Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Regulation of mucin gene expression by CREB via a nonclassical retinoic acid signaling pathway.

Vitamin A and its metabolite retinoic acid (RA) are essential elements for normal lung development and the differentiation of lung epithelial cells. We previously showed that RA rapidly activated cyclic AMP response element-binding protein (CREB) in a nonclassical manner in normal human tracheobronchial epithelial (NHTBE) cells. In the present study, we further demonstrated that this nonclassical signaling of RA on the activation of CREB plays a critical role in regulating the expression of airway epithelial cell differentiation markers, the MUC2, MUC5AC, and MUC5B genes. We found that RA rapidly activates the protein kinase Calpha isozyme and transmits the activation signal to CREB via the Raf/MEK/extracellular signal-regulated kinase/p90 ribosomal S6 kinase (RSK) pathway. Activated RSK translocated from the cytoplasm to the nucleus, where it phosphorylates CREB. Activated CREB then binds to a cis-acting replication element motif on the promoter (at nucleotides [nt] -878 to -871) of the MUC5AC gene. The depletion of CREB using small interfering RNA abolished not only the RA-induced MUC5AC but also RA-induced MUC2 and MUC5B. Taken together, our findings demonstrate that CREB activation via this nonclassical RA signaling pathway may play an important role in regulating the expression of mucin genes and mediating the early biological effects of RA during normal mucous differentiation in NHTBE cells.

Nonclassical mechanisms of progesterone action in the brain: I. Protein kinase C activation in the hypothalamus of female rats.

The modulation of gene regulation by progesterone (P) and its classical intracellular regulation by progestin receptors in the brain, resulting in alterations in physiology and behavior has been well studied. The mechanisms mediating the short latency effects of P are less well understood. Recent studies have revealed rapid nonclassical signaling action of P involving the activation of intracellular signaling pathways. We explored the involvement of protein kinase C (PKC) in P-induced rapid signaling in the ventromedial nucleus of the hypothalamus (VMN) and preoptic area (POA) of the rat brain. Both the Ca2+-independent (basal) PKC activity representing the activation of PKC by the in vivo treatments and the Ca+2-dependent (total) PKC activity assayed in the presence of exogenous cofactors in vitro were determined. A comparison of the two activities demonstrated the strength and temporal status of PKC regulation by steroid hormones in vivo. P treatment resulted in a rapid increase in basal PKC activity in the VMN but not the POA. Estradiol benzoate priming augmented P-initiated increase in PKC basal activity in both the VMN and POA. These increases were inhibited by intracerebroventricular administration of a PKC inhibitor administered 30 min prior to P. The total PKC activity remained unchanged demonstrating maximal PKC activation within 30 min in the VMN. In contrast, P regulation in the POA significantly attenuated total PKC activity +/- estradiol benzoate priming. These rapid changes in P-initiated PKC activity were not due to changes in PKC protein levels or phosphorylation status.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

First steps towards probabilistic justification logic

In this article, we introduce the probabilistic justification logic PJ, a logic in which we can reason about the probability of justification statements. We present its syntax and semantics, and establish a strong completeness theorem. Moreover, we investigate the relationship between PJ and the logic of uncertain justifications.