Title: Knowing and Measuring

Speaker: Adam Bjorndahl (CMU)

Time: 9:00 -12:00 (Sep. 20th)

Location: Room 106, Buidling No.2, Lee Shau Kee Humanities Buildings, PKU

Online: Zoom Meeting ID: ‪824 4525 5756‬; Passcode: 613078

Abstract:

This talk begins by presenting an epistemic interpretation of nondeterministic program execution (or, more generally, nondeterministic action): working in an enriched logical setting, we represent nondeterminism as a relationship between a program and an agent deriving from the agent's (in)ability to fully measure the true state of the system. More precisely, using topology to capture the observational powers of an agent, we define the nondeterministic outcomes of a given program execution to be those that the agent is unable in principle to rule out in advance of execution.

Analysing these models leads naturally to the consideration of measurements that may themselves affect the state of the system in some way. Formalizing this leads to a generalization of the notion of a topological space and an operator of "measurable truth" analogous to an interior operator but satisfying weaker properties. We propose a logical language and semantics for this framework and consider potential axioms.