在动态认知逻辑（Van Ditmarsch、Van Der Hoek与Kooi，2008）中，通常使用行动框架（action frame，Baltag与Moss，2004；Baltag、Moss与Solecki，1998）来描述单一行动的不同视角。本文对行动框架进行扩展，使其支持添加或移除主体，我们将这类框架称为主体更新框架（agent-update frame）。这种扩展可以选择性地进行，即仅让特定主体获取更新信息，可用于建模多个有趣的案例，比如私人更新与欺骗，这类场景此前已被Baltag和Moss（2004）、Sakama（2015）、Van Ditmarsch、Van Eijck、Sietsma与Wang（2012）研究过。\nKripke模型经行动框架作用后的积更新（product update），是描述执行该行动后得到的变换后Kripke模型的简化方式。在新的设置下，这一机制被大幅扩展为Kripke模型经主体更新框架作用的和积更新（sum-product update）。这些思路被应用于故事建模这一AI问题中。我们证明，更新模态基于主体更新框架的动态认知逻辑，依然具备可靠且完全的证明系统。模型检测与可满足性的判定过程具有预期的复杂度。对于一个子语言，存在多项式空间算法。
英文摘要：
In dynamic epistemic logic (Van Ditmarsch, Van Der Hoek, & Kooi, 2008) it is customary to use an action frame (Baltag & Moss, 2004; Baltag, Moss, & Solecki, 1998) to describe different views of a single action. In this article, action frames are extended to add or remove agents, we call these agent-update frames. This can be done selectively so that only some specified agents get information of the update, which can be used to model several interesting examples such as private update and deception, studied earlier by Baltag and Moss (2004); Sakama (2015); Van Ditmarsch, Van Eijck, Sietsma, and Wang (2012). The product update of a Kripke model by an action frame is an abbreviated way of describing the transformed Kripke model which is the result of performing the action. This is substantially extended to a sum-product update of a Kripke model by an agent-update frame in the new setting. These ideas are applied to an AI problem of modelling a story. We show that dynamic epistemic logics, with update modalities now based on agent-update frames, continue to have sound and complete proof systems. Decision procedures for model checking and satisfiability have expected complexity. For a sublanguage, there are polynomial space algorithms.
We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and prove decidability for our logic via a finite model argument. We also provide a polynomial embedding of our logic into Fagin & Halpern's logic of general awareness and establish a complexit…
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been largely used to specify the agent's belief state - whether representing the agent's `explicit beliefs' or as a computational model for her belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in a dynamic epi…
Institute of Mathematics and Statistics, Federal University of Bahia - UFBA（巴伊亚联邦大学数学与统计学院）
AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent's belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. Particularly, it has been shown that some postulates can be characterised through transfo…
We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual be…
We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the …
With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino Pérez. First, at the level of representation of the information, we pass from belief bases to complex epistemic states. Second, the profiles are represented as functions of finite societies to the set of epistemic states (a sort of vectors) and not as multisets of epistemic states. Third, we extend the set of rational postulates in order to consider the epistemic versions of the classical p…
This chapter provides an introduction to some basic concepts of epistemic logic, basic formal languages, their semantics, and proof systems. It also contains an overview of the handbook, and a brief history of epistemic logic and pointers to the literature.
Universidad Simón Bolívar（西蒙玻利瓦尔大学）；Universidad de Los Andes（德洛斯安第斯大学）
In most classical models of belief change, epistemic states are represented by theories (AGM) or formulas (Katsuno-Mendelzon) and the new pieces of information by formulas. The Representation Theorem for revision operators says that operators are represented by total preorders. This important representation is exploited by Darwiche and Pearl to shift the notion of epistemic state to a more abstract one, where the paradigm of epistemic state is indeed that of a total preorder over interpretations. In this work, we introduce a 3-valued logic where the formulas can be identified with a generalisa…
Many dialogue management frameworks allow the system designer to directly define belief rules to implement an efficient dialog policy. Because these rules are directly defined, the components are said to be hand-crafted. As dialogues become more complex, the number of states, transitions, and policy decisions becomes very large. To facilitate the dialog policy design process, we propose an approach to automatically learn belief rules using a supervised machine learning approach. We validate our ideas in Student-Advisor conversation domain, where we extract latent beliefs like student is curiou…
In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper, we propose a general representation language for multi-agent epistemic planning where the initial KB and the goal, the preconditions and effects of actions can be arbitrary multi-agent epistemic formula…
School of Computing Queen’s University（女王大学计算机学院）；University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦图灵研究所）；Faculty of Computer Science University of Bozen-Bolzano（博岑-博尔扎诺大学计算机学院）；Department of Computer Science University of Toronto（多伦多大学计算机科学系）；School of Computing and Information Systems University of Melbourne（墨尔本大学计算与信息系统学院）
Many AI applications involve the interaction of multiple autonomous agents, requiring those agents to reason about their own beliefs, as well as those of other agents. However, planning involving nested beliefs is known to be computationally challenging. In this work, we address the task of synthesizing plans that necessitate reasoning about the beliefs of other agents. We plan from the perspective of a single agent with the potential for goals and actions that involve nested beliefs, non-homogeneous agents, co-present observations, and the ability for one agent to reason as if it were another…
Ludwig-Maximilians-University of Munich (LMU)（慕尼黑大学（LMU））；Friedrich Alexander University Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；Birkbeck College London（伦敦伯克贝克学院）
We start with the distinction of outcome- and belief-based Bayesian models of the sequential update of agents' beliefs and subjective reliability of sources (trust). We then focus on discussing the influential Bayesian model of belief-based trust update by Eric Olsson, which models dichotomic events and explicitly represents anti-reliability. After sketching some disastrous recent results for this perhaps most promising model of belief update, we show new simulation results for the temporal dynamics of learning belief with and without trust update and with and without communication. The result…
