The Epistemology of Nondeterminism

This paper proposes new semantics for propositional dynamic logic (PDL), replacing the standard relational semantics. Under these semantics, program execution is represented as fundamentally deterministic (i.e., functional), while nondeterminism emerges an epistemic relationship between agent and system: intuitively, nondeterministic outcomes of a given process are precisely those that cannot be ruled out in advance. We formalize notions using topology framework topological (DTL) (Kremer Mints Ann Pure Appl Logic 131:133–158, 2005). show DTL can used to interpret language PDL manner captures intuition above, moreover continuous functions this setting correspond exactly processes. also prove certain axiomatizations remain sound complete with respect corresponding classes models. Finally, we extend incorporate knowledge machinery subset space (Dabrowski et al. 78:73–110, 1996), interpretation public announcements Bjorndahl (in: van Ditmarsch Sandu (eds) Jaakko Hintikka on game theoretical outstanding contributions Logic, vol 12, Springer, 2018) coincides natural test programs.