Related papers: Multi-sorted logic, models and logical geometry
Knowledge base question answering (KBQA) aims to answer user questions in natural language using rich human knowledge stored in large KBs. As current KBQA methods struggle with unseen knowledge base elements at test time,we introduce…
Large knowledge bases (KBs) are useful in many tasks, but it is unclear how to integrate this sort of knowledge into "deep" gradient-based learning systems. To address this problem, we describe a probabilistic deductive database, called…
Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and…
Much has been discussed about how Large Language Models, Knowledge Graphs and Search Engines can be combined in a synergistic manner. A dimension largely absent from current academic discourse is the user perspective. In particular, there…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
A fuzzy multipreference semantics has been recently proposed for weighted conditional knowledge bases, and used to develop a logical semantics for Multilayer Perceptrons, by regarding a deep neural network (after training) as a weighted…
Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms…
In every variety of algebras $\Theta$ we can consider its logic and its algebraic geometry. In the previous papers geometry in equational logic, i.e., equational geometry has been studied. Here we describe an extension of this theory…
Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…
The problem of knowledge graph (KG) reasoning has been widely explored by traditional rule-based systems and more recently by knowledge graph embedding methods. While logical rules can capture deterministic behavior in a KG they are brittle…
Wikidata is a knowledge graph increasingly adopted by many communities for diverse applications. Wikidata statements are annotated with qualifier-value pairs that are used to depict information, such as the validity context of the…
Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In…
We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting…
In epistemic logic, a way to deal with knowledge-wh is to interpret them as a kind of mention-some knowledge (MS-knowledge). But philosophers and linguists have challenged both the sufficiency and necessity of such an account: some argue…
Knowledge Base Question Answering (KBQA) tasks that in-volve complex reasoning are emerging as an important re-search direction. However, most KBQA systems struggle withgeneralizability, particularly on two dimensions: (a) acrossmultiple…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on…
Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…