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...
We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic ru...
—We design an intuitionistic predicate logic that supports a limited amount of classical reasoning, just enough to prove a variant of Markov’s principle suited for predicate lo...
We show that IPC, K4, GL, and S4, as well as all logics inheriting their admissible rules, have independent bases of admissible rules. Key words: admissible rule, independent basi...
We give an exponential lower bound on number of proof-lines in intuitionistic propositional logic, IL, axiomatised in the usual Frege-style fashion; i.e., we give an example of IL...