Related papers: Bilingual analogical proportions via hedges

Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel…

Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…

This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…

Analogical reasoning, particularly in multimodal contexts, is the foundation of human perception and creativity. Multimodal Large Language Model (MLLM) has recently sparked considerable discussion due to its emergent capabilities. In this…

The first aim of this paper is to introduce and study symmetric (Bi)Hom-Leibniz algebras, which are left and right Leibniz algebras. We discuss $\alpha^k\beta^l$-generalized derivations, $\alpha^k\beta^l$ -quasi-derivations and…

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…

The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…

Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…

Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…

A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…

Analogical reasoning is effective in capturing linguistic regularities. This paper proposes an analogical reasoning task on Chinese. After delving into Chinese lexical knowledge, we sketch 68 implicit morphological relations and 28 explicit…

Despite the remarkable progress in neural models, their ability to generalize, a cornerstone for applications such as logical reasoning, remains a critical challenge. We delineate two fundamental aspects of this ability: compositionality,…

We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering $n$ points with $k$ centers, we define fairness as proportionality to mean that any $n/k$…

The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of…

Recent work (Ross et al., 2025, 2024) has argued that the ability of humans and LLMs respectively to generalize to novel adjective-noun combinations shows that they each have access to a compositional mechanism to determine the phrase's…

Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language. They presume semantics under which `and' and `or' are related by the dually paired distributive and absorption laws.…

This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…

In this work, the hom-center-symmetric algebras are constructed and discussed. Their bimodules, dual bimodules and matched pairs are defined. The relation between the dual bimodules of hom-center-symmetric algebras and the matched pairs of…

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…