Month: February 2017

Computable reducibility and the Baire hierarchy of functions

Linda Brown Westrick

Various notions of computable reducibility, such as Turing reduction, truth table reduction, and many-one reduction, provide coarse- and fine-grained ways of saying that one infinite sequence can compute another one. Infinite sequences have discrete bits with discrete addresses, so what it means to “compute” one is clear: given an address as input, an algorithm should return the appropriate bit. What it means to “compute” a continuous function is less obvious, but also well established. However, for a larger class of functions (in particular those of the Baire hierarchy, which I will define) it is not at all clear what it means to compute one. I will present one possibility and describe its degree structure and how this structure relates to features of the Baire hierarchy. This is joint work with Adam Day and Rod Downey.

Modality and Classical Logic

Melissa Fusco

My favored joint solution to the Puzzle of Free Choice Permission (Kamp 1973) and Ross’s Paradox (Ross 1941) involves (i) giving up the duality of natural language deontic modals, and (ii) moving to a two-dimensional propositional logic which has a classical Boolean character only as a special case. In this talk, I’d like to highlight two features of this radical view: first, the extent to which Boolean disjunction is imperiled by other natural language phenomena not involving disjunction, and second, the strength of the general position that natural language semantics must treat deontic, epistemic, and circumstantial modals alike.