Related papers: Adding the Power-Set to Description Logics
Biomedical ontologies contain numerous concept or role names involving negative knowledge such as lacks_part, absence_of. Such a representation with labels rather than logical constructors would not allow a reasoner to interpret lacks_part…
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
We study the problem of fitting a description logic (DL) ontology to a given set of positive and negative examples that take the form of an ABox and a Boolean query. While previous work has investigated this problem for the expressive DLs…
Ontology embeddings map classes, roles, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
We consider model-theoretic properties related to the expressive power of three analogues of $L_{\omega_1, \omega}$ for metric structures. We give an example showing that one of these infinitary logics is strictly more expressive than the…
Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…
The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…
Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just…
We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast,…
Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
Description logics (DL) are a family of formal languages for representing and reasoning about structured knowledge in terms of concepts and their relationships. A central reasoning problem in DL is concept subsumption. Although this problem…
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging…
We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…
Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {\em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been…
Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of Ernst…
We study the separation of positive and negative data examples in terms of description logic concepts in the presence of an ontology. In contrast to previous work, we add a signature that specifies a subset of the symbols that can be used…