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)
A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively… (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)
A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction class, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively… (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)