- Cet évènement est passé

The workshop of the CELLO team will be held on Monday June 13th 2017 in room B013 at LORIA.

**Program : **

- 12:50 – 13:00
**coffee and tea**

- 13:00 – 13:40
**speaker**: Alessandra Palmigiano, Technical University of Delft, NETHERLANDS**title**: Toward an epistemic-logical theory of categorization**abstract**: Categories,understood as types of collective identities for broad classes of objects or of agents, are the most basic cognitive tools, and are key to the use of language, the construction of knowledge and identity, and the formation of agents’ evaluations and decisions. The literature on categorization is expanding rapidly, motivated by – and in connection with – the theories and methodologies of a wide range of fields in the social sciences and AI. We proposed a framework of a positive (i.e. negation-free and implication-free) normal multi-modal logic as an epistemic logic of categories and agents’ categorical perception, with an algebraic and Kripke-style semantics. The present talk reports on an even simpler and more general framework, where the (rather technical) restrictions on the Kripke-style models are dropped. We use this logical framework to formalize core notions in databases and management science, as a step towards building systematic connections between modern categorization theory and epistemic logic.

- 13:40 – 14:20
**speaker**: Helle Hansen, Technical University of Delft, NETHERLANDS**title**: Coalgebraic Dynamic Logics**abstract**: In Propositional Dynamic Logic (PDL) programs are interpreted as relations, and program constructs as operations on relations. The axiomatisation of PDL essentially consists of modal logic K together with reduction axioms for program constructs. Similarly, in Parikh’s Game Logic (GL), games are interpreted as monotonic neighbourhood functions, and game constructs by operations on these. Completeness of Game Logic remains an open question, but the proposed axiomatisation is essentially monotonic modal logic M together with reduction axioms. These similarities suggest that a more general picture exists that encompasses both. In this talk I will present a coalgebraic generalisation of PDL and GL in which programs (or games) are coalgebras for a monad T, the program constructs arise from Kleisli composition and algebraic structure on T, and the axioms of these logics correspond to certain compatibility requirements between the modalities and this structure. This setup allows us to prove two general completeness results: strong completeness without iteration, and (weak) completeness with iteration and “negation-free” pointwise operations. This is joint work with Clemens Kupke.

- 14:20 – 15:00
**speaker**: Miguel Couceiro, LORIA / University of Lorraine, FRANCE**title**: On normal form systems of Boolean functions.**abstract**: Normal Form Systems (NFS) of Boolean functions can be thought of as factorizations of the class of all Boolean functions into a composition of clones. Typical examples include the CNF, DNF and median NFSs. In this talk we will discuss the efficiency of NFSs that yield terms built using one or several connectives taken in a fixed order, and applied to literals and constants. Here, efficiency is measured by the minimal size of terms representing a function. We will present a classification of NFSs in terms of efficiency and discuss some related topics. For instance, each clone is finitely generated but can have different sets of generators. We show that the choice of generators used in a given NFS does not impact its efficiency, up to polynomial equivalence. This talk is based on joint work with S. Foldes, E. Lehtonen, P. Mercuriali, R. Péchoux and A. Saffidine.

- 15:00 – 15:30
**coffee and tea**

- 15:30 – 16:10
**speaker**: Achim Jung, University of Birmingham, ENGLAND**title**: Quotients and presentations of d-frames**abstract**: There is a well-developed theory of quotients and free constructions for frames, and one could say that it forms the basis for almost everything in frame theory. The structures introduced by the speaker and Drew Moshier in 2006, d-frames, are attractive from the point of view of bitopology and non-classical logic, but for a long time they resisted any attempts at defining quotients and free constructions. This obstacle has recently been overcome by Tomas Jakl, Ales Pultr, and the speaker. The constructions involved are quite transparent.

- 16:10 – 16:50
**speaker**: Alexander Kurz, University of Leicester, ENGLAND**title**: Boolean Valued Coalgebraic Logic**abstract**: In the beautiful paper ‘How True It Is = Who Says It’s True’ Fitting extends Kripke’s modal logic to a multi-agent setting via indexing by agents not the modal Box but instead the truth-values. We will give an exposition of Fitting’s paper and indicate how it generalises from Kripke models to coalgebras.

- 16:50 – 17:30
**speaker**: Philippe Balbiani, IRIT / CNRS, FRANCE**title**: Undecidable problems for modal definability**abstract**: The core of our talk will be Chagrova’s Theorem about modal definability of given elementary conditions. Its proof is based on the undecidability of a variant of the halting problem concerning Minsky machines. It cannot be easily repeated for showing that, with respect to different classes of frames, the problem of deciding the modal definability of given elementary conditions is undecidable too. We will give a new proof of Chagrova’s Theorem. We will also give the proofs of new variants of Chagrova’s Theorem. In particular, we will study modal correspondence theory in the class of all Euclidean frames by showing that with respect to this class of frames, every modal formula is first-order definable and the problem of deciding the modal definability of given elementary conditions is undecidable.