Coalition logic with individual, distributed and common knowledge1

Abstract

Coalition logic is currently one of the most popular logics for multi-agent systems. While logics combining coalitional and epistemic operators have received considerable attention, completeness results for epistemic extensions of coalition logic have so far been missing. In this paper we provide several such results and proofs. We prove completeness for epistemic coalition logic with common knowledge, with distributed knowledge, and with both common and distributed knowledge, respectively. Furthermore, we completely characterise the complexity of the satisfiability problem for each of the three logics. We also study logics with interaction axioms connecting coalitional ability and knowledge.

Knowing-How under Uncertainty (Extended Abstract)

“…Several modal logical systems that capture the interplay between knowledge and know-how strategies without uncertainty have been proposed. Ågotnes and Alechina [2019] introduced a complete axiomatization of an interplay between single-agent knowledge and coalition know-how modalities to achieve a goal in one step. A modal logic that combines the distributed knowledge modality with the coalition know-how modality to maintain a goal was axiomatized by us in [Naumov and Tao, 2017a].…”

“…The first four of these axioms come from [Naumov and Tao, 2015]. The Strategic Positive Introspection axiom without a degree of uncertainty first appeared in [Ågotnes and Alechina, 2019] and is also present in [Wang, 2018;Fervari et al, 2017;Naumov and Tao, 2017b;2017a;2018b;2018a;2018c]. Blending the know-how and the degree of uncertainty lines of research into one logical system that captures non-trivial interplay between the two notions is the main contribution of this article.…”

Intelligence in Strategic Games

“…However, since allies do not know the location of Russian mines, even after they receive information about German plans, they still would not know how to save the convoy. It has been suggested in several recent works that, in the the case of the games with imperfect information, strategic power modality in Marc Pauly logic should be restricted to existence of know-how 1 strategies [29,30,31,32,33,34]. That is, modality [C]ϕ should stands for "coalition C has a strategy, it knows that it has a strategy, and it knows what the strategy is".…”

Navigability with intermediate constraints

“…Naumov and Tao [23] used the term "executable strategy". Agotnes and Alechina gave a complete axiomatization of an interplay between single-agent knowledge and know-how modalities [2]. Naumov and Tao [23] axiomatized interplay between distributed knowledge modality and know-how coalition strategies for enforcing a condition indefinitely.…”