In a recent paper, Bentzen proposes a semantically characterised logic called Action Type Deontic Logic, where normative concepts are applied to action expressions, rather than propositional statements. The logic offers solutions to many of the paradoxes of deontic logic. In particular, Bentzen’s semantics solves many puzzles involving the interaction of permission with conjunction and disjunct...

The efficacy of anisotropic versus isotropic filtering is analyzed with respect to general phase-based metrics for early vision attributes. We verified that the spectral information content gathered through oriented frequency channels is characterized by high compactness and flexibility, since a wide range of visual attributes emerge from different hierarchical combinations of the same channels...

By applying a reflection principle we set up fully explicit representation formulas for the harmonic Green’s function for orthogonal sectors of the annulus of the unit ball of R. From the harmonic Green’s function we then can determine the Bergman kernel function of Clifford holomorphic functions by applying an appropriate vector differentiation. As a concrete application we give an explicit an...

If F is a global function field of characteristic p > 3, we employ Tate’s theory of analytic uniformization to give an alternative proof of a theorem of Igusa describing the image of the natural Galois representation on torsion points of non-isotrivial elliptic curves defined over F . Along the way, using basic properties of Faltings heights of elliptic curves, we offer a detailed proof of the ...

We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics underyling equilibrium entailment, namely hereand-there with strong negation and its strengthening classica...

We show that two concepts involving equational provability can be elegantly formalized in terms of a relational algebra, equipped with two special-purpose mappings. We derive some calculus in order to prove that these concepts are equivalent, and that they are sound and complete. We illustrate the use of the relational framework by a few examples. We show how decidability of provability of an e...

We present an extension of classical tableau-based model checking procedures to the case of innnite-state systems, using deductive methods in an incremental construction of the behavior graph. Logical formulas are used to represent innnite sets of states in an abstraction of this graph, which is repeatedly reened in the search for a counterexample computation, ruling out large portions of the g...

In this paper we study a relatively new combinatorial object called staircase tableaux. Staircase tableaux were introduced by Corteel and Williams in the connection with Asymmetric Exclusion Process and has since found interesting connections with Askey–Wilson polynomials. We develop a probabilistic approach that allows us to analyze several parameters of a randomly chosen staircase tableau of ...

The paper proposes a way to analyze logical reasoning in a deductive version of the Mastermind game implemented within the Math Garden educational system. Our main goal is to derive predictions about the cognitive difficulty of game-plays, e.g., the number of steps needed for solving the logical tasks or the working memory load. Our model is based on the analytic tableaux method, known from pro...

Résumé. Dans le domaine de l’apprentissage supervisé, les méthodes de groupage des modalités d’un attribut symbolique permettent de construire un nouvel attribut synthétique conservant au maximum la valeur informationnelle de l’attribut initial et diminuant le nombre de modalités. Nous proposons ici une généralisation de l’algorithme de discrétisation Khiops pour le problème du groupage des mod...