Weyl and Marchaud derivatives: a forgotten history

In this paper we recall the contribution given by Hermann Weyl and Andr\'e Marchaud to the notion of fractional derivative. In addition we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.Comment: arXiv admin note: text overlap with arXiv:1705.00953 by other author

On existential declarations of independence in IF Logic

We analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of IF sentences; we give a syntactical criterion for deciding whether a sentence beginning with such prefix exists such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences. The main theorem allows us to describe the behaviour of various particular classes of quantifier prefixes, and to prove as a remarkable corollary that all existential IF sentences are equivalent to first-order sentences. As a further consequence, we prove that the fragment of IF sentences with knowledge memory has only first-order expressive power (up to truth equivalence)

Lightweight Ontologies

Ontologies are explicit specifications of conceptualizations. They are often thought of as directed graphs whose nodes represent concepts and whose edges represent relations between concepts. The notion of concept is understood as defined in Knowledge Representation, i.e., as a set of objects or individuals. This set is called the concept extension or the concept interpretation. Concepts are often lexically defined, i.e., they have natural language names which are used to describe the concept extensions (e.g., concept mother denotes the set of all female parents). Therefore, when ontologies are visualized, their nodes are often shown with corresponding natural language concept names. The backbone structure of the ontology graph is a taxonomy in which the relations are “is-a”, whereas the remaining structure of the graph supplies auxiliary information about the modeled domain and may include relations like “part-of”, “located-in”, “is-parent-of”, and many others