The i.-calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with I-terms. However, if one goes further and uses bn-conversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with total functions from calues to values) that may jeopardise the applicability of theoretical results, In this paper we introduce calculi. based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.

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 skolemization method for intuitionistic logic as well. All proofs in [2] were semantical. In this paper a proof-theoretic proof of the completeness of eskolemization with respect to existential quantifiers is presented. Keywords: Skolemization, eskolemization, orderization, Herbrand’s theorem, intuitionistic logic, existence logic, Gentzen calculi.

Access control is a crucial concern to build secure IT systems and, more specifically, to protect the confidentiality of information. However, access control is necessary, but not sufficient. Actually, IT systems can manipulate data to provide services to users. The results of a data processing may disclose information concerning the objects used in the data processing itself. Therefore, the control of information flow results fundamental to guarantee data protection. In the last years many information flow control models have been proposed. However, these frameworks mainly focus on the detection and prevention of improper information leaks and do not provide support for the dynamical creation of new objects. In this

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 was proved to hold as well. In this paper we extend the method to universal quantifiers and show that for theories satisfying the witness property the method is sound and complete for all formulas. We prove a Herbrand theorem and, as an example, apply the method to several constructive theories. We show that for the theories with a decidable quantifier-free fragment, also the strong existential quantifier fragment is decidable. Keywords: Skolemization, eskolemization, Herbrand’s theorem, constructive theories, intuitionistic logic, decidability.