Related papers: Efficient Computation of General Modules for ALC O…
Optimization problems seek to find the best solution to an objective under a set of constraints, and have been widely investigated in real-world applications. Modeling and solving optimization problems in a specific domain typically require…
Modeling the logical architecture is an often underestimated development step to gain an early insight into the fundamental functional properties of an automotive system. An architectural description supports developers in making design…
Large Language Models (LLMs) demonstrate impressive capabilities in natural language processing but suffer from inaccuracies and logical inconsistencies known as hallucinations. This compromises their reliability, especially in domains…
Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software…
Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionistic basis through single-succedent sequent calculi. We adapt…
Concept Induction refers to the problem of creating complex Description Logic class descriptions (i.e., TBox axioms) from instance examples (i.e., ABox data). In this paper we look particularly at the case where both a set of positive and a…
This paper describes a new technique, called "knowledge patterns", for helping construct axiom-rich, formal ontologies, based on identifying and explicitly representing recurring patterns of knowledge (theory schemata) in the ontology, and…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there…
The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…
We explore the relationships between Description Logics and Set Theory. The study is carried on using, on the set-theoretic side, a very rudimentary axiomatic set theory Omega, consisting of only four axioms characterizing binary union, set…
Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
We propose a new mechanism for integration of OWL ontologies using semantic import relations. In contrast to the standard OWL importing, we do not require all axioms of the imported ontologies to be taken into account for reasoning tasks,…
The connection method has earned good reputation in the area of automated theorem proving, due to its simplicity, efficiency and rational use of memory. This method has been applied recently in automatic provers that reason over ontologies…
We present KNOW--the Knowledge Navigator Ontology for the World--the first ontology designed to capture everyday knowledge to augment large language models (LLMs) in real-world generative AI use cases such as personal AI assistants. Our…
We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic it is also a logic of terms that admits a (sound)…
Ontologies usually suffer from the semantic heterogeneity when simultaneously used in information sharing, merging, integrating and querying processes. Therefore, the similarity identification between ontologies being used becomes a…