David Etlin氏 (The University of Groningen)
岸田功平氏 (University of Amsterdam)
Vague Desire: the Sorites and the Money Pump (David Etlin)
Topological Semantics for the Logic of Verifiability and Falsifiability (岸田功平)
Topological Semantics for the Logic of Verifiability and Falsifiability
(Kohei Kishida, Institute for Logic, Language and Computation, University of Amsterdam)
This talk introduces the notion of observability into the setting of
neighborhood semantics for modal logic, so that the box and diamond
operators signify the verifiability and falsifiability of propositions.
We also lay out a set of assumptions on observability from which we can
“deduce” topological semantics. This result provides a semantic
justification for system S4 of epistemic logic (as oppsed to the
conventional, axiomatic justification that the so-called positive
introspection axiom is an intuitively plausible principle of knowledge).
More importantly, the resulting interpretation of topology agrees with
ones found in computer science, and most notably in formal learning
theory (e.g., Kevin Kelly, The Logic of Reliable Inquiry (1996); another
notable one is in point-free topology, e.g., Steven Vickers, Topology
via Logic (1989)). Hence our topological semantics and epistemic
interpretation can provide a basis for modal logic of other notions in
learning theory (whereas Kripke semantics cannot, since it cannot
properly accommodate the notion of observability).