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Many important properties of multi-agent systems refer to the participants'ability to achieve a given goal, or to prevent the system from an undesirableevent. Among intelligent agents, the goals are often of epistemic nature, i.e.,concern the ability to obtain knowledge about an important fact \phi. Suchproperties can be e.g. expressed in ATLK, that is, alternating-time temporallogic ATL extended with epistemic operators. In many realistic scenarios,however, players do not need to fully learn the truth value of \phi. They maybe almost as well off by gaining some knowledge; in other words, by reducingtheir uncertainty about \phi. Similarly, in order to keep \phi secret, it isoften insufficient that the intruder never fully learns its truth value.Instead, one needs to require that his uncertainty about \phi never drops belowa reasonable threshold.  With this motivation in mind, we introduce the logic ATLH, extending ATL withquantitative modalities based on the Hartley measure of uncertainty. The newlogic enables to specify agents' abilities w.r.t. the uncertainty of a givenplayer about a given set of statements. It turns out that ATLH has the sameexpressivity and model checking complexity as ATLK. However, the new logic isexponentially more succinct than ATLK, which is the main technical result ofthis paper.

Playing to Learn, or to Keep Secret: Alternating-Time Logic Meets Information Theory