Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields

We give a definition, in the ring language, of Z_p inside Q_p and of F_p[[t]] inside F_p((t)), which works uniformly for all $p$ and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining Z_p inside Q_p uniformly for all p. For any fixed finite extension of Q_p, we give an existential formula and a universal formula in the ring language which define the valuation ring

An extension of SPARQL for expressing qualitative preferences

In this paper we present SPREFQL, an extension of the SPARQL language that allows appending a PREFER clause that expresses "soft" preferences over the query results obtained by the main body of the query. The extension does not add expressivity and any SPREFQL query can be transformed to an equivalent standard SPARQL query. However, clearly separating preferences from the "hard" patterns and filters in the WHERE clause gives queries where the intention of the client is more cleanly expressed, an advantage for both human readability and machine optimization. In the paper we formally define the syntax and the semantics of the extension and we also provide empirical evidence that optimizations specific to SPREFQL improve run-time efficiency by comparison to the usually applied optimizations on the equivalent standard SPARQL query.Comment: Accepted to the 2017 International Semantic Web Conference, Vienna, October 201

Anticipation as prediction in the predication of data types

Every object in existence has its type. Every subject in language has its predicate. Every intension in logic has its extension. Each therefore has two levels but with the fundamental problem of the relationship between the two. The formalism of set theory cannot guarantee the two are co-extensive. That has to be imposed by the axiom of extensibility, which is inadequate for types as shown by Bertrand Russell's rami ed type theory, for language as by Henri Poincar e's impredication and for intension unless satisfying Port Royal's de nitive concept. An anticipatory system is usually de ned to contain its own future state. What is its type? What is its predicate? What is its extension? Set theory can well represent formally the weak anticipatory system, that is in a model of itself. However we have previously shown that the metaphysics of process category theory is needed to represent strong anticipation. Time belongs to extension not intension. The apparent prediction of strong anticipation is really in the structure of its predication. The typing of anticipation arises from a combination of and | respectively (co) multiplication of the (co)monad induced by adjointness of the system's own process. As a property of cartesian closed categories this predication has signi cance for all typing in general systems theory including even in the de nition of time itself