Related papers: A Logic for Reasoning about Evidence
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
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…
Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…
"[M]athematicians care no more for logic than logicians for mathematics." Augustus de Morgan, 1868. Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional…
In this article, we employ mathematical concepts as a tool to examine the phenomenon of consciousness experience and logical phenomena. Through our investigation, we aim to demonstrate that our experiences, while not confined to…
Defeasible logic is an efficient logic for defeasible reasoning. It is defined through a proof theory and, until now, has had no model theory. In this paper a model-theoretic semantics is given for defeasible logic. The logic is sound and…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
In this paper we discuss contrastive explanations for formal argumentation - the question why a certain argument (the fact) can be accepted, whilst another argument (the foil) cannot be accepted under various extension-based semantics. The…
Motivated reasoning posits that people distort how they process information in the direction of beliefs they find attractive. This paper creates a novel experimental design to identify motivated reasoning from Bayesian updating when people…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…
Evidence-grounded reasoning requires more than attaching retrieved text to a prediction: a model should make decisions that depend on whether the provided evidence supports the target claim. In practice, this often fails because supervision…