From IF to BI: a tale of dependence and separation

We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Vaananen, and their compositional semantics due to Hodges. We show how Hodges' semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O'Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural role, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural r\^ole.Comment: 28 pages, journal versio

AN EXTENSION OF A THEOREM OF ZERMELO

We show that if (M, is an element of(1), is an element of(2)) satisfies the first-order Zermelo-Fraenkel axioms of set theory when the membership relation is is an element of(1) and also when the membership relation is is an element of(2), and in both cases the formulas are allowed to contain both is an element of(1) and is an element of(2), then (M, is an element of(1)) congruent to (M, is an element of(2)), and the isomorphism is definable in (M, is an element of(1 ),( )is an element of(2)). This extends Zermelo's 1930 theorem in [6].Peer reviewe

Diversity, dependence and independence

We propose a very general, unifying framework for the concepts of dependence and independence. For this purpose, we introduce the notion of diversity rank. By means of this diversity rank we identify total determination with the inability to create more diversity, and independence with the presence of maximum diversity. We show that our theory of dependence and independence covers a variety of dependence concepts, for example the seemingly unrelated concepts of linear dependence in algebra and dependence of variables in logic.Peer reviewe

Inhibition of GGTase-I and FTase disrupts cytoskeletal organization of human PC-3 prostate cancer cells

The mevalonate synthesis pathway produces intermediates for isoprenylation of small GTPases, which are involved in the regulation of actin cytoskeleton and cell motility. Here, we investigated the role of the prenylation transferases in the regulation of the cytoskeletal organization and motility of PC-3 prostate cancer cells. This was done by using FTI-277, GGTI-298 or NE-10790, the specific inhibitors of FTase (farnesyltransferase), GGTase (geranylgeranyltransferase)-I and -II, respectively. Treatment of PC-3 cells with GGTI-298 and FTI-277 inhibited migration and invasion in a time- and dose-dependent manner. This was associated with disruption of F-actin organization and decreased recovery of GFP-actin. Immunoblot analysis of various cytoskeleton-associated proteins showed that the most striking change in GGTI-298- and FTI-277-treated cells was a markedly decreased level of total and phosphorylated cofilin, whereas the level of cofilin mRNA was not decreased. The treatment of PC-3 cells with GGTI-298 also affected the dynamics of GFP-paxillin and decreased the levels of total and phosphorylated paxillin. The levels of phosphorylated FAK (focal adhesion kinase) and PAK (p-21-associated kinase)-2 were also lowered by GGTI-298, but levels of paxillin or FAK mRNAs were not affected. In addition, GGTI-298 had a minor effect on the activity of MMP-9. RNAi knockdown of GGTase-I beta inhibited invasion, disrupted F-actin organization and decreased the level of cofilin in PC-3 cells. NE-10790 did not have any effect on PC-3 prostate cancer cell motility or on the organization of the cytoskeleton. In conclusion, our results demonstrate the involvement of GGTase-I- and FTase-catalysed prenylation reactions in the regulation of cytoskeletal integrity and motility of prostate cancer cells and suggest them as interesting drug targets for development of inhibitors of prostate cancer metastasis