An intuitionistic formula hierarchy based on high‐school identities

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e., sequent) isomorphisms corresponding to the high‐school identities, we show that one can obtain a more compact variant of a proof system, consisting of non‐invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalization procedure. Moreover, for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non‐invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first‐order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism.     

Chemical toxicology searching: a comparative study of online data-bases

A collaborative project to compare and evaluate information resources and searching techniques for the retrieval of chemical toxicology information has been carried out by 14 organizations. The project involved independent searching of test queries, with subsequent extensive evaluation of results and failure analysis. The results relating particularly to online searching are presented and discussed.     

Analysis of the 33-133-133-1final state in photon-photon collisions

The reactione ⁺ e ^- e ⁺ e ^{- 00}e ⁺ e ^- 6 has been analysed using the full data sample taken with the Crystal Ball detector at the DORIS II storage ring at DESY. The ⁰⁰ invariant mass spectrum is dominated by the ', for which we determine the radiative width (') to be (4.5±0.3±0.5)keV. Near 1.9 GeV/c² we observe a second enhancement in the ⁰⁰ mass distribution. Assuming that these events are created by the production and subsequent decay of a wide resonanceX(1900), we have investigated the decay modes, the invariant mass distributions of the ⁰ and ⁰⁰ subsystems and the angular distributions of the final state mesons. We find that the data is best described byJ ^PC=2. For thisJ ^P assignment the resonance parameters are (X) BR(X)=(0.95±0.27±0.20) keV _tot (X)=(221±92±44)MeV, andM(X)=(1881±32±40) MeV/c².Deceased