We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics using the Hodges semantics, e.g., IF-logic and dependence logic. For this we introduce the multivalued dependence atom and observe the similarities with the, by Väänänen and Grädel, newly introduced independence atom.
We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.
Computable versions of Kolmogorov complexity have been used in the context of pattern discovery . However, these complexity measures do not take the psychological dimension of pattern discovery into account. We propose a method for pattern discovery based on a version of Kolmogorov complexity where computations are restricted to a cognitive model with… (More)
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as " there exists uncountable many. " Both of the… (More)
We propose a method for generating comprehensible explanations in description logic. Such explanations could be of potential use for e.g. engineers, doctors, and users of the semantic web. Users commonly need to understand why a logical statement follows from a set of hypotheses. Then, automatically generated explanations that are easily understandable… (More)
We present a multi-domain computational model for symbolic reasoning that was designed with the aim of matching human performance. The computational model is able to reason by deduction, induction, and abduction. It begins with an arbitrary theory in a given domain and gradually extends this theory as new regularities are learned from positive and negative… (More)
We expand the notion of resplendency to theories of the kind T + p↑, where T is a first-order theory and p↑ expresses that the type p is omitted. We investigate two different formulations and prove necessary and sufficient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author's… (More)
Let (M, X) |= ACA0 be such that P X , the collection of all unbounded sets in X , admits a definable complete ultrafilter and let T be a theory extending first order arithmetic coded in X such that M thinks T is consistent. We prove that there is an end-extension N |= T of M such that the subsets of M coded in N are precisely those in X. As a special case… (More)