Computational Logic Seminar
Speaker: Vincent Fella Hendricks University of Copenhagen
Title: Structures of Social Proof
“Social proof” means that single agents assume beliefs, norms or actions of other agents in an attempt to reflect the correct view, stance, behavior for a given situation. The structure and modularity of social proof is unravelled including formal characterizations of derived socio-informational phenomena like bystander-effects and cascades. Sometimes social proof may be responsible for information spinning out of control – in very unfortunate ways. Joint work with Rasmus K. Rendsvig.
Models of PA
Speaker: Athar Abdul-Quader CUNY Grad Center
Title: When are subsets of a model “coded”?
I will present a result by J. Schmerl that characterizes when a collection of subsets of a given model, M, will appear as the coded sets in some elementary end extension of M. This is an analogue to Scott’s theorem, which characterizes when a collection of sets of natural numbers can be the standard system of some model of PA. If there is time, I will also present some extensions of the result.
HoTT Reading Group
Speaker: Dustin Mulcahey
Title: Types, Spaces, and Higher Groupoids
Last time we discussed fibrations of sets, spaces, and types. We noted that path induction allows us to prove that the type family of equalities over a given type A is “homotopy equivalent” to A.
This week, we will continue with this and discuss the groupoid structure of spaces (paths) and types (equalities). In doing so, we will establish the “interchange law” for 2-categories, and see that in the particular case of spaces and types that this allows us to prove that the composition law is commutative (up to a higher equivalence) for 2-paths and 2-equivalences that begin and end at the same point.
We shall also discuss how non-dependent functions between types give rise to functors on the associated groupoids of equivalences. This leads to the problem of what to do for dependent functions, and it turns out that fibrations give us a solution to this, and thus we will have come full circle.
Model theory seminar
Speaker: Alice Medvedev City College — CUNY
Friday, November 22, 2013 2:00 pm GC 6417
Speaker: Tamar Lando Columbia University
Title: Measure semantics for modal logics
Long before Kripke semantics became standard in modal logic, Tarski showed us that the basic propositional modal language can be interpreted in topological spaces. In Tarski’s semantics for the modal logic $S4$, each propositional variable is evaluated to an arbitrary subset of a fixed topological space. I develop a related, measure theoretic semantics, in which modal formulas are interpreted in the Lebesgue measure algebra, or algebra of Borel subsets of the real interval $[0,1]$, modulo sets of measure zero. This semantics was introduced by Dana Scott in the last several years. I discuss some of my own completeness results, and ways of extending the semantics to more complex modal languages.
Computational Logic Seminar
Speaker: Che-Ping Su The University of Melbourne
Title: Paraconsistent Justification Logic
In the literature of belief revision, there is one approach called belief base belief revision, where the belief set is not required to be closed under a consequence relation. According to Sven Ove Hansson, in belief base belief revision, there are two ways to define the revision operator:
revision = expansion + contraction
revision = contraction + expansion
Hansson has a result that these two ways of defining the revision operator do not collapse into the same operator. Hansson also thinks that in the first way, there is an intermediate inconsistent epistemic state that occurs after expansion. Paraconsistent justification logic is intended to model the agent’s justification structure, when the agent is in such an inconsistent epi-state. My hope is that this logic could help us better model belief revision.
In my talk, the motivation will be better clarified. And, a paraconsistent justification logic system will be introduced.