Related papers: Parallelisable Existential Rules: a Story of Piece…
Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find…
We study the problem of checking whether an existential sentence (that is, a first-order sentence in prefix form built using existential quantifiers and all Boolean connectives) is true in a finite partially ordered set (in short, a poset).…
Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
Ontologies such as taxonomies, product catalogs or web directories are heavily used and hence evolve frequently to meet new requirements or to better reflect the current instance data of a domain. To effectively manage the evolution of…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Despite enormous progress in object detection and classification, the problem of incorporating expected contextual relationships among object instances into modern recognition systems remains a key challenge. In this work we propose…
Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
Event logs extracted from information systems offer a rich foundation for understanding and improving business processes. In many real-world applications, it is possible to distinguish between desirable and undesirable process executions,…
This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove…
Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…