We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic) Epistemic Logic. Regarding non-predetermined possibilities, we propose a constructive epistemic logic and prove soundness and completeness theorems for it. We extend the proposed logic by adding a public announcement operator. To declare the significance of our work, we formulate the well-known Surprise Exam Paradox, $\mathbf{SEP}$, via the proposed constructive epistemic logic and then put forward a solution for the paradox. We clarify that the puzzle in the $\mathbf{SEP}$ is because of students'(wrong) assumption that the day of the exam is necessarily predetermined.
Public announcement logic(PAL) is an extension of epistemic logic (EL) with some reduction axioms. In this paper, we propose a cut-free labelled sequent calculus for PAL, which is an extension of that for EL with sequent rules adapted from the reduction axioms. This calculus admits cut and allows terminating proof search.
Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and Coalition Announcement Logic. They allow us to reason about what groups of agents can achieve through joint announcements in non-competitive and competitive environments. In this paper, we consider a combination of these logics -- Coalition and Group Announcement Logic and provide its complete axiomatisation. Moreover, we partially answer the question of how…
Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and Coalition Announcement Logic. They allow us to reason about what groups of agents can achieve through joint announcements in non-competitive and competitive environments. In this paper, we consider a combination of these logics -- Coalition and Relativised Group Announcement Logic and provide its complete axiomatisation. Moreover, we partially answer the que…
Arbitrary public announcement logic (APAL) reasons about how the knowledge of a set of agents changes after true public announcements and after arbitrary announcements of true epistemic formulas. We consider a variant of arbitrary public announcement logic called positive arbitrary public announcement logic (APAL+), which restricts arbitrary public announcements to announcement of positive formulas. Positive formulas prohibit statements about the ignorance of agents. The positive formulas correspond to the universal fragment in first-order logic. As two successive announcements of positive for…
Quantification over public announcements shifts the perspective from reasoning strictly about the results of a particular announcement to reasoning about the existence of an announcement that achieves some certain epistemic goal. Depending on the type of the quantification, we get different formalisms, the most known of which are arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). It has been an open question whether the logics have the finite model property, and in the paper we answer the question negatively. We also discuss how …
IRIT（图卢兹计算机研究所）；CNRS（法国国家科学研究中心）；University of Toulouse（图卢兹大学）；LORIA（洛林计算机科学及其应用实验室）；University of Lorraine（洛林大学）
We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a function of her initial uncertainty and of the announcements she has received. Beliefs need not be truthful, because announcements already made may not yet have been received. As announcements are true when sent, certain message sequences can be ruled …
In standard epistemic logic, knowing that p is the same as knowing that p is true, but it does not say anything about understanding p or knowing its meaning. In this paper, we present a conservative extension of Public Announcement Logic (PAL) in which agents have knowledge or belief about both the truth values and the meanings of propositions. We give a complete axiomatization of PAL with Boolean Definitions and discuss various examples. An agent may understand a proposition without knowing its truth value or the other way round. Moreover, multiple agents can agree on something without agreei…
Labortoire IBISC, UEVE（UEVE IBISC实验室）；IRIT Toulouse（图卢兹IRIT研究所）；LORIA – CNRS（洛林计算机及其应用研究实验室（CNRS））；Université de Lorraine（洛林大学）；Department of Computing（计算系）；University of Liverpool（利物浦大学）
In this paper we introduce {\em global and local announcement logic} (GLAL), a dynamic epistemic logic with two distinct announcement operators -- $[ϕ]^+_A$ and $[ϕ]^-_A$ indexed to a subset $A$ of the set $Ag$ of all agents -- for global and local announcements respectively. The boundary case $[ϕ]^+_{Ag}$ corresponds to the public announcement of $ϕ$, as known from the literature. Unlike standard public announcements, which are {\em model transformers}, the global and local announcements are {\em pointed model transformers}. In particular, the update induced by the announcement may be differe…
