Intelligent autonomous agents need to reason about different kinds of uncertainty in a Multi-Agent System (MAS): first, due to the occurrence of randomization and, second, their inability to completely observe the state of the system. In this paper, we investigate the verification of system specifications in probabilistic variants of the logics ATL and ATL* under imperfect information (II). The resulting setting combines these two sources of uncertainty and captures the situation in which agents have qualitative uncertainty about the local state as well as quantitative uncertainty about the occurrence of future events. Since the model-checking problem is undecidable when considered in the context of strategies with perfect recall, we focus on memoryless (positional) strategies. As the main result, we show that, in stochastic MAS under II, model-checking Probabilistic ATL is in EXPTIME when agents play probabilistic strategies. Filling the gap in recent work, we also show that model-checking Probabilistic ATL* is PSPACE-complete when the proponent coalition is restricted to deterministic strategies.

In this paper, we investigate the probabilistic variants of the strategy logics ATL and ATL* under imperfect information. Specifically, we present novel decidability and complexity results when the model transitions are stochastic and agents play uniform strategies. That is, the semantics of the logics are based on multi-agent, stochastic transition systems with imperfect information, which combine two sources of uncertainty, namely, the partial observability agents have on the environment, and the likelihood of transitions to occur from a system state. Since the model checking problem is undecidable in general in this setting, we restrict our attention to agents with memoryless (positional) strategies. The resulting setting captures the situation in which agents have qualitative uncertainty of the local state and quantitative uncertainty about the occurrence of future events. We illustrate the usefulness of this setting with meaningful examples.

In online advertising, search engines sell ad placements for keywords continuously through auctions. This problem can be seen as an infinitely repeated game since the auction is executed whenever a user performs a query with the keyword. As advertisers may frequently change their bids, the game will have a large set of equilibria with potentially complex strategies. In this paper, we propose the use of natural strategies for reasoning in such setting as they are processable by artificial agents with limited memory and/or computational power as well as understandable by human users. To reach this goal, we introduce a quantitative version of Strategy Logic with natural strategies in the setting of imperfect information. In a first step, we show how to model strategies for repeated keyword auctions and take advantage of the model for proving properties evaluating this game. In a second step, we study the logic in relation to the distinguishing power, expressivity, and model-checking complexity for strategies with and without recall.

This report documents the program and the outcomes of Dagstuhl Seminar 11101 ``Reasoning about Interaction: From Game Theory to Logic and Back''. The notion of interaction is crucial in several disciplines, including social science, operational research, and economics. Two frameworks are most prominent in the formal treatment of interaction: game theory and mathematical logic. Quantitative analysis is usually conducted using models and tools of game theory. At the same time, logic provides vocabulary and methods to study interaction in a qualitative way. The aim of the seminar was to bring together researchers who approach interaction-related phenomena from different perspectives (and with different conceptual tools). We hoped that, by synergy and exchange of expertise, a more integrative view of interaction could be obtained. In particular, we focussed on how interaction between individual entities (be it humans, robots and/or virtual creatures) can lead to emergence of social structures, collective behavior, and teamwork - and, ultimately, help all involved parties benefit from cooperation.

students realize that the same abstract machinery (e.g., mathematical logic) can be used in a completely dierent,way to create models of reality; on the other hand, dierent,methodologies can refer to the same class of concepts, and have a close formal relationship. 1 Background. Students should have basic knowledge,about propositional and predicate

We make the case for using logics as a representation formalism for reasoning about the world. While almost everything can be done with logic, the formalization is often awkward and cumbersome. We illustrate this with theWumpus world and Sudoku-puzzles. We introduce two sorts of calculi for propositional logics: a Hilbert type and a resolution calculus. We introduce first-order logic (FOL) and reconsider the Wumpus world. The dynamics of the changing world can be modeled with the terms: they enable us to explicitly denote the situation we are in and to reason about it: McCarthy's situation calculus.