Related papers: On Bisimulations for Description Logics
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
We compare different epistemic notions in the presence of awareness of propositional variables: the logics of implicit knowledge (in which explicit knowledge is definable), explicit knowledge, and speculative knowledge. Different notions of…
The growing range of applications of Machine Learning (ML) in a multitude of settings motivates the ability of computing small explanations for predictions made. Small explanations are generally accepted as easier for human decision makers…
While there has been a great deal of work on the development of reasoning algorithms for expressive description logics, in most cases only Tbox reasoning is considered. In this paper we present an algorithm for combined Tbox and Abox…
We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from…
It is well known that models used in conventional regression analysis are commonly misspecified. A standard response is little more than a shrug. Data analysts invoke Box's maxim that all models are wrong and then proceed as if the results…
Small additive ensembles of symbolic rules offer interpretable prediction models. Traditionally, these ensembles use rule conditions based on conjunctions of simple threshold propositions $x \geq t$ on a single input variable $x$ and…
Symbolic knowledge can provide crucial inductive bias for training neural models, especially in low data regimes. A successful strategy for incorporating such knowledge involves relaxing logical statements into sub-differentiable losses for…
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and quantitative…
An active learning (AL) algorithm seeks to construct an effective classifier with a minimal number of labeled examples in a bootstrapping manner. While standard AL heuristics, such as selecting those points for annotation for which a…
Robust reinforcement learning agents using high-dimensional observations must be able to identify relevant state features amidst many exogeneous distractors. A representation that captures controllability identifies these state elements by…
Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…
Description Logics are knowledge representation formalisms which have been used in a wide range of application domains. Owing to their appealing expressiveness, we consider in this paper extensions of the well-known concept language ALC…
Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…
In spite of the rapidly increasing number of applications of machine learning in various domains, a principled and systematic approach to the incorporation of domain knowledge in the engineering process is still lacking and ad hoc solutions…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
We introduce $\mathcal{DLR}^+$, an extension of the n-ary propositionally closed description logic $\mathcal{DLR}$ to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and global and local…