Related papers: Alpay Algebra IV: Symbiotic Semantics and the Fixe…
This paper extends the self-referential framework of Alpay Algebra into a multi-layered semantic game architecture where transfinite fixed-point convergence encompasses hierarchical sub-games at each iteration level. Building upon Alpay…
This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stages, is identical to the unique equilibrium of an unbounded…
Alpay Algebra is introduced as a universal, category-theoretic framework that unifies classical algebraic structures with modern needs in symbolic recursion and explainable AI. Starting from a minimal list of axioms, we model each algebra…
In this second installment of the Alpay Algebra framework, I formally define identity as a fixed point that emerges through categorical recursion. Building upon the transfinite operator $\varphi^\infty$, I characterize identity as the…
This paper introduces a formal framework for modeling observer-dependent collapse dynamics and temporal identity drift within artificial and mathematical systems, grounded entirely in the symbolic foundations of Alpay Algebra. Building upon…
We present a new theoretical framework that unifies category-theoretic fixed-point constructions, transfinite recursion, and game-based semantics to model how interpretations of language can stabilize through unlimited self-reference. By…
In the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are…
Semantic information in embodied AI is inherently multi-source and multi-stage, making it challenging to fully leverage for achieving stable perception-to-action loops in real-world environments. Early studies have combined manual…
There is growing evidence that independently trained AI systems come to represent the world in the same way. In other words, independently trained embeddings from text, vision, audio, and neural signals share an underlying geometry. We call…
Recent advances in AI call for a paradigm shift from bit-centric communication to goal- and semantics-oriented architectures, paving the way for AI-native 6G networks. In this context, we address a key open challenge: enabling heterogeneous…
Embodied Artificial Intelligence (AI) is an intelligent system formed by agents and their environment through active perception, embodied cognition, and action interaction. Existing embodied AI remains confined to human-crafted setting, in…
Artificial agents capable of understanding and aligning with others' intentions are essential for safe and socially robust artificial intelligence. We introduce a computational framework for empathy in active inference agents, grounded in…
We propose Embodied AI as the next fundamental step in the pursuit of Artificial General Intelligence, juxtaposing it against current AI advancements, particularly Large Language Models. We traverse the evolution of the embodiment concept…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Human-in-the-loop validation is essential in safety-critical clinical AI, yet the transition between initial model inference and expert correction is rarely analyzed as a structured signal. We introduce a diagnostic alignment framework in…
We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma…
AI support of collaborative interactions entails mediating potential misalignment between interlocutor beliefs. Common preference alignment methods like DPO excel in static settings, but struggle in dynamic collaborative tasks where the…
As Artificial Intelligence (AI) integrates deeper into diverse sectors, the quest for powerful models has intensified. While significant strides have been made in boosting model capabilities and their applicability across domains, a glaring…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
Current AI systems rely on opaque reasoning processes that hinder human oversight and collaborative potential. Conventional explainable AI approaches offer post-hoc justifications and often fail to establish genuine symbiotic collaboration.…