Abstract
We introduce dynamic algebras and show how they can be used to give an algebraic interpretation to propositional dynamic logic (PDL). Dynamic algebras include all Kripke models, the standard interpretation of PDL. We give a simple algebraic condition on *-free dynamic algebras that is necessary and sufficient for representation by *-free Kripke models. In the presence of*, the condition is sufficient for representation by a nonstandard Kripke model. This result leads to a duality between certain topological Kripke models and dynamic algebras analogous to the duality between Boolean algebras and their Stone spaces.
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Kozen, D. (1980). A representation theorem for models of *-free PDL. In: de Bakker, J., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 1980. Lecture Notes in Computer Science, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10003-2_83
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DOI: https://doi.org/10.1007/3-540-10003-2_83
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