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

The Modal Logic of Stepwise Removal

We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic ($\textsf{MLSR}$) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a complete Hilbert-style axiomatization for the logic of stepwise removal in a hybrid language enriched with nominals and public announcement operators. Next, we show that model-checking for $\textsf{MLSR}$ is PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we consider an issue of fine-structure: the expressive power gained by adding the stepwise removal modality to fragments of first-order logic

Excess portal venous long-chain fatty acids induce syndrome X via HPA axis and sympathetic activation

We tested the hypothesis that excessive portal venous supply of long-chain fatty acids to the liver contributes to the development of insulin resistance via activation of the hypothalamus-pituitary-adrenal axis (HPA axis) and sympathetic system. Rats received an intraportal infusion of the long-chain fatty acid oleate (150 nmol/min, 24 h), the medium-chain fatty acid caprylate, or the solvent. Corticosterone (Cort) and norepinephrine (NE) were measured as indexes for HPA axis and sympathetic activity, respectively. Insulin sensitivity was assessed by means of an intravenous glucose tolerance test (IVGTT). Oleate infusion induced increases in plasma Cort (Δ = 13.5 ± 3.6 µg/dl; P < 0.05) and NE (Δ = 235 ± 76 ng/l; P < 0.05), whereas caprylate and solvent had no effect. The area under the insulin response curve to the IVGTT was larger in the oleate-treated group than in the caprylate and solvent groups (area = 220 ± 35 vs. 112 ± 13 and 106 ± 8, respectively, P < 0.05). The area under the glucose response curves was comparable [area = 121 ± 13 (oleate) vs. 135 ± 20 (caprylate) and 96 ± 11 (solvent)]. The results are consistent with the concept that increased portal free fatty acid is involved in the induction of visceral obesity-related insulin resistance via activation of the HPA axis and sympathetic system.

Symbolic Model Checking for Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, existing DEL implementations are ad-hoc, so we do not know how the framework really performs. For this purpose, we want to hook up with the best available model-checking and SAT techniques in computational logic. We do this by first providing a bridge: a new faithful representation of DEL models as so-called knowledge structures that allow for symbolic model checking. Next, we show that we can now solve well-known benchmark problems in epistemic scenarios much faster than with existing DEL methods. Finally, we show that our method is not just a matter of implementation, but that it raises significant issues about logical representation and update