746 research outputs found
Thinking culturally about place
This paper explains the bases for an alternative approach to place branding and marketing, based on the disciplines of Cultural Mapping and Cultural Planning. After an introduction of key cultural mapping and planning concepts and issues, the paper discusses some innovative practical examples of culturally sensitive place branding and marketing from Sweden and the UK, and concludes by outlining some components of a possible future agenda for action
Free Heyting algebra endomorphisms: Ruitenburg’s Theorem and beyond
Ruitenburg\u2019s Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ulti- mately periodic if f fixes all the generators but one. More precisely, there is N 65 0 such that f^N+2 = f^N , thus the period equals 2. We give a semantic proof of this theorem, using duality techniques and bounded bisimulation ranks. By the same techniques, we tackle investigation of arbitrary endomorphisms of free algebras. We show that they are not, in general, ultimately periodic. Yet, when they are (e.g. in the case of locally finite subvarieties), the period can be explicitly bounded as function of the cardinality of the set of generators
EXISTENTIALLY CLOSED BROUWERIAN SEMILATTICES
The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results, it has a model completion (whose models are the existen- tially closed structures). In this paper, we supply a finite and rather simple axiomatization of the model completio
Admissibility of Î <sub>2</sub>-inference rules: Interpolation, model completion, and contact algebras
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus S2IC, where we also supply a finite axiomatization of the model completion of its algebraic counterpart, via the equivalent theory of contact algebras. Using this result we obtain a finite basis for admissible Î 2-rules
Quantifier-Free Interpolation of a Theory of Arrays
The use of interpolants in model checking is becoming an enabling technology
to allow fast and robust verification of hardware and software. The application
of encodings based on the theory of arrays, however, is limited by the
impossibility of deriving quantifier- free interpolants in general. In this
paper, we show that it is possible to obtain quantifier-free interpolants for a
Skolemized version of the extensional theory of arrays. We prove this in two
ways: (1) non-constructively, by using the model theoretic notion of
amalgamation, which is known to be equivalent to admit quantifier-free
interpolation for universal theories; and (2) constructively, by designing an
interpolating procedure, based on solving equations between array updates.
(Interestingly, rewriting techniques are used in the key steps of the solver
and its proof of correctness.) To the best of our knowledge, this is the first
successful attempt of computing quantifier- free interpolants for a variant of
the theory of arrays with extensionality
Fixed-point elimination in the intuitionistic propositional calculus
It is a consequence of existing literature that least and greatest
fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic
models of the Intuitionistic Propositional Calculus-always exist, even when
these algebras are not complete as lattices. The reason is that these extremal
fixed-points are definable by formulas of the IPC. Consequently, the
-calculus based on intuitionistic logic is trivial, every -formula
being equivalent to a fixed-point free formula. We give in this paper an
axiomatization of least and greatest fixed-points of formulas, and an algorithm
to compute a fixed-point free formula equivalent to a given -formula. The
axiomatization of the greatest fixed-point is simple. The axiomatization of the
least fixed-point is more complex, in particular every monotone formula
converges to its least fixed-point by Kleene's iteration in a finite number of
steps, but there is no uniform upper bound on the number of iterations. We
extract, out of the algorithm, upper bounds for such n, depending on the size
of the formula. For some formulas, we show that these upper bounds are
polynomial and optimal
hungry bone syndrome after parathyroidectomy for primary hyperthyroidism
Parathyroidectomy is the treatment of choice in patients with primary hyperparathyroidism (PHPT). This disease affects calcium metabolism at the level of bone tissue and renal tubules, resulting in hypercalcaemia, often asymptomatic, associated with hypophosphataemia and hypomagnesaemia. Sudden suppression of parathyroid hormone (PTH), caused by successful parathyroidectomy, in patients with preoperative high levels of PTH and hypercalcaemia from enhanced bone turnover, may induce severe postoperative hypocalcaemia that may lead to symptoms of tetany. This relatively uncommon condition is known as "hungry bone syndrome" (HBS), because it is believed to be due mainly to enhanced bone formation. Several risk factors have been advocated for HBS, and the syndrome is reported to be more likely to rise in subjects with severe preoperative bone disease. Other modifiable risk factors are preoperative vitamin D deficiency and high PTH and calcium levels. Treatment of HBS is basically the administration of high amounts of calcium immediately after the onset of postoperative hypocalcaemia. Supplements of active metabolites of vitamin D, as well as magnesium in depleted subjects are complementary in supporting bone remineralization. Oral supplementation may be requested for months after parathyroidectomy. Prevention is poorly documented, but it is reasonable to propose the correction of vitamin D deficit and the use of bisphosphonates aimed to lower PTH levels and bone resorption before parathyroidectomy
Finitely generated free Heyting algebras via Birkhoff duality and coalgebra
Algebras axiomatized entirely by rank 1 axioms are algebras for a functor and
thus the free algebras can be obtained by a direct limit process. Dually, the
final coalgebras can be obtained by an inverse limit process. In order to
explore the limits of this method we look at Heyting algebras which have mixed
rank 0-1 axiomatizations. We will see that Heyting algebras are special in that
they are almost rank 1 axiomatized and can be handled by a slight variant of
the rank 1 coalgebraic methods
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