Related papers: Probabilistic Epistemic Updates on Algebras
Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show…
Epistemic Logic Programs (ELPs), that is, Answer Set Programming (ASP) extended with epistemic operators, have received renewed interest in recent years, which led to a flurry of new research, as well as efficient solvers. An important…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We discuss the syntax and semantics of relational Horn logic (RHL) and partial Horn logic (PHL). RHL is an extension of the Datalog programming language that allows introducing and equating variables in conclusions. PHL is a syntactic…
We develop a new duality for distributive and implicative meet semi-lattices. For distributive meet semi-lattices our duality generalizes Priestley's duality for distributive lattices and provides an improvement of Celani's duality. Our…
Querying large datasets with incomplete and vague data is still a challenge. Ontology-based query answering extends standard database query answering by background knowledge from an ontology to augment incomplete data. We focus on…
The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…
Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) -- also known as Scientific Machine Learning -- with particular focus to those PEML strategies developed to tackle dynamical systems' challenges. The need to…
We prove a completeness result for Multiplicative Exponential Linear Logic (MELL): we show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relational model is exactly axiomatized…
Deep learning techniques are increasingly popular in the textual entailment task, overcoming the fragility of traditional discrete models with hard alignments and logics. In particular, the recently proposed attention models (Rockt\"aschel…
This paper presents a two-dimensional modal logic for reasoning about the changing patterns of knowledge and social relationships in networks organised on the basis of a symmetric 'friendship' relation, providing a precise language for…
Gradually typed languages allow statically typed and dynamically typed code to interact while maintaining benefits of both styles. The key to reasoning about these mixed programs is Siek-Vitousek-Cimini-Boyland's (dynamic) gradual…
What-if (provisioning for an update to a database) and how-to (how to modify the database to achieve a goal) analyses provide insights to users who wish to examine hypothetical scenarios without making actual changes to a database and…
We construct a representation of the blob algebra over a ring allowing base change to every interesting (i.e. non--semisimple) specialisation which, in quasihereditary specialisations, passes to a full tilting module.
Modern language models have the capacity to store and use immense amounts of knowledge about real-world entities, but it remains unclear how to update such knowledge stored in model parameters. While prior methods for updating knowledge in…
Entity linkage (EL) is a critical problem in data cleaning and integration. In the past several decades, EL has typically been done by rule-based systems or traditional machine learning models with hand-curated features, both of which…
In recent years, there has been extensive research on how to extend general-purpose programming language semantics with domain-specific modeling constructs. Two areas of particular interest are (i) universal probabilistic programming where…
In this paper we present some novel applications of Explanation-Based Learning (EBL) technique to parsing Lexicalized Tree-Adjoining grammars. The novel aspects are (a) immediate generalization of parses in the training set, (b)…