Quantifier-free epistemic term-modal logic with assignment operator

In standard epistemic logic, the names and the existence of agents are usually assumed to be common knowledge implicitly. This is unreasonable for various applications in computer science and philosophy. Inspired by term-modal logic and assignment operators in dynamic logic, we introduce a lightweight modal predicate logic where names can be non-rigid, and the existence of agents can be uncertain. The language can handle various de dicto/de re distinctions in a natural way. We characterize the expressive power of our language, obtain complete axiomatisations of the logics over several classes of varying-domain/constant-domain epistemic models, and show their (un)decidability.     

Ambident Reactivity of Imidazolium Cations as Evidence of the Dynamic Nature of N-Heterocyclic Carbene-Mediated Organocatalysis

This work reveals ambident nucleophilic reactivity of imidazolium cations towards carbonyl compounds at the C2 or C4 carbene centers depending on the steric properties of the substrates and reaction conditions. Such an adaptive behavior indicates the dynamic nature of organocatalysis proceeding via a covalent interaction of imidazolium carbenes with carbonyl substrates and can be explained by generation of the H-bonded ditopic carbanionic carbenes.     

Reasoning about proof and knowledge

In previous work [15], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from Gödel's interpretation of IPC in S4, our modal systems contain IPC in the way established in [13]. The modal operator can be viewed as a predicate for intuitionistic truth, i.e. proof. Epistemic principles are partially adopted from Intuitionistic Epistemic Logic IEL [4]. In the present paper, we show that the S5-style systems of our hierarchy correspond to an extended Brouwer–Heyting–Kolmogorov interpretation and are complete w.r.t. a relational semantics based on intuitionistic general frames. In this sense, our S5-style logics are adequate and complete systems for the reasoning about proof combined with belief or knowledge. The proposed relational semantics is a uniform framework in which also IEL can be modeled. Verification-based intuitionistic knowledge formalized in IEL turns out to be a special case of the kind of knowledge described by our S5-style systems.     

Existential monadic second order logic of undirected graphs: The Le Bars conjecture is false

In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) on undirected graphs. He proved that there exists an EMSO sentence ? such that $\mathsf{P}(G_n??)$ does not converge as $n\to \infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\{1,\dots ,n\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-one law holds. In this paper, we disprove this conjecture.     

Alkane Shape- and Size-Recognized Selective Vapor Sorption in “Channel-Like” Crystals Based on Thiacalixarene Assemblies

Alkanes composed of C−C and C−H show a low electric polarization, and therefore, there is only very weak interaction between alkanes and adsorbents. Thus, it is difficult to separate a specific alkane from a mixture of alkanes by adsorption. Here, two activated “channel-like” crystals generated from brominated thiacalix[4]arene propyl ethers, which adopt 1,3-alternate and partial cone conformations, recognize specific alkane vapors depending on alkane-shape and -size, sorting in three-type alkane guests such as linear, branched, and cyclic alkanes. Two activated crystals, which are prepared by removal of solvent upon heating under reduced pressure, incorporate branched and/or cyclic alkane vapors by a unique “gate-opening” mechanism via a crystal transformation in the process. Linear alkane vapors do not trigger gate opening and are not taken up by the activated crystals. The shape and size molecular-recognition properties of the activated crystals promises considerable usefulness for the separation of linear, branched, and cyclic alkanes.     

Gated Channels and Selectivity Tuning of CO2 over N2 Sorption by Post‐Synthetic Modification of a UiO‐66‐Type Metal–Organic Framework

The highly porous and stable metal–organic framework (MOF) UiO‐66 was altered using post‐synthetic modifications (PSMs). Prefunctionalization allowed the introduction of carbon double bonds into the framework through a four‐step synthesis from 2‐bromo‐1,4‐benzenedicarboxylic acid; the organic linker 2‐allyl‐1,4‐benzenedicarboxylic acid was obtained. The corresponding functionalized MOF (UiO‐66‐allyl) served as a platform for further PSMs. From UiO‐66‐allyl, epoxy, dibromide, thioether, diamine, and amino alcohol functionalities were synthesized. The abilities of these compounds to adsorb CO₂ and N₂ were compared, which revealed the structure–selectivity correlations. All synthesized MOFs showed profound thermal stability together with an increased ability for selective CO₂ uptake and molecular gate functionalities at low temperatures.     

Study of “Racemic Compound-Like” Behavior of Diastereomeric Mixture of Pinanyl Sulfoxides by X-Ray Diffraction,IR Spectroscopy,and DFT Calculations

Abstract

The oxidation of a β-hydroxysulfide in the pinane series by use of m-chloroperbenzoic acid resulted in the formation of the corresponding β-hydroxysulfoxide as a mixture of two diastereomers in 4:5 ratio. According to single-crystal X-ray diffraction (XRD) results, it is established that the diastereomeric mixture of sulfoxides crystallizes in the “racemic compound-like” manner under formation of asymmetric dimers through S=O··H–O interactions. This asymmetric dimer formed from diastereomeric molecules is a structural unit in both crystal modifications, the triclinic and the monoclinic one. The behavior of the diastereomeric mixture of pinane derived sulfoxides in crystals, melts and in tetrachloromethane solutions was studied by IR spectroscopy. The density functional theory (DFT) method with 6-31G (d, p) basis set was used to calculate the optimized geometrical parameters and vibrational frequencies of different associates in solutions. The calculated vibrational frequencies are compared with experimental IR spectra.     

Studies on the Particle Morphology of Waterborne Cationic Polyurethane/Polyacrylate Microemulsions

Polyurethane containing tertiary nitrogen atoms was synthesized from polyol, diphenylmethane diisoccyanate (MDI) and N‐methyl diethanolamine. The polymer was converted into cationomers by quarternizing with methacrylic acid (MAA) and then dispersed in water. In this reaction, methyl methacrylate (MMA) was used to decrease viscosity; at the same time, it was the monomer in the later reaction. Finally the cationic polyurethane dispersions were further polymerized with an oil‐soluble initiator, azobisisobutyronitrile (AIBN), water‐soluble initiator, K₂S₂O₈ (KPS) and the mixture of AIBN and KPS. The different emulsion particles with shell‐core structure, “invert” shell‐core structure and “irregular” sandwich structure were obtained; the morphological structures were characterized by TEM observation, FT‐IR and particle size analysis.