ion of variables A useful combinator: • linear identity: I ≡ S(1)K[ ] satisfies Ix̄ = { x0 if |x̄| = 1 0 otherwise Abstraction on monomials (i) λ∗x.t ≡ Kt if degx(t) = 0 (ii) λ∗x.x ≡ Iion on monomials (i) λ∗x.t ≡ Kt if degx(t) = 0 (ii) λ∗x.x ≡ I (iii) λ∗x.t0[t1, . . . , tk] ≡ Sn̄[λ∗x.t0][λ∗x.t1, . . . , λx.tk] with n̄ = (degx(t0), . . . , degx(tk)) and ∃i. degx(ti) 6= 0. (iv) ... and on polynomials...

This paper presents an online tuning strategy for model predictive control. Specifically, the tuning strategy adjusts automatically the prediction horizon, P, the diagonal elements of the input weight matrix, Λ, and the diagonal elements of the output weight matrix, Γ. The control horizon is left constant because its relative value with respect to P is more important. The MPC parameters are adj...

We show various (syntactic and behavioral) properties of random λ-terms. Our main results are that at least 3/4 of the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators) the result is different. We show that almost all terms are not strongly normalizing, beca...

In the folklore of linear logic, a common intuition is that the structure of finiteness spaces, introduced by Ehrhard, semantically reflects the strong normalization property of cut-elimination. We make this intuition formal in the context of the non-deterministic λ-calculus by introducing a finiteness structure on resource terms, which is such that a λ-term is strongly normalizing iff the supp...

Hereditary substitution is a form of type-bounded iterated substitution, first made explicit by Watkins et al. and Adams in order to show normalization of proof terms for various constructive logics. This paper is the first to apply hereditary substitution to show normalization of a type theory corresponding to a non-constructive logic, namely the λ∆-calculus as formulated by Rehof. We show tha...

Fuzzy logic is a soft computing technique that has been very successful in recent years when it is used as a complement to improve meta-heuristic optimization. In this paper, we present a new variant of the bio-inspired optimization algorithm based on the self-defense mechanisms of plants in the nature. The optimization algorithm proposed in this work is based on the predator-prey model origina...

Hereditary substitution is a form of type-bounded iterated substitution, first made explicit by Watkins et al. and Adams in order to show normalization of proof terms for various constructive logics. This paper is the first to apply hereditary substitution to show normalization of a type theory corresponding to a non-constructive logic, namely the λ ∆-calculus as formulated by Rehof. We show th...

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban’s work on classical sequent calculus. However the compu...