Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics.

Prometheus Framework for Fuzzy Information Retrieval in Semantic Spaces

This paper introduces a novel vision for further enhanced Internet of Things services. Based on a variety of data (such as location data, ontology-backed search queries, in- and outdoor conditions) the Prometheus framework is intended to support users with helpful recommendations and information preceding a search for context-aware data. Adapted from artificial intelligence concepts, Prometheus proposes user-readjusted answers on umpteen conditions. A number of potential Prometheus framework applications are illustrated. Added value and possible future studies are discussed in the conclusion.

A Logical Descriptor for Regular Languages via Stone Duality

In this paper we introduce a class of descriptors for regular languages arising from an application of the Stone duality between finite Boolean algebras and finite sets. These descriptors, called classical fortresses, are object specified in classical propositional logic and capable to accept exactly regular languages. To prove this, we show that the languages accepted by classical fortresses and deterministic finite automata coincide. Classical fortresses, besides being propositional descriptors for regular languages, also turn out to be an efficient tool for providing alternative and intuitive proofs for the closure properties of regular languages.

Admissibility via natural dualities

It is shown that admissible clauses and quasi-identities of quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may be characterized using natural dualities. In particular, axiomatizations are obtained for the admissible clauses and quasi-identities of bounded distributive lattices, Stone algebras, Kleene algebras and lattices, and De Morgan algebras and lattices.

Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.

Clinical Course of acute-on-chronic liver failure syndrome and effects on prognosis

Acute-on-chronic liver failure (ACLF) is characterized by acute decompensation (AD) of cirrhosis, organ failure(s), and high 28-day mortality. We investigated whether assessments of patients at specific time points predicted their need for liver transplantation (LT) or the potential futility of their care. We assessed clinical courses of 388 patients who had ACLF at enrollment, from February through September 2011, or during early (28-day) follow-up of the prospective multicenter European Chronic Liver Failure (CLIF) ACLF in Cirrhosis study. We assessed ACLF grades at different time points to define disease resolution, improvement, worsening, or steady or fluctuating course. ACLF resolved or improved in 49.2%, had a steady or fluctuating course in 30.4%, and worsened in 20.4%. The 28-day transplant-free mortality was low-to-moderate (6%-18%) in patients with nonsevere early course (final no ACLF or ACLF-1) and high-to-very high (42%-92%) in those with severe early course (final ACLF-2 or -3) independently of initial grades. Independent predictors of course severity were CLIF Consortium ACLF score (CLIF-C ACLFs) and presence of liver failure (total bilirubin ≥12 mg/dL) at ACLF diagnosis. Eighty-one percent had their final ACLF grade at 1 week, resulting in accurate prediction of short- (28-day) and mid-term (90-day) mortality by ACLF grade at 3-7 days. Among patients that underwent early LT, 75% survived for at least 1 year. Among patients with ≥4 organ failures, or CLIF-C ACLFs >64 at days 3-7 days, and did not undergo LT, mortality was 100% by 28 days. CONCLUSIONS Assessment of ACLF patients at 3-7 days of the syndrome provides a tool to define the emergency of LT and a rational basis for intensive care discontinuation owing to futility.

Cutting Arcs For Torus Links And Trees

Among all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An , Dn , E6 , E7 and E8 ) among all positive tree-like Hopf plumbings.