Reasoning about Joint Action and Coalitional Ability in K n with Intersection

Abstract

Abstract. In this paper we point out that standard PDL-like logics with intersection are useful for reasoning about game structures. In particular, they can express coalitional ability operators known from coalition logic and ATL. An advantage of standard, normal, modal logics is a well understood theoretical foundation and the availability of tools for automated verification and reasoning. We study a minimal variant, multi-modal K with intersection of modalities, interpreted over models corresponding to game structures. There is a restriction: we consider only game structures that are injective. We give a complete axiomatisation of the corresponding models, as well as a characterisation of key complexity problems. We also prove a representation theorem identifying the effectivity functions corresponding to injective games.

Group Norms for Multi-Agent Organisations

“…Research about the concept of shared actorship can be found in work on joint action and coalitions (e.g., Borgo [2007], Ågotnes and Alechina [2011], and Grossi et al [2007]). This line of investigation is relevant, as it looks into individual deliberation when coordination is required.…”

“…This amounts to finding all minimal coalition of agents who can achieve ϕ collectively[Ågotnes and Alechina 2011].…”

Reasoning with Group Norms in Software Agent Organisations

“…However, these approaches only deal with the element of shared responsibility, neglecting the element of shared actorship. Research about the concept of shared actorship can be found in work on joint action and coalitions (e.g., [5,1,16]). This line of investigation is relevant as it looks into individual deliberation when coordination is required, whereas work on delegation (e.g., [11,25]) sheds light on how norms can be transferred among individuals and groups.…”

Embedding Coalition Logic in the Minimal Normal Multimodal Logic with Intersection

“…The paper is based on [19]; the main additional contribution of the current paper is the sharpening of the embedding result. In [19], we defined a translation from C L into joint action logic with a fixed number of actions.…”

“…In [19], we defined a translation from C L into joint action logic with a fixed number of actions. In the current paper, we define a translation from C L which "reads off" the required number of actions from the C L formula.…”