Related papers: A Unified Algebraic Framework for Non-Monotonicity
In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data. Background:…
A growing body of research suggests that the cognitive processes of large language models (LLMs) differ fundamentally from those of humans. However, existing interpretability methods remain limited in explaining how cognitive abilities are…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
Abstract reasoning, i.e., inferring complicated patterns from given observations, is a central building block of artificial general intelligence. While humans find the answer by either eliminating wrong candidates or first constructing the…
We investigate properties of ABA+, a formalism that extends the well studied structured argumentation formalism Assumption-Based Argumentation (ABA) with a preference handling mechanism. In particular, we establish desirable properties that…
While sequential reasoning enhances the capability of Vision-Language Models (VLMs) to execute complex multimodal tasks, their reliability in grounding these reasoning chains within actual visual evidence remains insufficiently explored. We…
A large amount of research about multimodal inference across text and vision has been recently developed to obtain visually grounded word and sentence representations. In this paper, we use logic-based representations as unified meaning…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
Since the introduction by Hodges, and refinement by V\"a\"an\"anen, team semantic constructions have been used to generate expressively enriched logics still conserving nice properties, such as compactness or decidability. In contrast,…
Leveraging outputs from multiple large language models (LLMs) is emerging as a method for harnessing their power across a wide range of tasks while mitigating their capacity for making errors, e.g., hallucinations. However, current…
Recent progress in large language models has renewed interest in how multi-step reasoning is represented internally. While prior work often treats reasoning as a linear chain, many reasoning problems are more naturally modeled as directed…
Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not…
In this paper, we present an abstract framework of many-valued modal logic with the interpretation of atomic propositions and modal operators as predicate lifting over coalgebras for an endofunctor on the category of sets. It generalizes…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector…
Presented, in this monograph, are the results of the U. S. Naval Academy Mathematical Logic Course Project. The propositional and predicate calculus is presented in a unique manner. All aspects are rigorously established using the the…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…