Related papers: A Separation Logic for Negative Dependence

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture…

The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…

Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations,…

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…

We introduce a novel variant of BSS machines called Separate Branching BSS machines (S-BSS in short) and develop a Fagin-type logical characterisation for languages decidable in non-deterministic polynomial time by S-BSS machines. We show…

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context…

In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…

In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy…

Logical atomicity has been widely accepted as a specification format for data structures in concurrent separation logic. While both lock-free and lock-based data structures have been verified against logically atomic specifications, most of…

In view of the paradigm shift that makes science ever more data-driven, in this thesis we propose a synthesis method for encoding and managing large-scale deterministic scientific hypotheses as uncertain and probabilistic data. In the form…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of…

Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…

We introduce a logical framework for the specification and verification of component-based systems, in which finitely many component instances are active, but the bound on their number is not known. Besides specifying and verifying…

Knowledge could be gained from experts, specialists in the area of interest, or it can be gained by induction from sets of data. Automatic induction of knowledge from data sets, usually stored in large databases, is called data mining. Data…

In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…

In systems modelling, a 'system' typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their…

Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation…