On the Solvability of Inductive Problems: A Study in Epistemic Topology
Alexandru Baltag (Institute for logic, Language, Computation., University of Amsterdam), Nina Gierasimczuk (Institute for Logic, Language, and Computation. University of Amsterdam), Sonja Smets (Institute for Logic,, Language, Computation. University of Amsterdam)
TL;DR
This paper explores the conditions under which inductive problems can be solved and learned by doxastic agents, using topological methods to characterize solvability and demonstrating the universality of AGM belief revision for solvable problems.
Contribution
It introduces topological characterizations of inductive problem solvability and proves that AGM belief revision can solve all solvable problems, establishing a universal framework.
Findings
Topological criteria for inductive problem solvability
AGM belief revision is universal for solvable problems
Characterization of learnability in epistemic topology
Abstract
We investigate the issues of inductive problem-solving and learning by doxastic agents. We provide topological characterizations of solvability and learnability, and we use them to prove that AGM-style belief revision is "universal", i.e., that every solvable problem is solvable by AGM conditioning.
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