A normal simulation of coalition logic and an epistemic extension

Abstract

In this paper we show how coalition logic can be reduced to the fusion of a normal modal STIT logic for agency and a standard normal temporal logic for discrete time, and how this multi-modal system can be suitably extended with an epistemic modality. Both systems are complete, and we provide a new axiomatization for the STIT-fragment. The epistemic extension enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. In accordance with established terminology in the planning community, we call this version of STIT the 'conformant STIT'. The conformant STIT enables us to express that agents are able to perform a uniform strategy. As a final word of recommendation for this paper we want to point out that its subject is at the junction of four academic fields, viz. modal logic, philosophy, game-theory and AI-planning.

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

“…However, the forcing operator is not defined in terms of intersection, and the operator is only defined for singleton coalitions. [4] have already shown that coalition logic can be embedded in a normal modal logic, namely in a variant of STIT (seeing-to-it-that) logic [3]. While this is a valuable result for several reasons, we argue that embedding in K ∩ n is of additional interest because the latter is a more standard logic (see the introduction).…”

“…Although other logics that are normal modal logics and/or have PDL-type operators and can express coalition operators have been studied recently [4,11], these typically have non-standard syntactic operators and/or non-standard semantics (see Section 7). The focus in the current paper is on reasoning about joint action in game structures using a minimal language with the intersection operator.…”

Strategic games and truly playable effectivity functions

“…Moreover, the correspondence has been used to obtain further results for CL: if the semantics can be defined equivalently in terms of strategic games and playable effectivity functions, they can be used interchangeably when proving properties of the logic. A similar remark applies to ATL and STIT, connected to Coalition Logic by a number of simulation results [4,6,7].…”

Coalition logic with individual, distributed and common knowledge1

“…The techiques developed for those logics influence developments for CL as well, especially since as observed in [10], CL is a fragment of AT L. Most of the known meta-logical results for the logics of coalitional ability have been about computational complexity and expressive power. Completeness results have been harder to obtain, with Goranko's and van Drimmelen's completeness proof for AT L [13], Pauly's completeness proof for CL [25] and Broersen and colleagues' completeness proofs for different variants of STiT logic [7,6,19] being notable exceptions.…”