Related papers: A Simple Generative Model of Logical Reasoning and…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its…
The recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic and learning are both practices of the human brain, it leads to another…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
A core tension in models of concept learning is that the model must carefully balance the tractability of inference against the expressivity of the hypothesis class. Humans, however, can efficiently learn a broad range of concepts. We…
Human reasoning can often be understood as an interplay between two systems: the intuitive and associative ("System 1") and the deliberative and logical ("System 2"). Neural sequence models -- which have been increasingly successful at…
Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…
Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the…
Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
The idea that the brain is a probabilistic (Bayesian) inference machine, continuously trying to figure out the hidden causes of its inputs, has become very influential in cognitive (neuro)science over recent decades. Here I present a…
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…
An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Value learning is a crucial aspect of safe and ethical AI. This is primarily pursued by methods inferring human values from behaviour. However, humans care about much more than we are able to demonstrate through our actions. Consequently,…
The human reasoning process is seldom a one-way process from an input leading to an output. Instead, it often involves a systematic deduction by ruling out other possible outcomes as a self-checking mechanism. In this paper, we describe the…
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we…