Hilbert-Post completeness for the state and the exception effects

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the "core" language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.Comment: Siegfried Rump (Hamburg University of Technology), Chee Yap (Courant Institute, NYU). Sixth International Conference on Mathematical Aspects of Computer and Information Sciences , Nov 2015, Berlin, Germany. 2015, LNC

Categoricity and Negation. A Note on Kripke’s Affirmativism

We argue that, if taken seriously, Kripke's view that a language for science can dispense with a negation operator is to be rejected. Part of the argument is a proof that positive logic, i.e., classical propositional logic without negation, is not categorical