Related papers: Bilingual analogical proportions via hedges
Rapid advancements in Large Language models (LLMs) has significantly enhanced their reasoning capabilities. Despite improved performance on benchmarks, LLMs exhibit notable gaps in their cognitive processes. Additionally, as reflections of…
We give an algebraic proof of the criterion for hereditary structural completeness of an intermediate logic, or, equivalently, of the primitiveness of a variety of Heyting algebras.
Dual Horn clauses mirror key properties of Horn clauses. This paper explores the ``other side of the looking glass'' to reveal some expected and unexpected symmetries and their practical uses. We revisit Dual Horn clauses as enablers of a…
The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an…
For every integer $d\ge 1$, there is a unital closed subalgebra $A_d\subset B(H)$ with similarity degree equal precisely to $d$, in the sense of our previous paper. This means that for any unital homomorphism $u\colon A_d\to B(H)$ we have…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Conceptual abstraction and analogy-making are key abilities underlying humans' abilities to learn, reason, and robustly adapt their knowledge to new domains. Despite of a long history of research on constructing AI systems with these…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
We introduce hybrid algebras as algebraic semantics for hybrid languages with nominals and, possibly, the satisfaction operator. We establish a duality between hybrid algebras and the descriptive two-sorted general frames of Ten Cate. We…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector…
We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two…
Human language defines the most complex outcomes of evolution. The emergence of such an elaborated form of communication allowed humans to create extremely structured societies and manage symbols at different levels including, among others,…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Logics with analogous semantics, such as Fuzzy Logic, have a number of explanatory and application advantages, the most well-known being the ability to help experts develop control systems. From a cognitive systems perspective, such…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
Is analogical reasoning a task that must be learned to solve from scratch by applying deep learning models to massive numbers of reasoning problems? Or are analogies solved by computing similarities between structured representations of…
Conversational AI is rapidly becoming a primary interface for information seeking and decision making, yet most systems still assume idealized users. In practice, human reasoning is bounded by limited attention, uneven knowledge, and…