Conference Paper

A Logic for Coalitions with Bounded Resources.

DOI: 10.1093/logcom/exq032 Conference: IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Pasadena, California, USA, July 11-17, 2009
Source: DBLP


Recent work on Alternating-Time Temporal Logic and Coalition Logic has allowed the expression of many interesting properties
of coalitions and strategies. However, there is no natural way of expressing resource requirements in these logics. In this
article, we present a Resource-Bounded Coalition Logic (RBCL) that has explicit representation of resource bounds in the language. We give a complete and sound axiomatization of RBCL, a procedure for deciding satisfiability of RBCL formulas, and a model-checking algorithm.

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Available from: Abdur Rakib, Jan 12, 2014
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    • "• some single-agent and multi-agent bounded resource logics [9] [3] [19] extending or modifying concurrent game models with some quantitative aspects by considering cost of agents' actions and reasoning about what players with bounded resources can achieve. "
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    ABSTRACT: We propose a logical framework combining a game-theoretic study of abilities of agents to achieve quantitative objectives in multi-player games by optimizing payoffs or preferences on outcomes with a logical analysis of the abilities of players for achieving qualitative objectives of players, i.e., reaching or maintaining game states with desired properties. We enrich concurrent game models with payoffs for the normal form games associated with the states of the model and propose a quantitative extension of the logic ATL* enabling the combination of quantitative and qualitative reasoning.
    Full-text · Article · Mar 2013
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    • "We note that an effectivity function for the " always " modality G was already constructed in [9]. Moreover, an effectivity function for reachability, i.e. for the F modality, has been presented in [1]. Our construction here differs significantly from both approaches, and allows to cover all kinds of effectivity that can be addressed in ATL. "
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    ABSTRACT: We consider models of multi-player games where abilities of players and coalitions are defined in terms of sets of outcomes which they can effectively enforce. We extend the well studied state effectivity models of one-step games in two different ways. On the one hand, we develop multiple state effectivity functions associated with different long-term temporal operators. On the other hand, we define and study coalitional path effectivity models where the outcomes of strategic plays are infinite paths. For both extensions we obtain representation results with respect to concrete models arising from concurrent game structures. We also apply state and path coalitional effectivity models to provide alternative, arguably more natural and elegant semantics to the alternating-time temporal logic ATL*, and discuss their technical and conceptual advantages.
    Full-text · Conference Paper · Jun 2012
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    • "Related works. In [2], Alechina et al. introduce the logic RBCL, whose language extends the one of CL with explicit representation of resource bounds. In [3], the same authors propose an analogous extension for ATL, called RB-ATL, and give a model checking procedure that runs in time O(|ϕ| 2·r+1 × S), where ϕ is the formula to be checked, S is the model, and r is the number of resources. "
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    ABSTRACT: Alternating-time Temporal Logic (ATL) and Coalition Logic (CL) are well-established logical formalisms particularly suitable to model games between dynamic coalitions of agents (like e.g. the system and the environment). Recently, the ATL formalism has been extended in order to take into account boundedness of the resources needed for a task to be performed. The resulting logic, called Resource-BoundedATL (RB-ATL), has been presented in quite a variety of scenarios. Even if the model checking problem for extensions of ATL dealing with resource bounds is usually undecidable, a model checking procedure for RB-ATL has been proposed. In this paper, we introduce a new formalism, called PRB-ATL, based on a different notion of resource bounds and we show that its model checking problem remains in EXPTIME and has a PSPACE lower bound.Then, we tackle the problem of coalition formation. How and why agents should aggregate is not a new issue and has been deeply investigated, in past and recent years, in various frameworks, as for example in algorithmic game theory, argumentation settings, and logic-based knowledge representation. We face this problem in the setting of priced resource-bounded agents with the goal specified by an ATL formula. In particular we solve the problem of determining the minimal cost coalitions of agents acting in accordance to rules expressed by a priced game arena and satisfying a given formula. We show that such problem is computationally not harder than verifying the satisfaction of the same formula with fixed coalitions.
    Full-text · Article · Nov 2011 · Electronic Notes in Theoretical Computer Science
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