Related papers: Multi-sorted logic, models and logical geometry
In this paper we discuss the relationships between conditional and preferential logics and neural network models, based on a multi-preferential semantics. We propose a concept-wise multipreference semantics, recently introduced for…
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
Representation learning of knowledge graphs encodes entities and relation types into a continuous low-dimensional vector space, learns embeddings of entities and relation types. Most existing methods only concentrate on knowledge triples,…
Inthispaperwedescribeaconcept-wisemulti-preferencesemantics for description logic which has its root in the preferential approach for modeling defeasible reasoning in knowledge representation. We argue that this proposal, beside satisfying…
Knowledge graph reasoning (KGR), aiming to deduce new facts from existing facts based on mined logic rules underlying knowledge graphs (KGs), has become a fast-growing research direction. It has been proven to significantly benefit the…
In a standard possibilistic logic, prioritized information are encoded by means of weighted knowledge base. This paper proposes an extension of possibilistic logic for dealing with partially ordered information. We Show that all basic…
Knowledge graphs (KGs), as structured representations of real world facts, are intelligent databases incorporating human knowledge that can help machine imitate the way of human problem solving. However, KGs are usually huge and there are…
We classify the computability-theoretic complexity of two index sets of classes of first-order theories: We show that the property of being an $\aleph_0$-categorical theory is $\Pi^0_3$-complete; and the property of being an Ehrenfeucht…
We present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are compatible with particular binary fuzzy relations called fuzzy…
The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and…
Representation learning of knowledge bases (KBs) aims to embed both entities and relations into a low-dimensional space. Most existing methods only consider direct relations in representation learning. We argue that multiple-step relation…
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…
We present a simple linear programming (LP) based method to learn compact and interpretable sets of rules encoding the facts in a knowledge graph (KG) and use these rules to solve the KG completion problem. Our LP model chooses a set of…
Multi-hop logical reasoning on knowledge graphs is a pivotal task in natural language processing, with numerous approaches aiming to answer First-Order Logic (FOL) queries. Recent geometry (e.g., box, cone) and probability (e.g., beta…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…