Over the last few years, the concept of Artificial Intelligence has become central in different tasks concerning both our daily life and several working scenarios. Among these tasks automated planning has always been central in the AI research community. In particular, this manuscript is focused on a specialized kind of planning known as Multi-agent Epistemic Planning (MEP). Epistemic Planning (EP) refers to an automated planning setting where the agent reasons in the space of knowledge/beliefs states and tries to find a plan to reach a desirable state from a starting one. Its general form, th…
University of Osnabrück（奥斯纳布吕克大学）；Cardiff University（卡迪夫大学）；University College London（伦敦大学学院）
Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted to new beliefs using update operators. While the use of probability functions puts this approach on a solid foundational basis, it also causes computational challenges as the amount of data to process depends exponentially on the number of arguments. This leads to bottlenecks in applications such as modelling opponent's beliefs for persuasion dialogues. We s…
In the field of knowledge representation, the considered epistemic states are often based on propositional interpretations, also called worlds. E.g., epistemic states of agents can be modelled by ranking functions or total preorders on worlds. However, there are usually different ways of how to describe a real world situation in a propositional language; this can be seen as different points of view on the same situation. In this paper we introduce the concept of model transformations to convert an epistemic state from one point of view to another point of view, yielding a novel notion of equiv…
Moores Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikkas interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a more accurate way our logical intuitions about the notion of belief without sacrificing the possibil…
CWI（荷兰国家数学与计算机科学研究中心）；ILLC, University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）
We investigate modal logics of high probability having two unary modal operators: an operator $K$ expressing probabilistic certainty and an operator $B$ expressing probability exceeding a fixed rational threshold $c\geq\frac 12$. Identifying knowledge with the former and belief with the latter, we may think of $c$ as the agent's betting threshold, which leads to the motto "belief is willingness to bet." The logic $\mathsf{KB.5}$ for $c=\frac 12$ has an $\mathsf{S5}$ $K$ modality along with a sub-normal $B$ modality that extends the minimal modal logic $\mathsf{EMND45}$ by way of four schemes r…
A General Framework of Epistemic Forgetting and its Instantiation by Ranking Functions
Faculty of Mathematics（数学系）；Computer Science, University of Hagen, 58084 Hagen, Germany（计算机科学，海因斯大学，德国）；Department of Computer Science, Technology Dortmund University, 44221 Dortmund, Germany（计算机科学系，多特蒙德技术大学，德国）
University of Udine（乌迪内大学）；New Mexico State University（新墨西哥州立大学）
Designing agents that reason and act upon the world has always been one of the main objectives of the Artificial Intelligence community. While for planning in "simple" domains the agents can solely rely on facts about the world, in several contexts, e.g., economy, security, justice and politics, the mere knowledge of the world could be insufficient to reach a desired goal. In these scenarios, epistemic reasoning, i.e., reasoning about agents' beliefs about themselves and about other agents' beliefs, is essential to design winning strategies. This paper addresses the problem of reasoning in mul…
Federal University of Bahia（巴伊亚联邦大学）；Pontifical Catholic University of Rio Grande do Sul（南里奥格兰德天主教大学）；Federal University of Rio Grande do Sul（南里奥格兰德联邦大学）
AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich and expressive semantic frameworks. While the connections of AGM-like operations and their encoding in dynamic doxastic logics have been studied before by the work of Segerberg, most works on the area of Dynamic Epistemic Logics (DEL) have not, to our knowledge, attempted to use those logics as tools to investigate mathematical properties of belief change o…
Stanford University（斯坦福大学）；Carnegie Mellon University（卡内基梅隆大学）；Santa Fe Institute（圣塔菲研究所）
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows exponentially as the argument expands. When a mathematician encounters a proof, how does she come to believe it? Here we show that, under a cognitively-plausible belief formation mechanism combining deductive and abductive reasoning, belief in mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump fro…
The Silent Scholar Problem: A Probabilistic Framework for Breaking Epistemic Asymmetry in LLM Agents
School of Science and Technology（科学与技术学院）；Kwansei Gakuin University（冈山大学）；School of Engineering & Computer Science（工程与计算机科学学院）；Victoria University of Wellington（惠灵顿维多利亚大学）
Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has been shown that the all-or-nothing version of possibility theory can be exactly captured by a minimal epistemic logic (MEL) that uses a very small fragment of the KD modal logic, without resorting to r…
An Epistemic Human-Aware Task Planner which Anticipates Human Beliefs and Decisions
LAAS-CNRS（法国国家科学研究中心自动化与系统分析实验室）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）；INSA（国立应用科学学院）；UPS（图卢兹第三大学）；Artificial and Natural Intelligence Toulouse Institute (ANITI)（图卢兹人工与自然智能研究所）
Scaling Multi-Agent Epistemic Planning through GNN-Derived Heuristics
Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia（工程科学与方法系，摩德纳和雷吉奥艾米利亚大学）；Department of Computer Science, University of Oxford（计算机科学系，牛津大学）；Department of Computer Science, University of Pisa（计算机科学系，比萨大学）
Cornell University（康奈尔大学）；University of New South Wales（新南威尔士大学）；Forrester Research（弗雷斯特研究公司）
While there have been many attempts, going back to BAN logic, to base reasoning about security protocols on epistemic notions, they have not been all that successful. Arguably, this has been due to the particular logics chosen. We present a simple logic based on the well-understood modal operators of knowledge, time, and probability, and show that it is able to handle issues that have often been swept under the rug by other approaches, while being flexible enough to capture all the higher- level security notions that appear in BAN logic. Moreover, while still assuming that the knowledge operat…
