The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1

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We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games. 1 1 Physics after the incompleteness theorems There is incompleteness in mathematics [22, 63, 65, 13, 9, 12, 51]. That means that there does not exist any reasonable (consistent) finite formal system from which all mathematical truth is derivable. And there exists a "huge" number [11] of mathematical assertions (e.g., the continuum hypothesis, the axiom of choice) which are independent of any particular formal system. That is, they as well as their negations are compatible with the formal system. Can such formal incompleteness be translated into physics or the natural sciences in general? Is there some question about the nature of things which is provable unknowable for rational thought? Is it conceivable that the natural phenomena, even if they occur deterministically, do not allow their complete d...

Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical evidence of the quantum world. We give a brief outline of quantum logic, and some of its algebraic properties, such as nondistributivity, whereby emphasis is given to concrete experimental setups related to quantum logical entities. A probability theory based on quantum logic is fundamentally and sometimes even spectacularly different from probabilities based on classical Boolean logic. We give a brief outline of its nonclassical aspects; in particular violations of Boole-Bell type consistency constraints on joint probabilities, as well as the Kochen-Specker theorem, demonstrating in a constructive, finite way the scarcity and even nonexistence of two-valued states interpretable as classical truth assignments. A more complete introduction of the author can be found in the book Quantum Logic (Springer, 1998) PACS numbers: 03.67.Hk,03.65.Ud,03.65.Ta,03.67.Mn