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OWL ontologies, whose formal semantics are rooted in Description Logic (DL), have been widely used for knowledge representation. Similar to Knowledge Graphs (KGs), ontologies are often incomplete, and maintaining and constructing them has…
The quest for acquiring a formal representation of the knowledge of a domain of interest has attracted researchers with various backgrounds into a diverse field called ontology learning. We highlight classical machine learning and data…
Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous…
Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, so as to leverage the complementary strengths of both of these, seemingly unrelated (maybe even contradictory) AI…
Description logics are knowledge representation formalisms that provide the formal underpinning of the semantic web and in particular of the $\text{OWL}$ Ontology Web Language. In this paper we investigate the expressive power of logic…
This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…
A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…
We further develop the paraconsistent G\"{o}del modal logic. In this paper, we consider its version endowed with Kripke semantics on $[0,1]$-valued frames with two fuzzy relations $R^+$ and $R^-$ (degrees of trust in assertions and denials)…
After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying…
In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a ${\cal C}^1$ fuzzy submanifold after reviewing ${\cal C}^1-$fuzzy manifold definition. In main section, we defined…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
The DL-Lite description logics allow for modeling domain knowledge on top of databases and for efficient reasoning. We focus on metric temporal extensions of DL-Lite_bool and its fragments, and study the complexity of satisfiability. In…
This paper introduces a novel generalized self-imitation learning ($\textbf{GSIL}$) framework, which effectively and efficiently aligns large language models with offline demonstration data. We develop $\textbf{GSIL}$ by deriving a…
We present DiffExplainer, a novel framework that, leveraging language-vision models, enables multimodal global explainability. DiffExplainer employs diffusion models conditioned on optimized text prompts, synthesizing images that maximize…
The concept of uncertainty is posed in almost any complex system including parallel robots as an outstanding instance of dynamical robotics systems. As suggested by the name, uncertainty, is some missing information that is beyond the…
This paper investigates the factuality of large language models (LLMs) as knowledge bases in the legal domain, in a realistic usage scenario: we allow for acceptable variations in the answer, and let the model abstain from answering when…
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish…
In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define exdended…
Bilingual word embeddings, which representlexicons of different languages in a shared em-bedding space, are essential for supporting se-mantic and knowledge transfers in a variety ofcross-lingual NLP tasks. Existing approachesto training…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…