Wojciech Jamroga

Comparing Semantics of Logics for Multi-Agent Systems

We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL.The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.

Constructive knowledge: what agents can achieve under imperfect information

We propose a non-standard interpretation of Alternating-time Temporal Logic with imperfect information, for which no commonly accepted semantics has been proposed yet. Rather than changing the semantic structures, we generalize the usual interpretation of formulae in single states to sets of states. We also propose a new epistemic operator for “practical” or “constructive” knowledge, and we show that the new logic (which we call Constructive Strategic Logic) is strictly more expressive than most existing solutions, while it retains the same model checking complexity. Finally, we study properties of constructive knowledge and other operators in this non-standard semantics.

Towards a theory of intention revision

Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent’s mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties.

Comparing variants of strategic ability: how uncertainty and memory influence general properties of games

Alternating-time temporal logic (ATL) is a modal logic that allows to reason about agents’ abilities in game-like scenarios. Semantic variants of ATL are usually built upon different assumptions about the kind of game that is played, including capabilities of agents (perfect vs. imperfect information, perfect vs. imperfect memory, etc.). ATL has been studied extensively in previous years; however, most of the research focused on model checking. Studies of other decision problems (e.g., satisfiability) and formal meta-properties of the logic (like axiomatization or expressivity) have been relatively scarce, and mostly limited to the basic variant of ATL where agents possess perfect information and perfect memory. In particular, a comparison between different semantic variants of the logic is largely left untouched. In this paper, we show that different semantics of ability in ATL give rise to different validity sets. The issue is important for several reasons. First, many logicians identify a logic with its set of true sentences. As a consequence, we prove that different notions of ability induce different strategic logics. Secondly, we show that different concepts of ability induce different general properties of games. Thirdly, the study can be seen as the first systematic step towards satisfiability-checking algorithms for ATL with imperfect information. We introduce sophisticated unfoldings of models and prove invariance results that are an important technical contribution to formal analysis of strategic logics.

Model Checking Logics of Strategic Ability: Complexity*

This chapter is about model checking and its complexity in some of the main temporal and strategic logics, e.g. LTL, CTL, and ATL. We discuss several variants of ATL (perfect vs. imperfect recall, perfect vs. imperfect information) as well as two different measures for model checking with concurrent game structures (explicit vs. implicit representation of transitions). Finally, we summarize some results about higher order representations of the underlying models.

Do agents make model checking explode (computationally)

Atl is a logic for multi-agent systems that enjoys model checking linear in the size of the models. Here, we point out that the size of an atl model is usually exponential in the number of agents. We establish the precise atl model checking complexity when the number of agents is considered a parameter: it turns out that the problem is Σ2P-complete for concurrent game structures, and NP-complete for alternating transition systems. We also show that atl model checking over the broader class of nondeterministic alternating transition systems is still NP-complete, which suggests that using the more general class of models may be convenient in practice.

Strategic games and truly playable effectivity functions

A well-known result in the logical analysis of cooperative games states that the so-called playable effectivity functions exactly correspond to strategic games. More precisely, this result states that for every playable effectivity function E there exists a strategic game that assigns to coalitions of players exactly the same power as E, and every strategic game generates a playable effectivity function. While the latter direction of the correspondence is correct, we show that the former does not hold for a number of infinite state games. We point out where the original proof of correspondence goes wrong, and we present examples of playable effectivity functions for which no equivalent strategic game exists. Then, we characterize the class of truly playable effectivity functions, that do correspond to strategic games. Moreover, we discuss a construction that transforms any playable effectivity function into a truly playable one while preserving the power of most (but not all) coalitions. We also show that Coalition Logic (CL), a formalism used to reason about effectivity functions, is not expressive enough to distinguish between playable and truly playable effectivity functions, and we extend it to a logic that can make that distinction while still enjoying the good meta-logical properties of CL, such as finite axiomatization and decidability via finite model property.

Intentions and strategies in game-like scenarios

In this paper, we investigate the link between logics of games and “mentalistic” logics of rational agency, in which agents are characterized in terms of attitudes such as belief, desire and intention. In particular, we investigate the possibility of extending the logics of games with the notion of agents’ intentions (in the sense of Cohen and Levesque’s BDI theory). We propose a new operator (straσ) that can be used to formalize reasoning about outcomes of strategies in game-like scenarios. We briefly discuss the relationship between intentions and goals in this new framework, and show how to capture dynamic logic-like constructs. Finally, we demonstrate how game-theoretical concepts like Nash equilibrium can be expressed to reason about rational intentions and their consequences.

Modular interpreted systems

We propose a new class of representations that can be used for modeling (and model checking) temporal, strategic and epistemic properties of agents and their teams. Our representations borrow the main ideas from interpreted systems of Halpern, Fagin et al.; however, they are also modular and compact in the way concurrent programs are. We also mention preliminary results on model checking alternating-time temporal logic for this natural class of models.

Strategic Planning through Model Checking of ATL Formulae

Model checking of temporal logic has already been proposed for automatic planning. In this paper, we introduce a simple adaptation of the ATL model checking algorithm that returns a strategy to achieve given goal. We point out that the algorithm generalizes minimaxing, and that ATL models generalize traditional game trees. The paper ends with suggestions about other game theory concepts that can be transfered to ATL-based planning.