A Probabilistic Logic for Resource-Bounded Multi-Agent Systems

Resource-bounded alternating-time temporal logic (RB-ATL), an extension of Coalition Logic (CL) and Alternating-time Temporal Logic (ATL), allows reasoning about resource requirements of coalitions in concurrent systems. However, many real-world systems are inherently probabilistic as well as resource-bounded, and there is no straightforward way of reasoning about their unpredictable behaviours. In this paper, we propose a logic for reasoning about coalitional power under resource constraints in the probabilistic setting. We extend RB-ATL with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic Resource-Bounded ATL (pRB-ATL).

Coalition logic with individual, distributed and common knowledge1

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.

The Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract)

We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.

THE LOGIC OF JOINT ABILITY IN TWO-PLAYER TACIT GAMES

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-typecoordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we callTwo-Player Strategic Coordination Logic(SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality.

The Ceteris Paribus Structure of Logics of Game Forms

The article introduces a ceteris paribus modal logic, called CP, interpreted on the equivalence classes induced by finite sets of propositional atoms. This logic is studied and then used to embed three logics of strategic interaction, namely atemporal STIT, the coalition logic of propositional control (CL−PC) and the starless fragment of the dynamic logic of propositional assignments (DL−PA). The embeddings highlight a common ceteris paribus structure underpinning the key operators of all these apparently very different logics and show, we argue, remarkable similarities behind some of the most influential formalisms for reasoning about strategic interaction