Related papers: Queries With Exact Truth Values in Paraconsistent …

Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…

With advancements in Large Language Models (LLMs), a major use case that has emerged is querying databases in plain English, translating user questions into executable database queries, which has improved significantly. However, real-world…

RDF and Description Logics work in an open-world setting where absence of information is not information about absence. Nevertheless, Description Logic axioms can be interpreted in a closed-world setting and in this setting they can be used…

Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled \emph{How a computer should think}. Belnap argued that instead of using a logic with two…

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…

In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…

Evaluating answers from state-of-the-art large language models (LLMs) is challenging: lexical metrics miss semantic nuances, whereas "LLM-as-Judge" scoring is computationally expensive. We re-evaluate a lightweight alternative --…

While there are numerous benchmarks comparing the performance of modern language models (LMs), end-task evaluations often conflate notions of *factual accuracy* ("truth") and *reasoning ability* ("rationality", or "honesty" in the sense of…

We study a fitting problem inspired by ontology-mediated querying: given a collection of positive and negative examples of the form $(\mathcal{A},q)$ with $\mathcal{A}$ an ABox and $q$ a Boolean query, we seek an ontology $\mathcal{O}$ that…

For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…

We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…

Natural Language Inference (NLI) models have been used in various ways to improve the factuality of LLM outputs. This is typically done by applying an NLI model to judge whether the model output is entailed from the supposed evidence,…

In the realm of Large Language Model (LLM) functionalities, providing reliable information is paramount, yet reports suggest that LLM outputs lack consistency. This inconsistency, often at-tributed to randomness in token sampling,…

Large language models frequently produce mutually inconsistent answers when reasoning over multiple related queries. We study case-file logical consistency: maintaining a globally satisfiable belief state across interdependent queries. We…

This paper proposes a connection method \`a la Bibel for an exception-tolerant family of description logics (DLs). As for the language, we assume the DL $\mathcal{ALCH}$ extended with two typicality operators: one on (complex) concepts and…

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL itself was proposed as an extension of Linear Temporal Logic (LTL) that…

The fundamental proposal in this article is that logical formulas of the form (f <-> ~f) are not contradictions, and that formulas of the form (t <-> t) are not tautologies. Such formulas, wherever they appear in mathematics, are instead…

Large language models (LLMs) are able to generate human-like responses to user queries. However, LLMs exhibit inherent limitations, especially because they hallucinate. This paper introduces LP-LM, a system that grounds answers to questions…

We develop a query answering system, where at the core of the work there is an idea of query answering by rewriting. For this purpose we extend the DL DL-Lite with the ability to support n-ary relations, obtaining the DL DLR-Lite, which is…

In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning…