Related papers: Alpay Algebra V: Multi-Layered Semantic Games and …
We present a theoretical framework in which a document and an AI model engage in a transfinite fixed-point interaction that leads to stable semantic alignment. Building on the foundations of Alpay Algebra, we introduce a functorial system…
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…
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…
Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning…
We focus on the problem of \emph{Answer-Level Fine-Tuning} (ALFT), where the goal is to optimize a language model based on the correctness or properties of its final answers, rather than the specific reasoning traces used to produce them.…
This paper presents a new model for word sense disambiguation formulated in terms of evolutionary game theory, where each word to be disambiguated is represented as a node on a graph whose edges represent word relations and senses are…
Classical game-theoretic models typically assume rational agents, complete information, and common knowledge of payoffs - assumptions that are often violated in real-world MAS characterized by uncertainty, misaligned perceptions, and nested…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
In this paper, we argue that the future of Artificial Intelligence research resides in two keywords: integration and embodiment. We support this claim by analyzing the recent advances of the field. Regarding integration, we note that the…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
This paper presents a substantially reworked examination of how advanced game-theoretic paradigms can serve as a foundation for the next-generation challenges in Artificial Intelligence (AI), forecasted to arrive in or around 2025. Our…
The main goal of this paper is to settle a conceptual framework for cooperative game theory in which the notion of composition/aggregation of games is the defining structure. This is done via the mathematical theory of algebraic operads: we…
We provide here an epistemic analysis of arbitrary strategic games based on the possibility correspondences. Such an analysis calls for the use of transfinite iterations of the corresponding operators. Our approach is based on Tarski's…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
The Distributional Alignment Game framework provides a powerful variational perspective on Answer-Level Fine-Tuning (ALFT). However, standard algorithms for these games rely on estimating logarithmic rewards from small batches, introducing…
Differences in perception, information asymmetries, and bounded rationality lead game-theoretic players to derive a private, subjective view of the game that may diverge from the underlying ground-truth scenario and may be misaligned with…
Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…
The integration of AI into modern critical infrastructure systems, such as healthcare, has introduced new vulnerabilities that can significantly impact workflow, efficiency, and safety. Additionally, the increased connectivity has made…
Conversational AI has a fundamental flaw as a knowledge interface: sycophantic chatbots induce epistemic entrenchment and delusional belief spirals even in rational agents. We propose the problem does not stem from the AI model, rooted…