Related papers: Evaluating the Competency of a First-Order Ontolog…

The main aim of the paper is to give a short self-contained proof of the decidability of language equivalence for deterministic pushdown automata, which is the famous problem solved by G. Senizergues, for which C. Stirling has derived a…

Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

Large Language Models (LLMs) have shown significant potential for ontology engineering. However, it is still unclear to what extent they are applicable to the task of domain-specific ontology generation. In this study, we explore the…

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…

Constructing comprehensive knowledge graphs requires the use of multiple ontologies in order to fully contextualize data into a domain. Ontology matching finds equivalences between concepts interconnecting ontologies and creating a cohesive…

Primitive Optimality Theory (OTP) (Eisner, 1997a; Albro, 1998), a computational model of Optimality Theory (Prince and Smolensky, 1993), employs a finite state machine to represent the set of active candidates at each stage of an Optimality…

This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using…

In ontology-mediated querying, description logic (DL) ontologies are used to enrich incomplete data with domain knowledge which results in more complete answers to queries. However, the evaluation of ontology-mediated queries (OMQs) over…

In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve…

Having a unified, coherent taxonomy is essential for effective knowledge representation in domain-specific applications as diverse terminologies need to be mapped to underlying concepts. Traditional manual approaches to taxonomy alignment…

This paper discusses the use of `ontologies' in Natural Language Processing. It classifies various kinds of ontologies that have been employed in NLP and discusses various benefits and problems with those designs. Particular focus is then…

Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…

We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…

The ontology engineering process is complex, time-consuming, and error-prone, even for experienced ontology engineers. In this work, we investigate the potential of Large Language Models (LLMs) to provide effective OWL ontology drafts…

We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order…

In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…

To achieve a flexible and adaptable system, capability ontologies are increasingly leveraged to describe functions in a machine-interpretable way. However, modeling such complex ontological descriptions is still a manual and error-prone…

This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present two decision algorithms based on a semantical characterization of…