Restricted Positive Quantification Is Not Elementary

We show that a restricted variant of constructive predicate logic with positive (covariant) quantification is of super-elementary complexity. The restriction is to limit the number of eigenvariables used in quantifier introductions rules to a reasonably usable level. This construction suggests that the known non-elementary decision algorithms for positive logic may actually be best possible

Enumerating proofs of positive formulae

We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This method is complete in the sense that each normal proof-term of the formula is produced by some scheme generated by the grammar. As a corollary, we get a similar description of the set of normal proofs of positive formulae for a large class of theories including simple type theory and System F

Proof search in multi-succedent sequent calculi for intuitionistic logics (Theory and Applications of Proof and Computation)

In this note, terminating and bicomplete proof search procedures with respect to the Kripke semantics are given in multi-succedent sequent calculi for intuitionistic propositional logic and fragments of intuitionistic predicate logic. G. Mints [11, 12] in his later years investigated a proof search procedure in single-succedent sequent calculus for intuitionistic predicate logic

The Audit Logic: Policy Compliance in Distributed Systems

We present a distributed framework where agents can share data along with usage policies. We use an expressive policy language including conditions, obligations and delegation. Our framework also supports the possibility to refine policies. Policies are not enforced a-priori. Instead policy compliance is checked using an a-posteriri auditing approach. Policy compliance is shown by a (logical) proof that the authority can systematically check for validity. Tools for automatically checking and generating proofs are also part of the framework.\u