On Thursday, March 15, there will be a special session of the LIRa seminar in Tilburg with three talks, starting at 2 p.m.. The program is below.
The special session will take place in the Dante building, room DZ 8, at Tilburg University. A map is here.
Program:
14:15-15:00 Sara Uckelman (Tilburg): Paul of Venice on a Puzzle About Uncertainty
15:15-16:00 Reinhard Muskens (Tilburg): A Non-extensional and Partial Type Logic
16:15-17:00 Dominik Klein (Tilburg): Languages to reason about knowledge: Types, Levels…
17:15-18:00 Drinks
Abstracts:
Sara Uckelman: Paul of Venice on a Puzzle About Uncertainty
In this talk I will report on work-on-progress looking at a late 14th C puzzle about uncertainty, “whether something known by someone is uncertain to him or not known to him”, discussed by Paul of Venice in the treatise \emph{De scire et dubitare} (‘On knowing and being uncertain’). We consider one of the arguments in favor of this position that Paul presents, and Paul’s objections to the argument. Understanding both the argument and the reply requires unpacking quite a bit of interesting information about medieval epistemology and medieval epistemic logic, some of which is eerily similar to its medieval counterparts, and some of which is radically different.
Reinhard Muskens: A Non-extensional and Partial Type Logic
In this talk I will report on ongoing work on a version of type theory that is not only based on Belnap’s four values, but is also truly intensional in the sense that the Axiom of Extensionality fails. The logic is a generalisation of the four-valued higher order logic I used in Muskens (1995) to model a version of Situation Semantics, but it comes with an analytic Gentzen Calculus in which each proof in general consists of two proof trees (as in Wintein & Muskens 2012).
Dominik Klein: Languages to reason about knowledge: Types, Levels…
There are different languages to model epistemic situations: epistemic logic usually thinks in Kripke models whereas a classical tool in epistemic game theory are Harsanyi type spaces. The difference between those two can roughly be described as a 3rd vs 1st person’s perspective on the situation. In this talk, I present a third option: Levels of knowledge as a proposition based method of presenting an epistemic situation. Surpsisingly, Parikh, Krasucki and Pacuit have shown that there are strictly more levels of belief than levels of knowledge. I will elaborate on this result and give a fine grained analysis of levels of knowledge.