Compact Proof Certificates For Linear Logic

Abstract. Linear logic is increasingly being used as a tool for communicating reasoning agents in domains such as authorization, access control, electronic voting, etc., where proof certificates represent evidence that must be verified by proof consumers as part of higher protocols. Controlling the size of these certificates is critical. We assume that the proof consumer is allowed to do some search to reconstruct details of the full proof that are omitted from the certificates. Because the decision problem for linear logic is unsolvable, the certificate must contain at least enough information to bound the search: we show how to use the sequence of contractions in the sequent proof for this bound. The remaining content of the proof, in particular the information about resource divisions, can then be omitted from the certificate. We also describe a technique for giving a variable amount of additional search hints to the proof consumer to limit its non-determinism.

Mixed valence radical cations and intermolecular complexes derived from indenofluorene-extended tetrathiafulvalenes

Engineering of mixed-valence (MV) radical cations and intermolecular complexes based on pi-extended tetrathiafulvalenes (TTFs) is central for the development of organic conductors. On another front, redox-controlled dimerization of radical cations has recently been recognized as an important tool in supramolecular chemistry. Here we show that pi-extended TTFs based on the indenofluorene core, prepared by Horner-Wadsworth-Emmons reactions, undergo reversible and stepwise one-electron oxidations and that the detectable, intermediate radical cation forms remarkably strong intermolecular MV ([neutral.cation]) and pi-dimer ([cation.cation]) complexes with near-infrared radical cation absorptions. The radical cation itself seems to be a so-called Class III MV species in the Robin-Day classification. The formation of MV dimers was corroborated by ESR spectroelectrochemical studies, revealing two slightly different ESR signals upon oxidation, one assigned to the MV dimer and the other to the cation monomer. Crystals of the radical cation with different anions (PF6- , BF4-, and TaF6-) were grown by electrocrystallization. Conductance studies revealed that the salts behave as semiconductors with the hexafluorotantalate salt exhibiting the highest conductance. Using a custom-built ESR spectrometer with sub-femtomole sensitivity, the magnetic properties of one crystal were investigated. While the spin-to-spin interaction between radical cations was negligible, a high cooperativity coupling to the microwave field was observed - as a result of an exceptionally narrow spin line width and high spin density. This could have great potential for applications in quantum computation where crystalline spin ensembles are exploited for their long coherence times

A forward unprovability calculus for intuitionistic propositional logic

The inverse method is a saturation based theorem proving technique; it relies on a forward proof-search strategy and can be applied to cut-free calculi enjoying the subformula property. This method has been successfully applied to a variety of logics. Here we apply this method to derive the unprovability of a goal formula G in Intuitionistic Propositional Logic. To this aim we design a forward calculus FRJ(G) for Intuitionistic unprovability. From a derivation of G in FRJ(G) we can extract a Kripke countermodel for G. Since in forward methods sequents are not duplicated, the generated countermodels do not contain redundant worlds and are in general very concise

Correction: Determination of the electronic structure of a dinuclear dysprosium single molecule magnet without symmetry idealization (Chemical Science (2019) 10 (2101–2110) DOI: 10.1039/C8SC03170C)

10.1039/C9SC90051AChemical Science10113429

Determination of the electronic structure of a dinuclear dysprosium single molecule magnet without symmetry idealization

10.1039/C8SC03170CChemical Science1072101-211