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We introduce a variant of free logic (i.e., a logic admitting terms with nonexistent referents) that accommodates truth-value gluts as well as gaps. Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify a…
Let $\Theta$ be a variety of algebras, $(H, \Psi, f)$ be a model, where $H$ is an algebra from $\Theta$, $\Psi$ is a set of relation symbols $\varphi$, $f$ is an interpretation of all $\varphi$ in $H$. Let $X^0$ be an infinite set of…
With the widespread use of machine learning to support decision-making, it is increasingly important to verify and understand the reasons why a particular output is produced. Although post-training feature importance approaches assist this…
The arrangement of things in n-dimensional space is specified as Spatial. Spatial data consists of values that denote the location and shape of objects and areas on the earths surface. Spatial information includes facts such as location of…
Recent advances in visual representation learning allowed to build an abundance of powerful off-the-shelf features that are ready-to-use for numerous downstream tasks. This work aims to assess how well these features preserve information…
Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty,…
Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between…
Entity images could provide significant visual information for knowledge representation learning. Most conventional methods learn knowledge representations merely from structured triples, ignoring rich visual information extracted from…
We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function.
This paper is to consider the problems of estimation and recognition from the perspective of sigma-max inference (probability-possibility inference), with a focus on discovering whether some of the unknown quantities involved could be more…
Encoding facts as representations of entities and binary relationships between them, as learned by knowledge graph representation models, is useful for various tasks, including predicting new facts, question answering, fact checking and…
Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…
We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F…
The success of neural networks builds to a large extent on their ability to create internal knowledge representations from real-world high-dimensional data, such as images, sound, or text. Approaches to extract and present these…
Multi-view datasets are frequently encountered in learning tasks, such as web data mining and multimedia information analysis. Given a multi-view dataset, traditional learning algorithms usually decompose it into several single-view…
Images encode both the state of the world and its content. The former is useful for tasks such as planning and control, and the latter for classification. The automatic extraction of this information is challenging because of the…
Neural network is a powerful learning paradigm for data feature learning in the era of big data. However, most neural network models are deterministic models that ignore the uncertainty of data. Fuzzy neural networks are proposed to address…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the…
Several deep learning (DL) approaches have been proposed to deal with image classification tasks. However, despite their effectiveness, they lack interpretability, as they are unable to explain or justify their results. To address the…