Related papers: Towards Unifying Perceptual Reasoning and Logical …
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a…
We study the correspondence between Bayesian Networks and graphical representation of proofs in linear logic. The goal of this paper is threefold: to develop a proof-theoretical account of Bayesian inference (in the spirit of the…
Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…
Reasoning is a distinctive human capacity, enabling us to address complex problems by breaking them down into a series of manageable cognitive steps. Yet, complex logical reasoning is still cumbersome for language models. Based on the dual…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
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…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
Cognitive modelling shares many features with statistical modelling, making it seem trivial to borrow from the practices of robust Bayesian statistics to protect the practice of robust cognitive modelling. We take one aspect of statistical…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…
Recent years have witnessed an increasing interest in training machines with reasoning ability, which deeply relies on accurately and clearly presented clue forms. The clues are usually modeled as entity-aware knowledge in existing studies.…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
In fact-checking applications, a common reason to reject a claim is to detect the presence of erroneous cause-effect relationships between the events at play. However, current automated fact-checking methods lack dedicated causal-based…
Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate…
We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly…
A central concept within informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the…
Enquiries concerning the underlying mechanisms and the emergent properties of a biological brain have a long history of theoretical postulates and experimental findings. Today, the scientific community tends to converge to a single…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…