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Language understanding is a key scientific issue in the fields of cognitive and computer science. However, the two disciplines differ substantially in the specific research questions. Cognitive science focuses on analyzing the specific…

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…

This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both…

Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

Recent advancements in Large Language Models (LLMs) have demonstrated remarkable capabilities in various domains. However, effective decision-making relies heavily on strong reasoning abilities. Reasoning is the foundation for…

In this paper, we propose a comprehensive benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Current explanation datasets often employ synthetic data with simple reasoning structures. Therefore,…

Multilingual reasoning remains a significant challenge for large language models (LLMs), with performance disproportionately favoring high-resource languages. Drawing inspiration from cognitive neuroscience, which suggests that human…

Application domains that require considering relationships among objects which have real-valued attributes are becoming even more important. In this paper we propose NeuralLog, a first-order logic language that is compiled to a neural…

This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…

An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…

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…

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their…

This position statement looks back on two decades of work on shallow embeddings of non-classical logics in classical higher-order logic (HOL), a line of research that expanded into a range of logic embeddings in HOL and inspired the LogiKEy…

The ability to conduct logical reasoning is a fundamental aspect of intelligent human behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, logic-based symbolic methods from the field…

Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…

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…

Over the past few years, the abilities of large language models (LLMs) have received extensive attention, which have performed exceptionally well in complicated scenarios such as logical reasoning and symbolic inference. A significant…