Logics of knowledge and action: critical analysis and challenges

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15176 Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Logics of knowledge and action: critical analysis and challenges Andreas HerzigAbstract We overview the most prominent logics of knowledge and action that were proposed and studied in the multiagent systems literature. We classify them according to these two dimensions, knowledge and action, and moreover introduce a distinction between individual knowledge and group knowledge, and between a nonstrategic an a strategic interpretation of action operators. For each of the logics in our classification we highlight problematic properties. They indicate weaknesses in the design of these logics and call into question their suitability to represent knowledge and reason about it. This leads to a list of research challenges.

Mutual Modelling in Robotics

“…ϕ is shared knowledge, and it is also shared knowledge that ϕ is shared knowledge, etc. (this presentation follows [27]). This illustrates how epistemic logic can represent non-trivial social knowledge situations.…”

“…knowledge changes). Van Ditmarsch proposes in [48] for instance a solution to embed a practical subset of situation calculus into a dynamic epistemic logic, and Herzig provides in [27] a broader overview of the interplay between current action and epistemic logics.…”

A Poor Man’s Epistemic Logic Based on Propositional Assignment and Higher-Order Observation

“…Our notion of common knowledge is however weaker than standard common knowledge because the induction axiom ϕ ∧ CK ϕ → i∈Agt K i ϕ → CK ϕ is invalid in INTR. Beyond the technical reason for that choice (such an infinitary constraint cannot be captured by formula built from visibility atoms) we follow [13,9] and assume that such a principle is too strong for a logic of common knowledge.…”

Beyond Knowing That: A New Generation of Epistemic Logics

“…(Gochet, 2013;Ågotnes et al, 2015) for up-to-date overviews). One problem that logicians in AI face is that simply combining "knowing that" and "ability" does not lead to a natural notion of knowing how, as sharply pointed out by Herzig (2015). For example, adding the knowing-that operator to alternating temporal logic (ATL) can result in a logic which can express one knows that there is a strategy to achieve some goal, which is in the de dicto shape of K∃xϕ(x) rather than the desired de re shape ∃xKϕ(x).…”

“…Note that it essentially has the familiar shape ∃xKϕ(x), which also inspired the semi-formal treatment by Lau and Wang (2016). 43 See (Herzig, 2015) for some existing solutions, e.g. by using epistemic STIT logic proposed by Broersen and Herzig (2015).…”