Karl Svozil, "Randomness & Undecidability in Physics", World Scientific, 1993, [chapters 10.2 - 10.5] also speaks about the simulaton argument.

It is not unreasonable - he says - to speculate about the logico-algebraic structure of "automaton" universes (universes "computer" generated). If there is a hidden computing entity, and if this computing entity is "universal", there is no reason to exclude the so called (intrinsic) "calculus of propositions". Physical properties corresponding to _experimental_ propositions are identified - in the quantum domain - with "projection" operators on the Hilbert space. Thus Hilbert "lattice" corresponds to a lattice of experimental propositions. Algebraic relations and operations between these experimental propositions are called "calculus of propositions". Hilbert lattice and calculus of propositions _should_ be equivalent, even in the quantum domain. (Lattice theory is a framework for organizing structures such as experimental or logical statements). There is no _recursive_ enumeration of the axioms of Hilbert lattices. It is not unreasonable asking something like: do we live in a (quantum) universe created by some "universal" computation ? Thus, to test such speculation, we must look for _phenomena_ which correspond to "automaton" calculus of propositions _not_ contained in a Hilbert lattice (or its subalgebras).