Related papers: Towards Unifying Logical Entailment and Statistica…

Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

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…

Many formalisms combining ontology languages with uncertainty, usually in the form of probabilities, have been studied over the years. Most of these formalisms, however, assume that the probabilistic structure of the knowledge remains…

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…

This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…

Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model…

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…

This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…

In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…

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…

We generalise the distribution semantics underpinning probabilistic logic programming by distilling its essential concept, the separation of a free random component and a deterministic part. This abstracts the core ideas beyond logic…

Recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic, as the laws of thought, is a product and practice of the human brain, it leads to…

This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…

There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…

The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

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…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…