Approximations of modal logics: K and beyond

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modal n-logics. The semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics K, T, D, S4 and S5. (c) 2008 Published by Elsevier B.V.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Thermo-solvatochromism of merocyanine polarity probes - What are the consequences of increasing probe lipophilicity through annelation?

The question raised in the title has been answered by comparing the solvatochromism of two series of polarity probes, the lipophilicities of which were increased either by increasing the length of an alkyl group (R) attached to a fixed pyridine-based structure or through annelation (i.e., by fusing benzene rings onto a central pyridine-based structure). The following novel solvatochromic probes were synthesized: 2,6-dibromo-4-[(E)-2-(1-methylquinolinium-4-yl)ethenyl]-phenolate (MeQMBr(2)) and 2,6-dibromo-4-[(E)-2-(1-methyl-acridinium-4- yl) ethenyl)]phenolate (MeAMBr(2) The solvatochromic behavior of these probes, along with that of 2,6dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl]phenol-ate(MePMBr(2)) was analyzed in terms of increasing probe lipophilicity, through annelation. Values of the empirical solvent polarity scale [E(T)(MePMBr(2))] in kcalmol(-1) correlated linearly with ET(30), the corresponding values for the extensively employed probe 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl)phenolate (RB). On the other hand, the nonlinear correlations of ET(MeQMBr(2)) or ET(MeAMBr(2)) with E(T)(30) are described by second-order polynomials. Possible reasons for this behavior include: i) self-aggregation of the probe, ii) photoinduced cis/trans isomerization of the dye, and iii) probe structure- and solvent-dependent contributions of the quinonoid and zwitterionic limiting formulas to the ground and excited states of the probe. We show that mechanisms (i) and (ii) are not operative under the experimental conditions employed; experimental evidence (NMR) and theoretical calculations are presented to support the conjecture that the length of the central ethenylic bond in the dye increases in the order MeAMBr(2) > MeQMBr(2) > MePMBr(2), That is, the contribution of the zwitterionic limiting formula predominates for the latter probe, as is also the case for RB, this being the reason for the observed linear correlation between the ET(MePMBr2) and the ET(30) scales. The effect of increasing probe lipophilicity on solvatochromic behavior therefore depends on the strategy employed. Increasing the length of R affects solvatochromism much less than annelation, because the former structural change hardly perturbs the energy of the intramolecular charge-transfer transition responsible for solvatochromism. The thermo-solvatochromic behavior (effect of temperature on solvatochromism) of the three probes was studied in mixtures of water with propanol and/or with DMSO. The solvation model used explicitly considers the presence of three ""species"" in the system: bulk solution and probe solvation shell [namely, water (W), organic solvent (Solv)], and solvent-water hydrogen-bonded aggregate (Solv-W). For aqueous propanol, the probe is efficiently solvated by Solv-W; the strong interaction of DMSO with W drastically decreases the efficiency of Solv-W in solvating the probe, relative to its precursor solvents. Temperature increases resulted in desolvation of the probes, due to the concomitant reduction in the structured characters of the components of the binary mixtures.