Tim French, Wiebe van der Hoek, Petar Iliev and Barteld Kooi. Succinctness of Epistemic Languages. In: T. Walsh (editor). Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11), pp. 881-886, AAAI Press, Menlo Park.

We study several modal languages in which some (sets of) generalized quantifiers can be represented; the main language we consider is suitable for defining any first order definable quantifier, but we also consider a sublanguage thereof, as well as a language for dealing with the modal counterparts of some higher order quantifiers. These languages are studied both from a modal logic perspective and from a quantifier perspective. Thus the issues addressed include normal forms, expressive power, completeness both of modal systems (...) and of systems in the quantifier tradition, complexity as well as syntactic characterizations of special semantic constraints. Throughout the paper several techniques current in the theory of generalized quantifiers are used to obtain results in modal logic, and conversely. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and give a (...) complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

We define balance games, which describe the formation of friendships and enmity in social networks. We show that if the agents give high priority to future profits over short term gains, all Pareto optimal strategies will eventually result in a balanced network. If, on the other hand, agents prioritize short term gains over the long term, every Nash equilibrium eventually results in a network that is stable but that might not be balanced.

We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that (...) the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional ctl logic. (shrink)

We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in game-like multi-agent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve φ” and “there exists a coalition C satisfying property P such that C can achieve φ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is (...) nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents. (shrink)

We propose an epistemic logic in which knowledge is fully introspective and implies truth, although truth need not imply epistemic possibility. The logic is presented in sequential format and is interpreted in a natural class of partial models, called balloon models. We examine the notions of honesty and circumscription in this logic: What is the state of an agent that only knows and which honest enable such circumscription? Redefining stable sets enables us to provide suitable syntactic and semantic criteria for (...) honesty. The rough syntactic definition of honesty is the existence of a minimal stable expansion, so the problem resides in the ordering relation underlying minimality. We discuss three different proposals for this ordering, together with their semantic counterparts, and show their effects on the induced notions of honesty. (shrink)

Hans van Ditmarsch, Wiebe van der Hoek and Barteld Kooi (2011). Reasoning about local properties in modal logic. In K. Tumer and P. Yolum and L. Sonenberg and P. Stone (editors). Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 711-718.

This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the (...) result of, indeed, public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in [15] give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates. Our closing observations are on recent developments that link the ‘standard’ topic of belief revision [1] to the dynamic epistemic logics introduced here. (shrink)

Understanding the flow of knowledge in multi-agent protocols is essential when proving the correctness or security of such protocols. Current logical approaches, often based on model checking, are well suited for modeling knowledge in systems where agents do not act strategically. Things become more complicated in strategic settings. In this paper we show that such situations can be understood as a special type of game – a knowledge condition game – in which a coalition “wins” if it is able to (...) bring about some epistemic condition. This paper summarizes some results relating to these games. Two proofs are presented for the computational complexity of deciding whether a coalition can win a knowledge condition game with and without opponents (Σ2P-complete and NP-complete respectively). We also consider a variant of knowledge condition games in which agents do not know which strategies are played, and prove that under this assumption, the presence of opponents does not affect the complexity. The decision problem without opponents is still NP-complete, but requires a different proof. (shrink)