Dynamic term-modal logics for first-order epistemic planning

Liberman, Andrés Occhipinti; Achen, Andreas; Rendsvig, Rasmus K.

doi:10.1016/j.artint.2020.103305

Cited by 14 publications

(11 citation statements)

References 55 publications

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“…The joint axiomatization of the latter two notions is also open, as well as the extendability of the results here to more restricted classes of frames, in particular in those cases where the agents know their own names. Another natural next step is to look at dynamic extensions of this language [14,17], and especially conditions under which agents can learn who are the members of certain groups. One should also study the possibility of postulating certain patterns of interactions between names.…”

Section: Discussionmentioning

confidence: 99%

“…Even though the idea appears earlier [28,18,13], Grove and Halpern's contribution, as well as [9], has been seminal for the development of socalled term modal logic-c.f. [17] and the references therein-which in turn have helped to understand, among others, de dicto and de re knowledge attributions. Since many term modal logics turn out to be undecidable, one important question in that literature has been to identify decidable fragments-c.f.…”

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confidence: 99%

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Revisiting Epistemic Logic with Names

Bílková

Christoff

Roy

2021

Electron. Proc. Theor. Comput. Sci.

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This paper revisits the multi-agent epistemic logic presented in [10], where agents and sets of agents are replaced by abstract, intensional "names". We make three contributions. First, we study its model theory, providing adequate notions of bisimulation and frame morphisms, and use them to study the logic's expressive power and definability. Second, we show that the logic has a natural neighborhood semantics, which in turn allows to show that the axiomatization in [10] does not rely on possibly controversial introspective properties of knowledge. Finally, we extend the logic with common and distributed knowledge operators, and provide a sound and complete axiomatization for each of these extensions. These results together put the original epistemic logic with names in a more modern context and opens the door for a logical analysis of epistemic phenomena where group membership is uncertain or variable.In [10], Grove and Halpern studied a generalized version of multi-agents epistemic logic where the usual labels for agents and sets of agents are replaced by abstract names whose extension might vary from state to state. 1 Despite being interpreted in standard multi-agents epistemic models, the resulting language does away with the familiar K i modalities, and instead contains two families of epistemic operators: S n , standing for "someone with name n knows", and E n , standing for "everyone with name n knows". This generalization is conceptually important. The "names" that index the S n and the E n modalities can refer intensionally to both individuals and groups. Since these extensions are not fixed in a given model, the logic allows to study social-epistemic phenomena that involve uncertainty or variability in the agents' identities or group membership. These phenomena are pervasive. [19,10] already provide convincing examples for distributed systems. Massive coordinated actions or social movements, especially online, also provide contemporary cases [1,4], where for instance we refer to group labels like "Trump supporters" or "trolls" without knowing exactly who the members of these groups are or even failing to know whether we, ourselves, are members of those groups. 2 The study in [10], however, focuses on the two modalities mentioned above, and in particular leaves aside notions of common and distributed knowledge. These notions are, however, central to theories of social conventions [16,2] and collective action [25].[19] study a closely related notion of common knowledge, to which we come back briefly in Section 4, but do not provide an axiomatization. Distributed knowledge for intensional or indexical group names has been studied in [20], but in a more expressive language with explicit quantification.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Revisiting Epistemic Logic with Names

Bílková

Christoff

Roy

2021

Electron. Proc. Theor. Comput. Sci.

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“…Wang and Fan showed that there is simply no reduction possible in Plaza's language and use a strengthened conditional Kv modality to axiomatize the logic [33,34]. Note that although de dicto announcements can possibly involve or change de re knowledge as nicely shown in [21,22], 1 it is not the most natural dynamic counterpart of the Kv i operator, as the table below Just like one can know a proposition after an announcement, one should be able to know the value of a after it is announced. However, announcing the value of a cannot be easily handled by announcing that, e.g., suppose the domain of a is the set of natural numbers, then you need to use infinitely many non-deterministic announcements in the form of a ≈ k for each k ∈ N. Does it mean we need to introduce constants for all the numbers in the language?…”

Section: De Re Knowledge and Updatesmentioning

confidence: 99%

De Re Updates

Cohen

Tang

Wang

2021

Electron. Proc. Theor. Comput. Sci.

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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 [35]. 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 and assignments.

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“…This would allow learners to reason about both their implicit and explicitly knowledge and how they are interrelated. An even more compact representation could possibly be obtained with first-order DEL (FODEL) action schemas such as those of Liberman et al [43], or with the succinct event models of Charrier and Schwarzentruber [17]. Since FODEL action schemas are represented with variables from first-order logic, learning them would require a non-trivial extension of existing methods.…”

Section: Computational Complexitymentioning

confidence: 99%

Learning to Act and Observe in Partially Observable Domains

Bolander,

Gierasimczuk,

Liberman

2021

Preprint

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We consider a learning agent in a partially observable environment, with which the agent has never interacted before, and about which it learns both what it can observe and how its actions affect the environment. The agent can learn about this domain from experience gathered by taking actions in the domain and observing their results. We present learning algorithms capable of learning as much as possible (in a well-defined sense) both about what is directly observable and about what actions do in the domain, given the learner's observational constraints. We differentiate the level of domain knowledge attained by each algorithm, and characterize the type of observations required to reach it. The algorithms use dynamic epistemic logic (DEL) to represent the learned domain information symbolically. Our work continues that of Bolander and Gierasimczuk (2015), which developed DEL-based learning algorithms based to learn domain information in fully observable domains.

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Dynamic term-modal logics for first-order epistemic planning

Cited by 14 publications

References 55 publications

Revisiting Epistemic Logic with Names

Revisiting Epistemic Logic with Names

De Re Updates

Learning to Act and Observe in Partially Observable Domains

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