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We present a notion of $\Delta$-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the existence of a zero morphism, a…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
Abstract argumentation is a reasoning model for evaluating arguments based on various semantics. SCC-recursiveness is a sophisticated property of semantics that provides a general schema for characterizing semantics through the…
The theory of distributed conceptual structures, as outlined in this paper, is concerned with the distribution and conception of knowledge. It rests upon two related theories, Information Flow and Formal Concept Analysis, which it seeks to…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory topological characterizations of closed…
Domain generalization methods aim to learn models robust to domain shift with data from a limited number of source domains and without access to target domain samples during training. Popular domain alignment methods for domain…
This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer.…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
Referring expressions are natural language descriptions that identify a particular object within a scene and are widely used in our daily conversations. In this work, we focus on segmenting the object in an image specified by a referring…
In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
This work addresses the challenge of factual consistency in text generation systems. We unify the tasks of Natural Language Inference, Summarization Evaluation, Factuality Verification and Factual Consistency Evaluation to train models…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
Establishing stable mappings between natural language expressions and visual percepts is a foundational problem for both cognitive science and artificial intelligence. Humans routinely ground linguistic reference in noisy, ambiguous…
Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…
Classifications organize entities into categories that identify similarities within a category and discern dissimilarities among categories, and they powerfully classify information in support of analysis. We propose a new classification…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Measuring the similarity of short written contexts is a fundamental problem in Natural Language Processing. This article provides a unifying framework by which short context problems can be categorized both by their intended application and…
The modern geographic information retrieval technology is based on quantitative models and methods. The semantic information in web documents and queries cannot be effectively represented, leading to information lost or misunderstanding so…