The core of this article is the modal correspondence theory in the class of all Euclidean frames. It shows that with respect to the class of all Euclidean frames, every modal formula is first-order definable and the problem of deciding the modal definability of sentences is undecidable.

The core of our article is the computability of the problem of deciding the modal definability of first-order sentences with respect to classes of frames. It gives a new proof of Chagrova's Theorem telling that, with respect to the class of all frames, the problem of deciding the modal definability of first-order sentences is undecidable. It also gives the proofs of new variants of Chagrova's Theorem.

We present a new general and language independent approach to the noisy text correction problem developed and implemented in the framework of the CULTURA project. We briefly describe the core candidate generator, REBELS, the complete system concept, its efficient implementation based on functional automata and its immediate applications. The quality of the whole system is empirically established in different experimental settings where language and noise sources are varied.

This paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical.

International audience

Incidence geometry is based on two-sorted structures consisting of ‘points’ and ‘lines’ together with an intersort binary relation called incidence. We introduce an equivalent one-sorted geometrical structure, called incidence frame, which is suitable for modal considerations. Incidence frames constitute the semantical basis of MIG, the modal logic of incidence geometry. A completeness theorem for MIG is proved: a modal formula is a theorem of MIG if and only if it is valid in all incidence frames. Extensions to projective and affine geometries are also considered.