Differences in perception, information asymmetries, and bounded rationality lead game-theoretic players to derive a private, subjective view of the game that may diverge from the underlying ground-truth scenario and may be misaligned with other players' interpretations. While typical game-theoretic assumptions often overlook such heterogeneity, hypergame theory provides the mathematical framework to reason about mismatched mental models. Although hypergames have recently gained traction in dynamic applications concerning uncertainty, their practical adoption in multi-agent system research has been hindered by the lack of a unifying, formal, and practical representation language, as well as scalable algorithms for managing complex hypergame structures and equilibria. Our work addresses this gap by introducing a declarative, logic-based domain-specific language for encoding hypergame structures and hypergame solution concepts. Leveraging answer-set programming, we develop an automated pipeline for instantiating hypergame structures and running our novel hypergame rationalisation procedure, a mechanism for finding belief structures that justify seemingly irrational outcomes. The proposed language establishes a unifying formalism for hypergames and serves as a foundation for developing nuanced, belief-based heterogeneous reasoners, offering a verifiable context with logical guarantees. Together, these contributions establish the connection between hypergame theory, multi-agent systems, and strategic AI.