2 research outputs found
The Topology of Statistical Verifiability
Topological models of empirical and formal inquiry are increasingly
prevalent. They have emerged in such diverse fields as domain theory [1, 16],
formal learning theory [18], epistemology and philosophy of science [10, 15, 8,
9, 2], statistics [6, 7] and modal logic [17, 4]. In those applications, open
sets are typically interpreted as hypotheses deductively verifiable by true
propositional information that rules out relevant possibilities. However, in
statistical data analysis, one routinely receives random samples logically
compatible with every statistical hypothesis. We bridge the gap between
propositional and statistical data by solving for the unique topology on
probability measures in which the open sets are exactly the statistically
verifiable hypotheses. Furthermore, we extend that result to a topological
characterization of learnability in the limit from statistical data.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Topological Subset Space Models for Public Announcements
We reformulate a key definition given by Wang and Agotnes (2013) to provide
semantics for public announcements in subset spaces. More precisely, we
interpret the precondition for a public announcement of {\phi} to be the "local
truth" of {\phi}, semantically rendered via an interior operator. This is
closely related to the notion of {\phi} being "knowable". We argue that these
revised semantics improve on the original and offer several motivating examples
to this effect. A key insight that emerges is the crucial role of topological
structure in this setting. Finally, we provide a simple axiomatization of the
resulting logic and prove completeness.Comment: 21 pages, 2 figure