Speaker: 
Alexandru Baltag

Title: 
From Probability to Knowledge: a Bayesian semantics for epistemic logic

Abstract: 
I present a qualitative epistemic framework, based on a Bayesian version of the so-called ``defeasibility theory of knowledge". A proposition P is undefeated belief iff its subjective probability stays high  (above a fixed threshold) whenever any true relevant information is learnt. Undefeated true belief is not (positively) introspective, nor conjunctive (both P and Q can be undefeated without their conjunction being so). However, there is a “reflexive” version of this notion, that seems apt as a formalisation of “conscious knowledge”, and is given by a circular definition: P is known iff both P and the fact that P is known are undefeated true belief. The resulting conception fits well with the latest developments in Bayesianism, and in particular with Leitgeb's “stability theory of belief”, while avoiding some of the latter's weaknesses. The stress on the ``relevant" information makes the theory more flexible and less stringent than both the original defeasibility theory and Leitgeb's conception. This approach fits the tenets of epistemic logic (satisfying the axioms of the modal system S4.3), and is applicable to statistical learning. Indeed, ``knowledge" of the true answer to an empirical inductive problem can be achieved after finitely many observations, whenever the Strong Law of Large Numbers is applicable.