Linear logic for constructive mathematics

We show that numerous distinctive concepts of constructive mathematics arise automatically from an interpretation of "linear higher-order logic" into intuitionistic higher-order logic via a Chu construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of classical concepts using the choice between multiplicative and additive linear connectives. Linear logic thus systematically "constructivizes" classical definitions and deals automatically with the resulting bookkeeping, and could potentially be used directly as a basis for constructive mathematics in place of intuitionistic logic.Comment: 39 page

Kripke Models for Classical Logic

We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

On Constructive Axiomatic Method

In this last version of the paper one may find a critical overview of some recent philosophical literature on Axiomatic Method and Genetic Method.Comment: 25 pages, no figure

Diphoton Production at Hadron Colliders and New Contact Interactions

We explore the capability of the Tevatron and LHC to place limits on the possible existence of flavor-independent $q \bar q \gamma\gamma$ contact interactions which can lead to an excess of diphoton events with large invariant masses. Assuming no departure from the Standard Model is observed, we show that the Tevatron will eventually be able to place a lower bound of 0.5-0.6 TeV on the scale associated with this new contact interaction. At the LHC, scales as large as 3-6 TeV may be probed with suitable detector cuts and an integrated luminosity of $100 fb^{-1}$.Comment: LaTex, 12pages plus 5 figures(available on request), SLAC-PUB-657

Deduction modulo theory

This paper is a survey on Deduction modulo theor

Dualized Simple Type Theory

We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and prove type preservation. DTT is based on a new propositional bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds on Pinto and Uustalu's logic L. DIL is a simplification of L by removing several admissible inference rules while maintaining consistency and completeness. Furthermore, DIL is defined using a dualized syntax by labeling formulas and logical connectives with polarities thus reducing the number of inference rules needed to define the logic. We give a direct proof of consistency, but prove completeness by reduction to L.Comment: 47 pages, 10 figure