Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Dampened Transient Actuation of Hydrogels Autonomously Controlled by pH-Responsive Bicontinuous Nanospheres

The fabrication of a soft actuator with a dampened actuation response is presented. This was achieved via the incorporation into an actuating hydrogel of urease-loaded pH-responsive bicontinuous nanospheres (BCNs), whose membrane was able to regulate the permeability and thus conversion of fuel urea into ammonia. The dampened response of these nanoreactors to the enzymatically induced pH change was translated to a pH-responsive soft actuator. In hydrogels composed of a pH-responsive and nonresponsive layer, the transient pH gradient yielded an asymmetric swelling behavior, which induced a bending response. The transient actuation profile could be controlled by varying the external fuel concentrations. Furthermore, we showed that the spatial organization of the BCNs within the actuator had a great influence on the actuation response. Embedding the urease-loaded nanoreactors within the active, pH-responsive layer resulted in a reduced response due to local substrate conversion in comparison to embedding them within the passive layer of the bilayer hydrogel. Finally, we were able to induce transient actuation in a hydrogel comprising two identical active layers by the immobilization of the BCNs within one specific layer. Upon addition of urea, a local pH gradient was generated, which caused accelerated swelling in the BCN layer and transient bending of the device before the pH gradient was attenuated over time.</p

Intramolecularly catalyzed dynamic polyester networks using neighboring carboxylic and sulfonic acid groups

Dynamic covalent bonds in a polymer network lead to plasticity, reshapability, and potential recyclability at elevated temperatures in combination with solvent-resistance and better dimensional stability at lower temperatures. Here we report a simple one-step procedure for the catalyst-free preparation and intramolecularly catalyzed stress-relaxation of dynamic polyester networks. The procedure is based on the coupling of branched OH-end functional polyesters (functionality ≥ 3) by pyromellitic dianhydride (PMDA) or 2,5-bis(methoxy-carbonyl) benzenesulfonic acid resulting in ester linkages with, respectively, a COOH or a SO3H group in a position ortho to the ester bond. This approach leads to an efficient external catalyst-free dynamic polyester network, in which the topology rearrangements occur via a dissociative mechanism involving anhydrides. The SO3H-containing network is particularly interesting, as it shows the fastest stress relaxation and does not suffer from unwanted additional transesterification reactions, as was observed in the COOH-containing network.</p

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201