Logics of Finite Hankel Rank

We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the Feferman-Vaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order logic with modular counting quantifiers. For sum-like operations it is CMSOL, the corresponding monadic second order logic. We discuss whether there are maximal logics satisfying Feferman-Vaught Theorems for finite structures.Comment: Appeared in YuriFest 2015, held in honor of Yuri Gurevich's 75th birthday. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23534-9_1

On the Parameterized Intractability of Monadic Second-Order Logic

One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms, where the parameter is the tree-width plus the size of the formula. An immediate question is whether this is best possible or whether the result can be extended to classes of unbounded tree-width. In this paper we show that in terms of tree-width, the theorem cannot be extended much further. More specifically, we show that if C is a class of graphs which is closed under colourings and satisfies certain constructibility conditions and is such that the tree-width of C is not bounded by \log^{84} n then MSO_2-model checking is not fpt unless SAT can be solved in sub-exponential time. If the tree-width of C is not poly-logarithmically bounded, then MSO_2-model checking is not fpt unless all problems in the polynomial-time hierarchy can be solved in sub-exponential time

Dependence Logic with Generalized Quantifiers: Axiomatizations

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as "there exists uncountable many." Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.Comment: 17 page

Pharmacy led medicine reconciliation at hospital: a systematic review of effects and costs

Background: Transition of patients care between settings presents an increased opportunity for errors and preventable morbidity. A number of studies outlined that pharmacy-led medication reconciliation (MR) might facilitate safer information transfer and medication use. MR practice is not well standardised and often delivered in combination with other healthcare activities. The question regarding the effects and costs of pharmacy-led MR and the optimum MR practice is warranted of value.  Objectives: To review the evidence for the effects and costs/ cost-effectiveness of complete pharmacy-led MR in hospital settings.  Methods: A systematic review searching the following database was conducted up to the 13th December 2015; EMBASE & MEDLINE Ovid, CINAHL and the Cochrane library. Studies evaluating pharmacy-led MR performed fully from admission till discharges were included. Studies evaluated non-pharmacy-led MR at only one end of patient care or transfer were not included. Articles were screened and extracted independently by two investigators. Studies were divided into those in which: MR was the primary element of the intervention and labelled as “primarily MR” studies, or MR combined with non-MR care activities and labelled as “supplemented MR” studies. Quality assessment of studies was performed by independent reviewers using a pre-defined and validated tool.  Results: The literature search identified 4,065 citations, of which 13 implemented complete MR. The lack of evidence precluded addressing the effects and costs of MR.  Conclusions: The composite of optimum MR practice is not widely standardised and requires discussion among health professions and key organisations. Research focused on evaluating cost-effectiveness of pharmacy-led MR is lacking