We define reachability games based on Dynamic Epistemic Logic (DEL), where the players' actions are finely described as DEL action models. We first consider the setting where an external controller with perfect information interacts with an environment and aims at reaching some epistemic goal state regarding the passive agents of the system. We study the problem of strategy existence for the controller, which generalises the classic epistemic planning problem, and we solve it for several types of actions such as public announcements and public actions. We then consider a yet richer setting whe…
We consider dynamic versions of epistemic logic as formulated in Baltag and Moss "Logics for epistemic programs" (2004). That paper proposed a logical language (actually families of languages parameterized by action signatures) for dynamic epistemic logic. It had been shown that validity in the language is Pi-1-1-complete, so there are no recursively axiomatized complete logical systems for it. In contrast, this paper proves a weak completeness result for the fragment without action iteration, and a strong completeness result for the fragment without action iteration and common knowledge. Our …
Institute of Philosophy and Human Sciences, UNICAMP（坎皮纳斯州立大学哲学与人文科学学院）；University of Toulouse, IRIT-CNRS（图卢兹大学IRIT-CNRS）；Indian Institut of Technology (IIT)（印度理工学院）
We present a basic dynamic epistemic logic of "knowing the value". Analogous to public announcement in standard DEL, we study "public inspection", a new dynamic operator which updates the agents' knowledge about the values of constants. We provide a sound and strongly complete axiomatization for the single and multi-agent case, making use of the well-known Armstrong axioms for dependencies in databases.
Communication within groups of agents has been lately the focus of research in dynamic epistemic logic (DEL). This paper studies a recently introduced form of partial (more precisely, topic-based) communication. This type of communication allows for modelling scenarios of multi-agent collaboration and negotiation, and it is particularly well-suited for situations in which sharing all information is not feasible/advisable. After presenting results on invariance and complexity of model checking, the paper compares partial communication to public announcements, probably the most well-known type o…
Dynamic Epistemic Logic (DEL) is a logical framework in which one can describe in great detail how actions are perceived by the agents, and how they affect the world. DEL games were recently introduced as a way to define classes of games with imperfect information where the actions available to the players are described very precisely. This framework makes it possible to define easily, for instance, classes of games where players can only use public actions or public announcements. These games have been studied for reachability objectives, where the aim is to reach a situation satisfying some …
In this paper, we propose a lightweight yet powerful dynamic epistemic logic that captures not only the distinction between de dicto and de re knowledge but also the distinction between de dicto and de re updates. The logic is based on the dynamified version of an epistemic language extended with the assignment operator borrowed from dynamic logic, following the work of Wang and Seligman (Proc. AiML 2018). We obtain complete axiomatizations for the counterparts of public announcement logic and event-model-based DEL based on new reduction axioms taking care of the interactions between dynamics …
We present a general framework for modelling and verifying epistemic properties over parameterized multi-agent systems that communicate by truthful public announcements. In our framework, the number of agents or the amount of certain resources are parameterized (i.e. not known a priori), and the corresponding verification problem asks whether a given epistemic property is true regardless of the instantiation of the parameters. For example, in a muddy children puzzle, one could ask whether each child will eventually find out whether (s)he is muddy, regardless of the number of children. Our fram…
Institute for Logic, Language and Computation University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）
Dynamic epistemic logic (DEL) is a logical framework for representing and reasoning about knowledge change for multiple agents. An important computational task in this framework is the model checking problem, which has been shown to be PSPACE-hard even for S5 models and two agents---in the presence of other features, such as multi-pointed models. We answer open questions in the literature about the complexity of this problem in more restricted settings. We provide a detailed complexity analysis of the model checking problem for DEL, where we consider various combinations of restrictions, such …
Reasoning About Knowledge on Regular Expressions is 2EXPTIME-complete
Chennai Mathematical Institute Chennai, India（钦奈数学研究所（钦奈，印度））；Indian Statistical Institute Chennai, India（印度统计研究所（钦奈，印度））；ENS De Lyon France（里昂高等师范学院（法国））
本文研究了多智能体认知规划中基于公开观察更新知识的逻辑，证明了 Public Observation Logic (POL) 的可满足性问题是 2EXPTIME 完全的。
