Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive ZermeloFraenkel Set Theory...
Set theories are traditionally based on first-order logic. We show that in a constructive setting, basing a set theory on a dependent logic yields many benefits. To this end, we...
This paper describes our methodology for building conformant planners, which is based on recent advances in the theory of action and change and answer set programming. The develop...
Phan Huy Tu, Tran Cao Son, Michael Gelfond, A. Ric...
We logically model uncertainty by expanding language without changing logical reasoning rules. We expand the language of set theory by adding new predicate symbols, uncertain membe...
We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our ...
Steven Awodey, Carsten Butz, Alex Simpson, Thomas ...