printable version

10:30-10:45 Arrival (coffee & tea)
10:45-11:30 Gabriel Sandu (Helsinki):
Deflationism and IF-logical consequence
11-30-11:45 break (more coffee & tea)
11:45-12:15 Theo Janssen (Amsterdam):
IF-logic as Quantum logic
12:15-13:00 Xavier Caicedo (Bogota):
Calculi and algebras for imperfect information logic

13:00-13:45 lunch

13:45-14:15 Elias Thijsse (Tilburg):
The minimal knowledge paradigm
14:15-14:45 Johan van Benthem (Amsterdam):
Games over Time: update and revision in temporal logic
14:45-15:15 Barteld Kooi (Groningen):
Model comparison games for update logics
15:15-15:20 Closing

16:00 PhD-defense of Francien Dechesne: "Game, Set, Maths: formal investigations into logic with imperfect information". (Aula)

Abstracts

Gabriel Sandu: Deflationism and IF-logical consequence
(pdf)

Theo M.V. Janssen: IF-logic as Quantum logic
Independence plays a role in quantum mechanics and reflects a difference with classical mechanics. In classical mechanics the position and impulse of an object can be measured independently of each other. In quantum mechanics (which involves subatomair particles) this is not possible, which is expressed by Heisenberg's uncertainty principle. Hintikka suggests that his IF logic (independence friendly logic) is suitable for capturing this difference. His analysis uses branching quantifiers; a construction well known from linguistic applications as in "Some friend of each townsman and some neighbour of each villager envy each other". We will investigate the interpretation of such sentences. It will turn out that the If logic can have a contribution to quantum logic, but not in the way Hintikka suggests.

Xavier Caicedo: Calculi and algebras for imperfect information logic
It is well known that there can not be a complete calculus for logic of imperfect information able to deduce for example those sentences for which the first player has a winning strategy in any structure, because the valid \Sigma _1^1-sentences are not recursively enumerable. However, our work with M. Krynicki, improved and corrected in later joint work with Theo Jansen and F. Dechesne, show the possibility of a reasonable calculus of equivalences \equiv_{X} for formulas with free variables in the set X, at least for regular formulas (those not containing the same variable bound and free in any subformula). This calculus is strong enough to obtain effectively prenex normal forms. We address some questions which arise naturally: how to eliminate the regularity restriction above, the completeness of the quantifier free fragment of this calculus and other fragmenrs, its possible extension to calculi of "logical consequences", an how could this calculi accelerate first order proofs. From another perspective, having equivalences among formulas, suggests considering the corresponding Lindenbaum algebras L_{X}. They are in this case Kleene algebras, a particular kind of DeMorgan lattices, more properly sequences of such algebras.

Elias Thijsse: The minimal knowledge paradigm
After introducing the idea of only knowing by means of an example, the concept of minimal knowledge is defined, and a general theory is developed to cope with several aspects of describing minimal knowledge: semantic (through model orders that are inspired by Ehrenfeucht-Fraïssé games), syntactic (through stable expansions) and deductive (through the `disjunction property test'). Rather than giving a survey of many proposals and possibilities in the field (cf. van der Hoek, Jaspars & Thijsse `Theories of Knowledge and Ignorance' [in S.Rahman et al. (eds.) Logic, Epistemology and the Unity of Science, Kluwer 2004] for such an overview), we focus on the most promising information order, discuss some applications, and (time permitted) speculate on further developments.

Johan van Benthem: Games over Time: update and revision in temporal logic
We will show how dynamic epistemic logics can be translated into epistemic-temporal logics over branching tree models. Next, in this light, we discuss connections between three frameworks: temporal run models (Fagin et al.), epistemic event structures (Parikh & Ramanujam), and BMS-style dynamic epistemic logic. Specific topics include: the role of protocols, the possibility of storing past experience in preconditions of events, and the behaviour of 'update evolution' as a dynamical system.

Barteld Kooi: Model comparison games for update logics
Update logics are extensions of epistemic logic with additional operators that express information change. These logics are especially suited for reasoning about higher order information change. Since all these logics are interpreted in the same class of models, a natural question is what the relative expressive power of these logics is. Model comparison games for these logics provide excellent means to investigate this. In the talk some old and some new results will be presented.