The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete ...
We consider an extension of bi-intuitionistic logic with the traditional modalities , , and from tense logic Kt. Proof theoretically, this extension is obtained simply by extendin...
We give a simple intuitionistic completeness proof of Kripke semantics with constant domain for intuitionistic logic with implication and universal quantification. We use a cut-fr...
A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andre...
In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic BK c4 , which is adequate to this sense of consis...