Related papers: Converting ALC Connection Proofs into ALC Sequents
Ontologies are one of the richest sources of knowledge. Real-world ontologies often contain thousands of axioms and are often human-made. Hence, they may contain inconsistency and incomplete information which may impair classical reasoners…
We present an approach to obtain formally verified implementations of classical Computational Logic algorithms. We choose the Why3 platform because it allows to implement functions in a style very close to the mathematical definitions, as…
Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which robustly generalize to novel scenarios. Recent work evaluates large language models (LLMs) on inductive reasoning…
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Appel and McAllester's "step-indexed" logical relations have proven to be a simple and effective technique for reasoning about programs in languages with semantically interesting types, such as general recursive types and general reference…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g.…
Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic…
Abductive reasoning generates explanatory hypotheses for new observations using prior knowledge. This paper investigates the use of forgetting, also known as uniform interpolation, to perform ABox abduction in description logic (ALC)…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
Large language models (LLMs) often suffer from hallucination, generating factually incorrect statements when handling questions beyond their knowledge and perception. Retrieval-augmented generation (RAG) addresses this by retrieving…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
The Abstraction and Reasoning Corpus (ARC) is designed to assess generalization beyond pattern matching, requiring models to infer symbolic rules from very few examples. In this work, we present a transformer-based system that advances ARC…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
The field of query-by-example aims at inferring queries from output examples given by non-expert users, by finding the underlying logic that binds the examples. However, for a very small set of examples, it is difficult to correctly infer…
Large language models (LLMs) have shown promise in table Question Answering (Table QA). However, extending these capabilities to multi-table QA remains challenging due to unreliable schema linking across complex tables. Existing methods…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…