Related papers: Automatic White-Box Testing of First-Order Logic O…
The delineation of logical definitions for each class in an ontology and the consistent application of these definitions to the assignment of instances to classes are important criteria for ontology evaluation. If ontologies are specified…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Logical specifications play a key role in the formal analysis of behavioural models. Automating the derivation of such specifications is particularly valuable in complex systems, where manual construction is time-consuming and error-prone.…
This paper investigates the logical reasoning capabilities of large language models (LLMs). For a precisely defined yet tractable formulation, we choose the conceptually simple but technically complex task of constructing proofs in Boolean…
Recent advances in large language models (LLMs) have shown promise in formal theorem proving, yet evaluating semantic correctness remains challenging. Existing evaluations rely on indirect proxies such as lexical overlap with…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized.…
Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…
Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…
We investigate the problem of verbalizing Web Ontology Language (OWL) axioms of domain ontologies in this paper. The existing approaches address the problem of fidelity of verbalized OWL texts to OWL semantics by exploring different ways of…
We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…
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 position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…
Recent work has shown how to prompt large language models with explanations to obtain strong performance on textual reasoning tasks, i.e., the chain-of-thought paradigm. However, subtly different explanations can yield widely varying…
Ontology Learning (OL) is the computational task of generating a knowledge base in the form of an ontology given an unstructured corpus whose content is in natural language (NL). Several works can be found in this area most of which are…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Formal Methods are mathematically-based techniques for software design and engineering, which enable the unambiguous description of and reasoning about a system's behaviour. Autonomous systems use software to make decisions without human…
Despite the impressive adaptability of large language models (LLMs), challenges remain in ensuring their security, transparency, and interpretability. Given their susceptibility to adversarial attacks, LLMs need to be defended with an…
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…