Formal argumentation gives a toolkit to analyze the problem of reasoning with conflicting information. I’ll introduce the basic definitions and ideas of formal argumentation theory. In particular, I’ll discuss how various "semantics" describe different reasoning types, and how, depending on our setting, we may desire our semantics to have certain properties. Among these desirable properties are existence (that our reasoning will come to some conclusion), directionality (any set S of arguments which are not contradicted from outside S can be reasoned on independently from the arguments outside S), and weak reinstatement (slightly more than saying that we should accept as true any argument that is not contradicted at all).
SCC-recursiveness, and in particular the semantics cf2 and stg2 were developed to satisfy these criteria among others. In the setting where we reason over finitely many arguments, this yields a desirable collection of properties for the semantics, suggesting that cf2 and stg2 represent forms of reasoning with conflicting information which are suitable to address many natural real-world (automated) reasoning problems. In this talk, I’ll explore what works and what doesn’t work when applying these same ideas in the setting where we reason over infinitely many arguments. Though the topic is slightly foreign to computability-theorists, the toolkit will be familiar, including transfinite recursion, compactness, and ill-founded trees.
This work is joint with Luca San Mauro.

Computable presentations of compact spaces can behave in surprising ways: while every computable presentation of a Stone space is homeomorphic to a computably compact one, the homeomorphism itself need not be computable. Because the inverse of a computable homeomorphism is not in general computable, attempts to classify presentations of computably compact Polish spaces up to computable homeomorphism naturally yield a reducibility: Given two presentations M and N of the same space up to homeomorphism then we define M is computably-topologically reducible to N – $M \leq_{ct} N$ – if there is a computable homeomorphism $f:N \to M$. In this talk, we'll investigate the ct-degrees of various Stone spaces. No background in computable topology will be assumed. This is joint work with Noam Greenberg, Sasha Melnikov, and Dan Turetsky.

TBA

TBA

TBA

TBA

TBA

TBA