An application of procedural knowledge space theory to the study of strategic planning in board games

Procedural knowledge space theory (PKST) integrates knowledge space theory and problem space theory to model human problem-solving. This study extends PKST to competitive, two-player games and presents the first empirical application of homomorphisms to derive abstract representations of complex problem spaces. Using tic-tac-toe and its numerical variant pick15 as test cases, the study demonstrates how PKST can model complex competitive scenarios effectively. An empirical study involving 148 participants validated these PKST extensions by analyzing their performance on pick15 tasks. Problem and knowledge spaces were derived at multiple levels of abstraction and tested using the Markov solution process model. Results indicated that abstract representations provided a better fit for participants with prior experience in tic-tac-toe, suggesting that expertise promotes the use of generalizable strategies. This work provides a rigorous proof of concept for applying homomorphisms to test theoretical predictions on problem-solving tasks. By linking abstract representations, like tactics, to problem-solving performance, the proposed methodology offers a concrete approach to evaluating cognitive theories of problem-solving and decision-making. These findings highlight the potential of PKST to model broader cognitive phenomena in interactive contexts. The study emphasizes the practical utility and flexibility of PKST for formalizing and empirically testing hypotheses, extending its relevance to diverse domains of cognitive science. (PsycInfo Database Record (c) 2026 APA, all rights reserved).