杂性以及其能够高效的情况，利用表述定理将模态推理纳入命题推理中。

多智体信仰的 PAC 语义学习性

Learnability with PAC Semantics for Multi-agent Beliefs

Epistemic logics typically talk about knowledge of individual agents or
groups of explicitly listed agents. Often, however, one wishes to express
knowledge of groups of agents specified by a given property, as in `it is
common knowledge among economists'. We introduce such a logic of common
knowledge, which we term abstract-group epistemic logic (AGEL). That is, AGEL
features a common knowledge operator for groups of agents given by concepts in
a separate agent logic that we keep generic, with one possible agent logic
being ALC. We show that AGEL is EXPTIME-complete, with the lower bound
established by reduction from standard group epistemic logic, and the upper
bound by a satisfiability-preserving embedding into the full $\mu$-calculus.
Further main results include a finite model property (not enjoyed by the full
$\mu$-calculus) and a complete axiomatization.

介绍了一种名为抽象组认知逻辑（AGEL）的逻辑，该逻辑为指定的属性中的代理组引入了一个共同知识运算符，具有完备的公理化和有限模型性质。