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This paper consists of a brief overview of the study of admissible rules.
In this paper we study the admissible rules of intermediate logics with the disjunction property. We establish some general results on extension of models and sets of formulas, and eventually specialize to provide a a basis for the admissible rules of the Gabbay-de Jongh logics and to show that that
This paper contains a proof theoretic treatment of some aspects of unification in intermediate logics. It is shown that many existing results can be extended to fragments that at least contain implication and conjunction. For such fragments the connection between valuations and most general unifiers
This paper contains a proof-theoretic account of unification in (fragments of) transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible. New proofs of theorems on unification types are given and these results are extended to fragments. I
In 2009 werd mij door de Nederlandse Wetenschaps Organisatie een Vidi beurs toegekend voor het project “The power of constructive proofs”. Het project is wiskundig van aard en valt binnen het NWO gebiedsbestuur Exacte Wetenschappen. Op uitnodiging van het ANTW heb ik een artikel geschreven dat gaat
In this paper a method to construct Kripke models for subtheories of constructive set theory is introduced that uses constructions from classical model theory such as constructible sets and generic extensions. Under the main construction all axioms except the collection axioms can be shown to hold i
This paper is a sequel to the papers [4,6] in which an alternative skolemization method called ekolemization was introduced that, when applied to the strong existential quantifiers in a formula, is sound and complete for constructive theories. Based on that method an analogue of Herbrand’s theorem w
In [2] an alternative skolemization method called eskolemization was introduced that is sound and complete for existence logic with respect to existential quantifiers. Existence logic is a conservative extension of intuitionistic logic by an existence predicate. Therefore eskolemization provides a s
Admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In this paper, a Gentzen-style framework is introduced for analytic proof systems that derive admissible rules of non-classical logics. While Gentzen systems for derivability treat sequents as basic o
The admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In a previous paper by the authors, formal systems for deriving the admissible rules of Intuitionistic Logic and a class of modal logics were defined in a proof-theoretic framework where the basic
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