Related papers: Knowledge Representation in Bicategories of Relati…
The first-order logical environment FOLE [5] provides a rigorous and principled approach to distributed interoperable first-order information systems. FOLE has been developed in two forms: a classification form and an interpretation form.…
Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…
Ontologies are widely used for representing domain knowledge and meta data, playing an increasingly important role in Information Systems, the Semantic Web, Bioinformatics and many other domains. However, logical reasoning that ontologies…
Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
Retrieval-Augmented Generation (RAG) systems combine Large Language Models (LLMs) with external knowledge, and their performance depends heavily on how that knowledge is represented. This study investigates how different Knowledge Graph…
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
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,…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Ontologies order and interconnect knowledge of a certain field in a formal and semantic way so that they are machine-parsable. They try to define allwhere acceptable definition of concepts and objects, classify them, provide properties as…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…
This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Developing and organizing new knowledge is a core activity for scholars. Recently, ontologies have been introduced as an approach for organizing knowledge. However, most ontologies do not readily support the development and organization of…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
The current learning systems typically lack the level of metacognitive awareness, self-directed learning, and time management skills. Most of the ontologically based learning management systems are in the proposed phase and those which are…