The result of forgetting some predicates in a first-order sentence may not exist in the sense that it might not be captured by any first-order sentences. This, indeed, severely restricts the usage of forgetting in applications. To address this issue, we propose a notion called k-forgetting, also called bounded forgetting in general, for any fixed number k. We present several equivalent characte...

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.

In this paper, we introduce EVE, a generic framework for event detection where events can also include outliers, model changes and drifts. Various methods for event detection have been proposed for different types of events. However, many of them make the same or very similar prior assumptions but use different notations and formalizations. EVE provides a general framework for event detection, ...

Let Ln be the first-order language for Nn. Thus, Ln contains the symbols =, 1, 2, . . . , n interpreted in Nn as the identity and the natural numbers 1, 2, . . . , n. By Fn we denote the set of all formulas of Ln. Hence, Fn is the smallest set such that: a. ti = tj ∈ Fn, b. if A,B ∈ Fn, then: ¬A, A → B, A∧B, A∨B, A ≡ B, ∨

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of a mapping between the source and the target schemas, and answering queries over target instances. A schema mapping is a condition, often expressed in a fragment of first-order logic, that relates instances of source and target schemas. Most commonly it is a conjunc...

We develop first-order logic and some extensions for incomplete information scenarios and consider related complexity issues.

In monitoring, we algorithmically check if a single behavior satisfies a property. Here, we consider monitoring for Multi-Lane Spatial Logic (MLSL). The behavior is given as a finite transition sequence of MLSL and the property is that a spatial MLSL formula should hold at every point in time within the sequence. In our procedure we transform the transition sequence and the formula to the first...

In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k...

We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not...