Related papers: Towards Propositional KLM-Style Defeasible Standpo…
Large Language Models (LLMs) often exhibit limited logical coherence, mapping premises to conclusions without adherence to explicit inference rules. We propose Proof-Carrying Reasoning with LLMs (PCRLLM), a framework that constrains…
Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain…
Recent advancements have significantly augmented the reasoning capabilities of Large Language Models (LLMs) through various methodologies, especially chain-of-thought (CoT) reasoning. However, previous methods fail to address reasoning…
We present a comprehensive approach to the automated formalization of legal texts using large language models (LLMs), targeting their transformation into Defeasible Deontic Logic (DDL). Our method employs a structured pipeline that segments…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…
Logical reasoning is fundamental for humans yet presents a substantial challenge in the domain of Artificial Intelligence. Initially, researchers used Knowledge Representation and Reasoning (KR) systems that did not scale and required…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead…
There are several contexts of non-monotonic reasoning where a priority between rules is established whose purpose is preventing conflicts. One formalism that has been widely employed for non-monotonic reasoning is the sceptical one known as…
Large Language Models (LLMs) have achieved impressive results across numerous domains, yet they experience notable deficiencies in legal question-answering tasks. LLMs often generate generalized responses that lack the logical specificity…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
Propositional Dynamic Logic, PDL, is a modal logic designed to formalize the reasoning about programs. By extending accessibility between states to states and state sets, concurrent propositional dynamic logic CPDL, is introduced to include…
Large language models (LLMs) are deployed on increasingly complex tasks that require multi-step decision-making. Understanding their algorithmic reasoning abilities is therefore crucial. However, we lack a diagnostic benchmark for…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Large Language Models (LLMs) have gained prominence in the AI landscape due to their exceptional performance. Thus, it is essential to gain a better understanding of their capabilities and limitations, among others in terms of nonmonotonic…
Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to…
Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose…
Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…