Related papers: Subsumption in $\mathcal{FL}_{\bot \mathit{reg}}$ …
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…
Latent reasoning via continuous chain-of-thoughts (Latent CoT) has emerged as a promising alternative to discrete CoT reasoning. Operating in continuous space increases expressivity and has been hypothesized to enable superposition: the…
Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. While the usual implication (i.e., the neck of a Horn clause) stands for…
Abduction is the task of computing a sufficient extension of a knowledge base (KB) that entails a conclusion not entailed by the original KB. It serves to compute explanations, or hypotheses, for such missing entailments. While this task…
This study intends to systematically disentangle pure logic reasoning and text understanding by investigating the contrast across abstract and contextualized logical problems from a comprehensive set of domains. We explore whether LLMs…
Functional relationships between objects, called `attributes', are of considerable importance in knowledge representation languages, including Description Logics (DLs). A study of the literature indicates that papers have made, often…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative…
Large language models (LLMs) have shown significant achievements in solving a wide range of tasks. Recently, LLMs' capability to store, retrieve and infer with symbolic knowledge has drawn a great deal of attention, showing their potential…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have…
Resolution over linear equations is a natural extension of the popular resolution refutation system, augmented with the ability to carry out basic counting. Denoted Res(lin_R), this refutation system operates with disjunctions of linear…
We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$…
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…
Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing…
Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual…
Large Language Models (LLMs) often struggle with deductive judgment in syllogistic reasoning, systematically conflating semantic plausibility with formal validity a phenomenon known as content effect. This bias persists even when models…
Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based…
In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…