We introduce a natural deduction formulation for the Logic of Proofs, a refinement of modal logic S4 in which the assertion 2A is replaced by [[s]]A whose intended reading is “s is a proof of A”. A term calculus for this formulation yields a typed lambda calculus λ that internalises intensional information on how a term is computed. In the same way that the Logic of Proofs internalises its own ...

We present λ→2, a concise formulation of a proof term calculus for the intuitionistic modal logic S4 that is well-suited for practical applications. We show that, with respect to provability, it is equivalent to other formulations in the literature, sketch a simple type checking algorithm, and prove subject reduction and the existence of canonical forms for well-typed terms. Applications includ...

We make preliminary investigations into the model theory of DeMorgan logics, attempting to make a case for the worth of such investigations before tackling the plight of particular mathematical theorems in these logics. We demonstrate that Loś’ Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case ...

Griffin [22] pointed out that, just as the pure λ-calculus corresponds to intuitionistic logic, a λ-calculus with firstclass continuations corresponds to classical logic. We study how first-class delimited continuations [13], in the form of Danvy and Filinski’s shift and reset operators [10, 11], can also be logically interpreted. First, we refine Danvy and Filinski’s type system for shift and ...

background : there are few published studies that use real data testing to examine the performance of outbreak detection methods. the aim of this study was to determine the performance of the exponentially weighted moving average (ewma) in real time detection of a local outbreak in mashhad city, eastern iran . methods : the ewma algorithms (both ewma 1 with λ=0.3 and ewma 2 with λ=0.6) were app...

This paper presents a work whose aim is to obtain information on execution time of λ-terms by semantic means. By execution time, we mean the number of steps in a computational model. As in [Ehrhard and Regnier 2006], the computational model considered in this paper will be Krivine’s machine, a more realistic model than β-reduction. Indeed, Krivine’s machine implements (weak) head linear reducti...