Abstract Concept Modelling in Conceptual Spaces: A Study on Chess Strategies

TL;DR

This paper introduces a geometric, trajectory-based framework within conceptual spaces to model and recognize abstract, temporally unfolding concepts like chess strategies, capturing different interpretations and supporting learning over time.

Contribution

It extends conceptual spaces theory to model dynamic, goal-directed concepts over time, demonstrated through a chess strategy recognition proof-of-concept.

Findings

Trajectory patterns align with expert commentary

Supports dual-perspective interpretation of concepts

Lays foundation for learning and refining abstract concepts

Abstract

We present a conceptual space framework for modelling abstract concepts that unfold over time, demonstrated through a chess-based proof-of-concept. Strategy concepts, such as attack or sacrifice, are represented as geometric regions across interpretable quality dimensions, with chess games instantiated and analysed as trajectories whose directional movement toward regions enables recognition of intended strategies. This approach also supports dual-perspective modelling, capturing how players interpret identical situations differently. Our implementation demonstrates the feasibility of trajectory-based concept recognition, with movement patterns aligning with expert commentary. This work explores extending the conceptual spaces theory to temporally realised, goal-directed concepts. The approach establishes a foundation for broader applications involving sequential decision-making and supports integration with knowledge evolution mechanisms for learning and refining abstract concepts over time.