On Modal Logic Formulae Minimization

From the intricate circuits of digital devices to the abstract realms of logical theory, formula minimization remains a cornerstone challenge with various implications. This paper explores the adaptation of formula minimization techniques to modal logic k, driven by the challenges of processing increasingly complex data structures. Our investigation begins by analyzing the inherent computational complexity of minimizing modal formulae, a critical step towards developing effective solutions. We, then, introduce a heuristic algorithm for the purpose. We prove its correctness, addressing the unique demands of modal logic. The implications of this work extend beyond theoretical interest, and include practical insights for the post-hoc treatment of symbolic models in modal logic K, as well as temporal, spatial, and other non-classical logics in advanced computational contexts.