Related papers: Topological Observations on Multiplicative Additiv…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
This paper explores how semantic-space reasoning, traditionally used in computational linguistics, can be extended to tactical decision-making in team sports. Building on the analogy between texts and teams -- where players act as words and…
Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…
This paper explores the interface between algebra, topology, and logic by developing the theory of sheaves and etale spaces for residuated lattices, algebraic structures central to substructural and fuzzy logics. We construct…
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{A}$ and $\mathbf{Game}_{B}$ and improve some classical results concerning topological games related to the duality between…
The present paper gives a mathematical, in particular, syntax-independent, formulation of intensionality and dynamics of computation in terms of games and strategies. Specifically, we give a game semantics for a higher-order programming…
In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…
We develop a new approach that computes approximate equilibrium strategies in Jotto, a popular word game. Jotto is an extremely large two-player game of imperfect information; its game tree has many orders of magnitude more states than…
We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Real-life agents seldom have unlimited reasoning power. In this paper, we propose and study a new formal notion of computationally bounded strategic ability in multi-agent systems. The notion characterizes the ability of a set of agents to…
Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…
Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are…
A topological argument is presented concering the structure of semantic space, based on the negative correlation between polysemy and word length. The resulting graph structure is applied to the modeling of free-recall experiments,…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…
The constructive approach to mathematics has the advantage that witnesses can be extracted from statements of existence and theorems can be unwound to give algorithms. Even better, constructive theorems can be interpreted in any topos,…
The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…