Related papers: Spectra of Cardinality Queries over Description Lo…
Circumscription is one of the main approaches for defining non-monotonic description logics (DLs). While the decidability and complexity of traditional reasoning tasks such as satisfiability of circumscribed DL knowledge bases (KBs) is well…
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…
In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the…
The Scott rank of a countable structure is a measure, coming from the proof of Scott's isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of $\mathcal{L}_{\omega_1 \omega}$)…
In 1952, Heinrich Scholz published a question in the Journal of Symbolic Logic asking for a characterization of spectra, i.e., sets of natural numbers that are the cardinalities of finite models of first order sentences. G\"unter Asser…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
It has been noticed since around 2007 that certain enumeration problems can be solved when an analytic or algebraic curve is identified. This curve is the key to the problem. In these lectures, a few such examples are presented. One is a…
The relationship between Lexical-Functional Grammar (LFG) {\em functional structures} (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that correctly explains…
Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one which can be answered without…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. As an example, we demonstrate that a quadratic…
We study the enumeration of answers to ontology-mediated queries when the ontology is formulated in a description logic that supports functional roles and the query is a CQ. In particular, we show that enumeration is possible with linear…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
We study the problem of finite ontology mediated query answering (FOMQA), the variant of OMQA where the represented world is assumed to be finite, and thus only finite models of the ontology are considered. We adopt the most typical setting…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…