The deduction theorem for strong propositional proof systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs

The Deduction Theorem for Strong Propositional Proof Systems

This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NPUnknown control sequence '\mathsf' -pairs. In particular, this yields a sufficient condition for the completeness of the canonical pair of Frege systems and provides a general framework for the search for complete NPUnknown control sequence '\mathsf' -pairs

Natural intensions

There is an attractive way to explain representation in terms of adaptivity: roughly, an item R represents a state of affairs S if it has the proper function of co-occurring with S (that is, if the ancestors of R co-occurred with S and this co-occurrence explains why R was selected for, and thus why R exists now). Although this may be an adequate account of the extension or reference of R, what such explanations often neglect is an account of the intension or sense of R: how S is represented by R. No doubt such an account, if correct, would be complex, involving such things as the proper functions of the mechanisms that use R, the mechanisms by which R fulfills its function, and more. But it seems likely that an important step toward such an account would be the identification of the norms that govern this process. The norms of validity and Bayes' Theorem can guide investigations into the actual inferences and probabilistic reasoning that organisms perform. Is there a norm that can do the same for intension-fixing? I argue that before this can be resolved, some problems with the biosemantic account of extension must be resolved. I attempt to do so by offering a complexity-based account of the natural extension of a representation R: for a given set of ancestral co-occurrences Z, the natural extension is the extension of the least complex intension that best covers Z. Minimal description length is considered as a means for measuring complexity. Some advantages of and problems with the account are identified

Mutations in PNKD causing paroxysmal dyskinesia alters protein cleavage and stability.

Paroxysmal non-kinesigenic dyskinesia (PNKD) is a rare autosomal dominant movement disorder triggered by stress, fatigue or consumption of either alcohol or caffeine. Attacks last 1-4 h and consist of dramatic dystonia and choreoathetosis in the limbs, trunk and face. The disease is associated with single amino acid changes (A7V or A9V) in PNKD, a protein of unknown function. Here we studied the stability, cellular localization and enzymatic activity of the PNKD protein in cultured cells and transgenic animals. The N-terminus of the wild-type (WT) long PNKD isoform (PNKD-L) undergoes a cleavage event in vitro, resistance to which is conferred by disease-associated mutations. Mutant PNKD-L protein is degraded faster than the WT protein. These results suggest that the disease mutations underlying PNKD may disrupt protein processing in vivo, a hypothesis supported by our observation of decreased cortical Pnkd-L levels in mutant transgenic mice. Pnkd is homologous to a superfamily of enzymes with conserved β-lactamase domains. It shares highest homology with glyoxalase II but does not catalyze the same reaction. Lower glutathione levels were found in cortex lysates from Pnkd knockout mice versus WT littermates. Taken together, our results suggest an important role for the Pnkd protein in maintaining cellular redox status