Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Hadi Banaee, Stephanie Lowry

TL;DR

The paper addresses modelling abstract, temporally unfolding concepts, using chess strategies as a testbed. It introduces a conceptual spaces framework that represents strategies as geometric regions across interpretable dimensions and tracks game trajectories to infer intent, including dual-perspective interpretations. Key contributions include a concrete design with seven dimensions across three domains, three abstract strategies, and trajectory-based recognition anchored in region convergence, plus a discussion of extending conceptual spaces to temporal, goal-directed concepts. The work lays groundwork for interpretable AI in sequential decision-making and highlights future directions for data-driven dimension discovery, region learning, and cross-domain applications.

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.

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

TL;DR

The paper addresses modelling abstract, temporally unfolding concepts, using chess strategies as a testbed. It introduces a conceptual spaces framework that represents strategies as geometric regions across interpretable dimensions and tracks game trajectories to infer intent, including dual-perspective interpretations. Key contributions include a concrete design with seven dimensions across three domains, three abstract strategies, and trajectory-based recognition anchored in region convergence, plus a discussion of extending conceptual spaces to temporal, goal-directed concepts. The work lays groundwork for interpretable AI in sequential decision-making and highlights future directions for data-driven dimension discovery, region learning, and cross-domain applications.

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.
Paper Structure (13 sections, 4 figures)

This paper contains 13 sections, 4 figures.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Conceptual Spaces Theory
  4. Chess Strategy in AI Systems
  5. Chess Conceptual Space: Design and Implementation
  6. Knowledge Acquisition: Abstract Strategy Concepts in Chess
  7. Space Construction: Dimension Grounding and Concept Anchoring
  8. Space Instantiation: Position Encoding and Game Trajectories
  9. Strategy Recognition and Interpretation Examples
  10. Discussion
  11. Generalisation and Framework Extensions
  12. Challenges and Implications
  13. Conclusion and Future Directions

Figures (4)

  • Figure 1: An illustration of the chess conceptual space, showing chess strategies anchored as regions across force, territory, and conflict domains.
  • Figure 2: Dual-perspective trajectories of chess board positions in chess conceptual space.
  • Figure 3: Strategy recognition examples aligned with concept regions in annotated master games.
  • Figure 4: Proposed framework architecture for geometric modelling of abstract concepts.