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Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which…

The validity of statistical inference depends critically on how data are collected. When data gathered through active data collection (ADC) are reused for a post-hoc inferential task, conventional inference can fail because the sampling is…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…

The discussion on causality in human history dates back to ancient Greece, yet to this day, there is still no consensus. Fundamentally, this stems from the nature of human cognition, as understanding causality requires abstract tools to…

Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…

Experiments are the gold standard for causal inference. In many applications, experimental units can often be recruited or chosen sequentially, and the adaptive execution of such experiments may offer greatly improved inference of causal…

Emerging research frontiers and computational advances have gradually transformed cognitive science into a multidisciplinary and data-driven field. As a result, there is a proliferation of cognitive theories investigated and interpreted…

Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…

Affordances, a foundational concept in human-computer interaction and design, have traditionally been explained by direct-perception theories, which assume that individuals perceive action possibilities directly from the environment.…

We develop the compositional theory of active inference by introducing activity, functorially relating statistical games to the dynamical systems which play them, using the new notion of approximate inference doctrine. In order to exhibit…

The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…

The roundworm C. elegans exhibits robust escape behavior in response to rapidly rising temperature. The behavior lasts for a few seconds, shows history dependence, involves both sensory and motor systems, and is too complicated to model…

Discovering statistically significant patterns from databases is an important challenging problem. The main obstacle of this problem is in the difficulty of taking into account the selection bias, i.e., the bias arising from the fact that…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying…

The study of citations in the scientific literature crosses the boundaries between the traditional branches of science and stands on its own as a most profitable research field dubbed the `science of science'. Although the understanding of…

A growing body of work makes use of probing to investigate the working of neural models, often considered black boxes. Recently, an ongoing debate emerged surrounding the limitations of the probing paradigm. In this work, we point out the…

Causal attribution, which aims to explain why events or behaviors occur, is crucial in causal inference and enhances our understanding of cause-and-effect relationships in scientific research. The probabilities of necessary causation (PN)…