LIRa session (online only): Dominik Klein

Speaker: Dominik Klein

Date and Time: Thursday, September 17th 2020, 16:30-18:30, Amsterdam time.

Venue: online.

Title: Four-Valued Probabilities

Abstract.

First degree entailment (fde) is a four valued propositional logic that complements the classical truth values True and False with two non-classical truth values Neither and Both. The latter two account for the possibility of the available information being incomplete or containing contradictory evidence about some proposition. In this talk, we present a probabilistic extension of fde, i.e. we allow agents to have probabilistic beliefs about the truth and falsity of a
proposition.

More specifically, we present two probabilistic versions of fde, one related to the bi-relational, the other to the four-valued semantics of first degree entailment. We provide sound and complete axiomatizations for both and identify a translation function between the two frameworks. Moreover, we identify policies for conditionalization and aggregation on the probability functions defined. More specifically, we analyze four-valued equivalents of Bayes’ and Jeffrey updating and also provide policies for aggregating information from different sources. This is joint work with Soroush Rafiee Rad and Ondrej Majer.

.