Calendar

Mar
28
Tue
Colloquium – Hao Wang (Alberta) @ Keller 301
Mar 28 @ 3:30 pm – 4:30 pm
Mar
29
Wed
Colloquium – Thorsten Heidersdorf (Bonn) @ Keller 302
Mar 29 @ 3:30 pm – 4:30 pm
Apr
3
Mon
grad student seminar @ keller 401
Apr 3 @ 1:00 pm – Apr 3 @ 2:00 pm
Logic Seminar: Marija B. Boričić Joksimović
Apr 3 @ 2:30 pm – 3:30 pm

Location: KELLER 313


Title: SEQUENT CALCULUS FOR CLASSICAL LOGIC PROBABILIZED

Abstract: Gentzen’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas that appeared in logic of the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized in the sequent calculus, we introduce the notion of ‘probabilized sequent’ $\Gamma\vdash_a^b\Delta$ with the intended meaning that “the probability of truthfulness of $\Gamma\vdash\Delta$ belongs to the interval $[a,b]$”. This method makes it possible to define a system of derivations based on ‘axioms’ of the form $\Gamma_i\vdash_{a_i}^{b_i}\Delta_i$, obtained as a result of empirical research, and then infer conclusions of the form $\Gamma\vdash_a^b\Delta$. We discuss the consistency, define the models, and prove the soundness and completeness for the defined
probabilized sequent calculus.

differential geometry seminar @ keller 313
Apr 3 @ 3:30 pm – 4:30 pm
Apr
4
Tue
Colloquium – Daniel Erman (Wisconsin-Madison) @ Keller 303
Apr 4 @ 3:30 pm – 4:30 pm
Apr
6
Thu
Prateek Kunwar PhD defense
Apr 6 @ 2:30 pm – 4:30 pm
Apr
14
Fri
Colloquium – Igor Pak (UCLA) @ Keller 302
Apr 14 @ 3:30 pm – 4:30 pm