Exploration Space Theory: Formal Foundations for Prerequisite-Aware Location-Based Recommendation
Madjid Sadallah

TL;DR
This paper introduces Exploration Space Theory (EST), a formal lattice-theoretic framework for modeling prerequisite dependencies in location-based recommender systems, enabling structurally sound and explainable recommendations.
Contribution
It formalizes prerequisite-aware location recommendation using lattice theory, connecting it to Formal Concept Analysis, and develops the Exploration Space Recommender System with structural guarantees.
Findings
Valid user exploration states form a finite distributive lattice.
Recommendations are structurally sound with a validity certificate.
The system guarantees sub-path optimality and provides structural explanations.
Abstract
Location-based recommender systems have achieved considerable sophistication, yet none provides a formal, lattice-theoretic representation of prerequisite dependencies among points of interest -- the semantic reality that meaningfully experiencing certain locations presupposes contextual knowledge gained from others -- nor the structural guarantees that such a representation entails. We introduce Exploration Space Theory (EST), a formal framework that transposes Knowledge Space Theory into location-based recommendation. We prove that the valid user exploration states -- the order ideals of a surmise partial order on points of interest -- form a finite distributive lattice and a well-graded learning space; Birkhoff's representation theorem, combined with the structural isomorphism between lattices of order ideals and concept lattices, connects the exploration space canonically to Formal…
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Taxonomy
TopicsConstraint Satisfaction and Optimization · Bayesian Modeling and Causal Inference · Rough Sets and Fuzzy Logic
