A multi-labelled sequent calculus for Topo-Logic

We present a labelled sequent calculus for a trimodal epistemic logic exhibitied in Baltag et al. (2017, Logic, Rationality, and Interaction, pp. 330–346), an extension of the so called ‘Topo-Logic’. To the best of our knowledge, our calculus is the first proof-calculus for this logic. This calculus is obtained via an adaptation of the label technique by internalizing a semantics over topological spaces. This internalization leads to the generation of two kinds of labels in our calculus and the labelling of formulae by pairs of labels. These novelties give tools to provide a simple calculus that is intuitively connected to the semantics. We prove that this calculus enjoys many structural properties such as admissibility of cut, admissibility of contraction and invertibility of its rules. Finally, we exhibit a proof search strategy for our calculus that allows us to prove completeness in a direct way by the extraction of a countermodel from a failure of proof. To define this strategy, we design a tool for controlling the generation of labels in the construction of a search tree, although the termination of this strategy is still open.

pH Behavior of Polymer Complexes between Poly(carboxylic acids) and Poly(acrylamide derivatives) Using a Fluorescence Label Technique

In order to clarify the local environment during interpolymer complex formation between poly(carboxylic acids) and poly(acrylamide derivatives) with different N-substitutions, a fluorescence label technique was used. 3-(2-propenyl)-9-(4-N,N-dimethylaminophenyl) phenanthrene (VDP) was used as an intramolecular fluorescence probe. All polymers were synthesized by free radical polymerization. Interpolymer complexation was monitored by charge transfer emission from the VDP unit. Both of the poly(carboxylic acids) formed interpolymer complexes with poly(N,N-dimethylacrylamide) (polyDMAM). The micro-environments around the VDP unit in the acidic pH region for the poly(methacrylic acid) (polyMAAc) and polyDMAM mixed systems were more hydrophobic than those of the poly(acrylic acid) (polyAAc) and polyDMAM mixed systems, as the α-methyl group of the MAAc unit contributed to hydrophobicity around the polymer chain during hydrogen bond formation. This suggests that, when the poly(carboxylic acids) and poly(acrylamide derivatives) were mixed, with a subsequent decrease in the solution pH, a hydrogen bond was partially formed, following which the hydrophobicity of the micro-environment around the polymer chains was changed, resulting in the formation of interpolymer complexes. Moreover, the electron-donating ability of the carbonyl group in the poly(acrylamide derivatives) had an effect on complexation with poly(carboxylic acids).