Related papers: Evaluating the Competency of a First-Order Ontolog…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
I introduce an approach for automated reasoning in first order set theories that are not finitely axiomatizable, such as $ZFC$, and describe its implementation alongside the automated theorem proving software E. I then compare the results…
Competency Questions (CQs) play a crucial role in validating ontology design. While manually crafting CQs can be highly time-consuming and costly for ontology engineers, recent studies have explored the use of large language models (LLMs)…
OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language.…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Ontology revision aims to seamlessly incorporate a new ontology into an existing ontology and plays a crucial role in tasks such as ontology evolution, ontology maintenance, and ontology alignment. Similar to repair single ontologies,…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Empirical methods to examine the capability of Large Language Models (LLMs) to use Automated Theorem Prover (ATP) reasoning strategies are studied. We evaluate the performance of State of the Art models from December 2023 and August 2024 on…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…
Capability ontologies are increasingly used to model functionalities of systems or machines. The creation of such ontological models with all properties and constraints of capabilities is very complex and can only be done by ontology…
Ontologies are known for their ability to organize rich metadata, support the identification of novel insights via semantic queries, and promote reuse. In this paper, we consider the problem of automated planning, where the objective is to…
In this note we observe that automated theorem provers (ATPs) that recursively enumerate theorems in a particular way will fail to identify some valid theorems for a reason that is analogous to how G\"odel proved the existence of what are…
We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong…