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Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…
The scientific method is the cornerstone of human progress across all branches of the natural and applied sciences, from understanding the human body to explaining how the universe works. The scientific method is based on identifying…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the…
Safety constraints are crucial to the development of mission-critical systems. The practice of developing software for systems of this type requires reliable methods for identifying and analysing project artefacts. This paper proposes a…
A discourse strategy is a strategy for communicating with another agent. Designing effective dialogue systems requires designing agents that can choose among discourse strategies. We claim that the design of effective strategies must take…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
The peer review process for scientific publications faces significant challenges due to the increasing volume of submissions and inherent reviewer biases. While artificial intelligence offers the potential to facilitate the process, it also…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…
Explanations for artificial intelligence (AI) systems are intended to support the people who are impacted by AI systems in high-stakes decision-making environments, such as doctors, patients, teachers, students, housing applicants, and many…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
We observed that safety arguments are prone to stay too abstract, e.g. solutions refer to large packages, argument strategies to complex reasoning steps, contexts and assumptions lack traceability. These issues can reduce the confidence we…
Formalising informal mathematical reasoning into formally verifiable code is a significant challenge for large language models. In scientific fields such as physics, domain-specific machinery (\textit{e.g.} Dirac notation, vector calculus)…
The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial,…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem…
This paper develops a comprehensive framework for artificial intelligence systems that operate under strict epistemic constraints, moving beyond stochastic language prediction to support structured reasoning, propositional commitment, and…