Related papers: Embedding Tarskian Semantics in Vector Spaces
We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…
The AI community is increasingly focused on merging logic with deep learning to create Neuro-Symbolic (NeSy) paradigms and assist neural approaches with symbolic knowledge. A significant trend in the literature involves integrating axioms…
We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary.…
Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an…
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…
The paper presents an approach to semantic grounding of language models (LMs) that conceptualizes the LM as a conditional model generating text given a desired semantic message formalized as a set of entity-relationship triples. It embeds…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
In this paper we present a unified framework for modeling multi-relational representations, scoring, and learning, and conduct an empirical study of several recent multi-relational embedding models under the framework. We investigate the…
Recent work has explored methods for learning continuous vector space word representations reflecting the underlying semantics of words. Simple vector space arithmetic using cosine distances has been shown to capture certain types of…
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as…
We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors. We demonstrate the effectiveness of the approach by proving of a number of integral identities with vector integrands.
We study the expressivity and computational aspects of first-order logic and its extensions in the semiring semantics developed by Gr\"adel and Tannen. We characterize the complexity of model checking and data complexity of first-order…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
Formal properties represent a cornerstone of the system-correctness proofs based on formal verification techniques such as model checking. Formalizing requirements into temporal properties may be very complex and error prone, due not only…
We construct yet another ${\mathcal N}=(4,4)$ gauged linear sigma model for the $A_N$-type ALE space. In our construction the toric data of the ALE space are manifest. Due to the $SU(2)_R$ symmetry, the F-term is automatically determined.…
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce…
To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
Human vision is able to compensate imperfections in sensory inputs from the real world by reasoning based on prior knowledge about the world. Machine learning has had a significant impact on computer vision due to its inherent ability in…