A new coalgebraic semantics for positive modal logic

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of Abstract Algebraic Logic. Celani and Jansana established a Priestley-style duality the category of positive modal algebras and the category of K+-spaces. In this paper, we establish a categorical equivalence between the category K+ of K+-spaces and the category Coalg(V) of coalgebras of a suitable endofunctor V on the category of Priestley spaces

Finitely generated free Heyting algebras via Birkhoff duality and coalgebra

Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and thus the free algebras can be obtained by a direct limit process. Dually, the final coalgebras can be obtained by an inverse limit process. In order to explore the limits of this method we look at Heyting algebras which have mixed rank 0-1 axiomatizations. We will see that Heyting algebras are special in that they are almost rank 1 axiomatized and can be handled by a slight variant of the rank 1 coalgebraic methods

Lipopolysaccharide from Gut-Associated Lymphoid-Tissue-Resident Alcaligenes faecalis: Complete Structure Determination and Chemical Synthesis of Its Lipid A

Alcaligenes faecalis is the predominant Gram-negative bacterium inhabiting gut-associated lymphoid tissues, Peyer's patches. We previously reported that an A. faecalis lipopolysaccharide (LPS) acted as a weak agonist for Toll-like receptor 4 (TLR4)/myeloid differentiation factor-2 (MD-2) receptor as well as a potent inducer of IgA without excessive inflammation, thus suggesting that A. faecalis LPS might be used as a safe adjuvant. In this study, we characterized the structure of both the lipooligosaccharide (LOS) and LPS from A. faecalis. We synthesized three lipid A molecules with different degrees of acylation by an efficient route involving the simultaneous introduction of 1- and 4′-phosphates. Hexaacylated A. faecalis lipid A showed moderate agonistic activity towards TLR4-mediated signaling and the ability to elicit a discrete interleukin-6 release in human cell lines and mice. It was thus found to be the active principle of the LOS/LPS and a promising vaccine adjuvant candidate