Fixed-point elimination in the intuitionistic propositional calculus

It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the IPC. Consequently, the $\mu$-calculus based on intuitionistic logic is trivial, every $\mu$-formula being equivalent to a fixed-point free formula. We give in this paper an axiomatization of least and greatest fixed-points of formulas, and an algorithm to compute a fixed-point free formula equivalent to a given $\mu$-formula. The axiomatization of the greatest fixed-point is simple. The axiomatization of the least fixed-point is more complex, in particular every monotone formula converges to its least fixed-point by Kleene's iteration in a finite number of steps, but there is no uniform upper bound on the number of iterations. We extract, out of the algorithm, upper bounds for such n, depending on the size of the formula. For some formulas, we show that these upper bounds are polynomial and optimal

Molecular dynamics simulation of aqueous solutions of 26-unit segments of p(NIPAAm) and of p(NIPAAm) "doped" with amino acid based comonomers

We have performed 75-ns molecular dynamics (MD) simulations of aqueous solutions of a 26-unit NIPAAm oligomer at two temperatures, 302 and 315 K, below and above the experimentally determined lower critical solution temperature (LCST) of p(NIPAAm). We have been able to show that at 315 K the oligomer assumes a compact form, while it keeps a more extended form at 302 K. A similar behavior has been demonstrated for a similar NIPAAm oligomer, where two units had been substituted by methacryloyl-l-valine (MAVA) comonomers, one of them being charged and one neutral. For another analogous oligomer, where the same units had been substituted by methacryloyl-l-leucine (MALEU) comonomers, no transition from the extended to the more compact conformation has been found within the same simulation time. Statistical analysis of the trajectories indicates that this transition is related to the dynamics of the oligomer backbone, and to the formation of intramolecular hydrogen bonds and water-bridges between distant units of the solute. In the MAVA case, we have also evidenced an important role of the neutral MAVA comonomer in stabilizing the compact coiled structure. In the MALEU case, the corresponding comonomer is not equally efficacious and, possibly, is even hindering the readjustment of the oligomer backbone. Finally the self-diffusion coefficient of water molecules surrounding the oligomers at the two temperatures for selected relevant times is observed to characteristically depend on the distance from the solute molecules

How to assess appearance distress and motivation in plastic surgery candidates: Italian validation of Derriford Appearance Scale 59 (DAS 59)

The Derriford Appearance Scale (DAS) 59 was specifically designed to measure psychosocial adjustment in patients with appearance problems. Previous studies using the DAS59 have proven it to be a reliable method of assessing the appearance-related quality of life after plastic surgery procedures. The aim of this study was to develop a valid and reliable Italian version of the DAS59

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

Administration of a tropomyosin receptor kinase inhibitor attenuates sarcoma-induced nerve sprouting, neuroma formation and bone cancer pain

Pain often accompanies cancer and most current therapies for treating cancer pain have significant unwanted side effects. Targeting nerve growth factor (NGF) or its cognate receptor tropomyosin receptor kinase A (TrkA) has become an attractive target for attenuating chronic pain

Admissible Bases Via Stable Canonical Rules

We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics

In vitro antileishmanial and antitrypanosomal activities of flavanones from Baccharis retusa DC. (Asteraceae)

Leishmaniasis and Chagas' are parasitic protozoan diseases that affect the poorest population in the world, causing a high mortality and morbidity. As a result of highly toxic and long-term treatments, novel, safe and more efficacious drugs are essential. in this work, the CH2Cl2 phase from MeOH extract from the leaves of Baccharis retusa DC. (Asteraceae) was fractioned to afford two flavonoids: naringenin (1) and sakuranetin (2). These compounds were in vitro tested against Leishmania spp. promastigotes and amastigotes and Ttypanosoma cruzi trypomastigotes and amastigotes. Compound 2 presented activity against Leishmania (L) amazonensis, Leishmania (V.) braziliensis, Leishmania (L) major, and Leishmania (L) chagasi with IC50 values in the range between 43 and 52 mu g/mL and against T. cruzi trypomastigotes (IC50= 20.17 mu g/mL). Despite of the chemical similarity, compound 1 did not show antiparasitic activity. Additionally, compound 2 was subjected to a methylation procedure to give sakuranetin-4'-methyl ether (3), which resulted in an inactive compound against both Leishmania spp. and T. cnizi. the obtained results indicated that the presence of one hydroxyl group at C-4' associated to one methoxyl group at C-7 is important to the antiparasitic activity. Further drug design studies aiming derivatives could be a promising tool for the development of new therapeutic agents for Leishmaniasis and Chagas' disease. (C) 2011 Elsevier Inc. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Pesquisa e DesenvolvimentoUniversidade Federal de São Paulo, Inst Ciencias Ambientais Quim & Farmaceut, Diadema, SP, BrazilInst Adolfo Lutz Registro, Dept Parasitol, São Paulo, BrazilUniv Fed ABC, Ctr Ciencias Nat & Humanas, Santo Andre, SP, BrazilUniv Presbiteriana Mackenzie, Ctr Ciencias & Humanidades, São Paulo, BrazilUniversidade Federal de São Paulo, Inst Ciencias Ambientais Quim & Farmaceut, Diadema, SP, BrazilFAPESP: 06/57626-5FAPESP: 08/11496-9Conselho Nacional de Pesquisa e Desenvolvimento: 473405/2008-3Conselho Nacional de Pesquisa e Desenvolvimento: 477422/2009-8Web of Scienc

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page