Related papers: Morpho-logic from a Topos Perspective: Application…
AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases. Recent technical…
This paper investigates whether LMs recruit shared computational mechanisms for general Theory of Mind (ToM) and language-specific pragmatic reasoning in order to contribute to the general question of whether LMs may be said to have…
The ability to manipulate logical-mathematical symbols (LMS), encompassing tasks such as calculation, reasoning, and programming, is a cognitive skill arguably unique to humans. Considering the relatively recent emergence of this ability in…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
Theory of Mind (ToM) refers to the ability of individuals to attribute mental states to others. While Large Language Models (LLMs) have shown some promise with ToM ability, they still struggle with complex ToM reasoning. Our approach…
The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…
The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can further the study of quantum logic and give rise to new…
Morphological analysis is an important subtask in text-to-speech conversion, hyphenation, and other language engineering tasks. The traditional approach to performing morphological analysis is to combine a morpheme lexicon, sets of…
The Distributed Ontology Language (DOL) is currently being standardized within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalized in…
Visual reasoning, particularly spatial reasoning, is a challenging cognitive task that requires understanding object relationships and their interactions within complex environments, especially in robotics domain. Existing vision_language…
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…
The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems…
Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear,…
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…
Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based…
Modelling musical structure is vital yet challenging for artificial intelligence systems that generate symbolic music compositions. This literature review dissects the evolution of techniques for incorporating coherent structure, from…
Designing mechanical linkages involves combinatorial topology selection and continuous parameter fitting. We show that language models can systematically improve linkage designs through symbolic representations. Language model agents…
The purpose of this paper is to present a fresh idea on how symbolic learning might be realized via analogical reasoning. For this, we introduce directed analogical proportions between logic programs of the form "$P$ transforms into $Q$ as…