In recent years there has been an increase of attention to Alternating time Temporal Logic. Two semantics for it have been proven to be equivalent, and attempts have been made to add an epistemic component to it. In our talk we briefly sketch some pitfalls that one can encounter by adding knowledge operators to ATL. We then suggest a number of ways to overcome this. This work is related to Barteld's work in the sense that it is about 'Knowledge' and 'Change'. Since ATL is especially attractive from a model checking perspective, and there currently is some work on probabilistic model checkers, chanches are that in the futurs ATL might also be enriched to reason about 'Chanche'.

Degrees of belief can be modelled with a sphere semantics, where each of some set of factual states (possible worlds) is associated with a templated order, that corresponds to the default rule for that state. If a distinguished outermost sphere is incorporated which corresponds to definitely excluded states, knowledge can be modelled as well. For interpreted and other multiagent systems, the system of spheres reduces to the following: the agent's knowledge induces a partition on the set of factual states, and default rules induce a templated order ('concentric circles') on each class of the partition. In plain English: a bag of onions, where an onion represents a state of knowledge, a peel a degree of belief, and the innermost peel the most normal or minimal beliefs (in belief revision the last is 'the to be revised belief set'). On such structures we can express both changes in knowledge and changes in degrees of belief in a logical language that combines dynamic modal operators for knowledge change with dynamic operators for belief revision. As in 'normal' dynamic epistemic logic, such modal revision operators can be seen as information state transformers, i.e., as binary relations between information states. This may then result in a change of minimal (preferred) states, as selected for most normal ('default') beliefs. In my own PhD I described knowledge changes in the murder game Cluedo. I did not extend my language to include beliefs and belief changes. Such beliefs also depend on the distribution of states over epistemic classes in models, and that can be addressed in probabilistic terms. Barteld Kooi has described in detail how to reason about probabilities within the precise setting of card game models as in Cluedo.

Discussions with Barteld Kooi have been a source of inspiration for me for the logical analysis of probability statements in game theory. Paradigms of precision and subtlety, his analyses of puzzles and paradoxes of probability are a trustworthy guide to a better understanding of probabilistic reasoning. I will discuss two results from Aumann&Brandenburger (1995): a ``preliminary observation'' about the epistemic assumptions of the *pure* Nash equilibrium, and a real theorem about the *mixed* Nash equilibrium. Logical analysis shows, I claim, that the distinction of pure vs. mixed is not the most relevant one, but that rather the two results provide characterizations of actions resp. beliefs. This means that the real distinction is the one between *practical* and *theoretical* rationality. And that is quite puzzling, or so I will argue.

Consider a political party which needs to agree on a party programme, or an appointment committee at a university which needs to decide which criteria the applicants satisfy. In each case, a group needs to make a decision regarding multiple propositions based on individual judgements. This raises the question of how to aggregate individual judgements into group judgements. It will be shown that the requirement of logical consistency imposes very strong restrictions on the possible decision making mechanisms.

Argumentation can be viewed as a game in many different ways. Sometimes these are just ways of revamping standard logic. But in this talk, we focus on the more procedural aspects of argumentation in a game setting, looking at (a) pro- and con- argument games (Prakken & Vreeswijk) which are basically graph games, (b) the procedural component of Lorenzen-style dialogue games, and (c) some simple numerical games that model weight of arguments, and various known effects, like 'half-life time' of arguments, and 'the success of success'.
References: "Logic in Games", ILLC, chapters 4 + 5, & some new material.

In Hintikka's book ``The Principles of Mathematics Revisited'' (1996), it is described how any IF-sentence can be translated into an existential second order-sentence (its truth condition), and how any e.s.o.-sentence is the truth condition of some IF-sentence. An IF-formula and its e.s.o.-translation are said to be equivalent. But this equivalence is only a weak equivalence: two IF-sentences can have the same truth condition, while having different `falsity-conditions'. By the interpration of negation as role exchange in GTS, a falsity condition of a formula is the truth condition of its negation. It can thus be obtained in the same manner, hence also as an e.s.o.-sentence. An IF-sentence is therefore strongly equivalent to a pair of e.s.o.-sentences. But conversely, not all pairs of e.s.o.-sentences correspond to an IF-sentence. A recent note of John Burgess on Henkin quantifiers answers the question which pairs of e.s.o.-sentences do.

We will discuss analogues of the Gale-Stewart theorem for infinite n-player games where the players have commonly known preferences. The usual Gale-Stewart theory for two players and two players with a draw will be recovered as a special case.