Related papers: Non-monotonic Extensions to Formal Concept Analysi…
In this paper, we introduce an explainable algorithm designed from a multi-modal foundation model, that performs fast and explainable image classification. Drawing inspiration from CLIP-based Concept Bottleneck Models (CBMs), our method…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…
Structural causal models (SCMs) allow us to investigate complex systems at multiple levels of resolution. The causal abstraction (CA) framework formalizes the mapping between high- and low-level SCMs. We address CA learning in a challenging…
We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions. This result encompasses Ghilardi-Meloni's and Suzuki's…
We investigate the standard context, denoted by $\mathbb{K}\left(\mathcal{L}_{n}\right)$, of the lattice $\mathcal{L}_{n}$ of partitions of a positive integer $n$ under the dominance order. Motivated by the discrete dynamical model to study…
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…
Developing human understandable interpretation of large language models (LLMs) becomes increasingly critical for their deployment in essential domains. Mechanistic interpretability seeks to mitigate the issues through extracts…
With the growing popularity of general-purpose Large Language Models (LLMs), comes a need for more global explanations of model behaviors. Concept-based explanations arise as a promising avenue for explaining high-level patterns learned 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…
We propose a layered hierarchical architecture called UCLA (Universal Causality Layered Architecture), which combines multiple levels of categorical abstraction for causal inference. At the top-most level, causal interventions are modeled…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
Motivated by the increased need for formalized representations of the domain of Data Mining, the success of using Formal Concept Analysis (FCA) and Ontology in several Computer Science fields, we present in this paper a new approach for…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this…
Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…
Dealing with uncertain, contradicting, and ambiguous information is still a central issue in Artificial Intelligence (AI). As a result, many formalisms have been proposed or adapted so as to consider non-monotonicity, with only a limited…
We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices,…
Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…