TY - CHAP
AB - In R.D. Sorkin's framework for logic in physics a clear separation is madebetween the collection of unasserted propositions about the physical world andthe affirmation or denial of these propositions by the physical world. Theunasserted propositions form a Boolean algebra because they correspond tosubsets of an underlying set of spacetime histories. Physical rules ofinference, apply not to the propositions in themselves but to the affirmationand denial of these propositions by the actual world. This physical logic mayor may not respect the propositions' underlying Boolean structure. We provethat this logic is Boolean if and only if the following three axioms hold: (i)The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is deniedthen its negation, or complement, is affirmed. When a physical system isgoverned by a dynamical law in the form of a quantum measure with the rule thatevents of zero measure are denied, the axioms (i) - (iii) prove to be too rigidand need to be modified. One promising scheme for quantum mechanics as quantummeasure theory corresponds to replacing axiom (iii) with axiom (iv) Nature isas fine grained as the dynamics allows.
AU - Clements,K
AU - Dowker,F
AU - Wallden,P
DO - 10.1007/978-3-319-43669-2
EP - 61
PB - Springer International Publishing
PY - 2017///
SP - 47
TI - Physical Logic
T1 - The Incomputable
UR - http://dx.doi.org/10.1007/978-3-319-43669-2
UR - http://arxiv.org/abs/1201.6266v2
ER -