Distributed representations (such as those based on embed-dings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We present a model theory/semantics for first order logic based on vectors of reals. We describe the model theory , discuss some interesting properties of such ...

This paper attempts to serve as an introduction to abstract model theory. We introduce the notion of abstract logics, explore first-order logic as an instance of and as the basis for abstract logics, and end by proving Lindström’s theorem.

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Axiomatizations of the General Theory of Relativity.have occasionally been conducted to achieve precision and clarification of underlying concepts. Rigorous and inspiring work towards that aim based on first-order logic has been performed by Professor Németi and his working group (see references below). A complementary approach (Benda 2008) constructs the relativistic spacetime manifold ab init...

Catch crops are an effective method for reducing nitrogen (N) leaching in agriculture, but the mineralization of incorporated catch crop residue N is difficult to predict and model. We conducted a five-month incubation experiment using fresh from three (hairy vetch, fodder radish ryegrass) with temperature treatments (2 °C, 15 °C 2–15 variable temperature) two termination methods (glyphosate un...

Isotherms for the adsorption of KCl in PVOH-borate hydrogel was studied at 303 K by determining the amount of potassium and chloride ions adsorbed in PVOH-borate hydrogel using ion exchange chromatography and potentiometric titrations respectively. Experimental data was tested for Frendulich’s, Langmuir’s, Temkin’s and Dubinin–Radushkevich isotherms equations. The adsorption data follows isothe...

In Escherichia coli, protein degradation in synthetic circuits is commonly achieved by the ssrA-tagged degradation system. In this work, we show that the degradation kinetics for the green fluorescent protein fused with the native ssrA tag in each cell exhibits the zeroth-order limit of the Michaelis-Menten kinetics, rather than the commonly assumed first-order. When measured in a population, t...