The Expressive Power of k-ary Exclusion Logic

In this paper we study the expressive power of k-ary exclusion logic, EXC[k], that is obtained by extending first order logic with k-ary exclusion atoms. It is known that without arity bounds exclusion logic is equivalent with dependence logic. By observing the translations, we see that the expressive power of EXC[k] lies in between k-ary and (k+1)-ary dependence logics. We will show that, at least in the case of k=1, the both of these inclusions are proper. In a recent work by the author it was shown that k-ary inclusion-exclusion logic is equivalent with k-ary existential second order logic, ESO[k]. We will show that, on the level of sentences, it is possible to simulate inclusion atoms with exclusion atoms, and this way express ESO[k]-sentences by using only k-ary exclusion atoms. For this translation we also need to introduce a novel method for "unifying" the values of certain variables in a team. As a consequence, EXC[k] captures ESO[k] on the level of sentences, and we get a strict arity hierarchy for exclusion logic. It also follows that k-ary inclusion logic is strictly weaker than EXC[k]. Finally we will use similar techniques to formulate a translation from ESO[k] to k-ary inclusion logic with strict semantics. Consequently, for any arity fragment of inclusion logic, strict semantics is more expressive than lax semantics.Comment: Preprint of a paper in the special issue of WoLLIC2016 in Annals of Pure and Applied Logic, 170(9):1070-1099, 201

Capturing k-ary Existential Second Order Logic with k-ary Inclusion-Exclusion Logic

In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k]. From this it follows that, on the level of sentences, INEX[k] captures the expressive power of ESO[k]. We also introduce several useful operators that can be expressed in INEX[k]. In particular, we define inclusion and exclusion quantifiers and so-called term value preserving disjunction which is essential for the proofs of the main results in this paper. Furthermore, we present a novel method of relativization for team semantics and analyze the duality of inclusion and exclusion atoms.Comment: Extended version of a paper published in Annals of Pure and Applied Logic 169 (3), 177-21

The finance of local government in Great Britain; legal and financial structures

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę

The effect of age on referral to and use of specialist palliative care services in adult cancer patients: a systematic review

Objective: to investigate variations in the use of specialist palliative care (SPC) services for adult cancer patients, in relation to age.Design: systematic review of studies examining use of or referral to SPC services in adult cancer patients.Search strategy and selection criteria: six electronic databases (Medline, Embase, Web of Science, HMIC, SIGLE and AgeInfo) were searched for studies published between 1966 and March 2005, and references in the articles identified were also examined. Inclusion criteria were all studies which provided data on age in relation to use of or referral to SPC. Two reviewers independently selected studies, extracted data and assessed methodological quality according to defined criteria.Main outcome measures: use of or referral to SPC services, determined from all sources of report (patient, informal carer, health care professional, health care records).Results: 14 studies were identified. All reported a statistically significant lower use of SPC among older cancer patients (65 and above or older) at a univariate level [crude odds ratios ranged from 0.33 (0.15-0.72) to 0.82 (0.80-0.82)]. However, there were important methodological weaknesses in all of the studies identified; most crucially, studies failed to consider variations in use in relation to need for SPC.Conclusions: there is some evidence that older people are less likely to be referred to, or to use, SPC. These findings require confirmation in studies using prospectively collected data which control for patient's need for SPC

Evaluation of a hydrographic technique to measure on-farm water storage volumes

Digital terrain models of on-farm water storages are required to assist in accurately measuring the on-farm water balance and water use efficiency components including storage capacity, inflow, seepage, evaporation and discharge volumes. A hydrographic surveying system combining a high-precision global positioning system (GPS) and a low-cost depth sounder was developed to facilitate the creation of a digital terrain model. The system was validated by comparing the hydrographic terrain model and volume measurements against both a traditional real time kinematic (RTK) land based survey and independent lead line depth measurements. Flat bottomed storage volumes were measured with errors of less than 1 percent using the hydrographic survey technique. A major proportion of the error in small storages was found to be associated with the ability to accurately identify the inflection point between the banks and floor of the storage. However, for larger storages, errors were primarily related to density of sampling points within the storage floor area. Recommendations are provided regarding the appropriate measurement procedures, including sampling point density, for a range of storage sizes

Bumblebees gain fitness through learning

Despite the widespread assumption that the learning abilities of animals are adapted to the particular environments in which they operate, the quantitative effects of learning performance on fitness remain virtually unknown. Here we evaluate the learning performance of bumblebees (_Bombus terrestris_) from multiple colonies in an ecologically relevant associative learning task under laboratory conditions, before testing the foraging performance of the same colonies under the field conditions. We demonstrate that variation in learning speed among bumblebee colonies is directly correlated with foraging performance, a robust fitness measure, under natural conditions. Colonies vary in learning speed by a factor of nearly 5, with the slowest learning colonies collecting 40% less nectar than the fastest learning colonies. Such a steep fitness function suggests strong selection for higher learning speed in bumblebees. Demonstrating the adaptive value of differences in learning performance under the real conditions in which animals function represents a major step towards understanding how cognitive abilities of animals are tuned to their environment

Strategies for maximizing sugarcane yield with limited water in the Bundaberg district

Between 1995 and 2003 sugarcane farmers in Bundaberg had access to limited irrigation water. Over this time water allocations were effectively a quarter of the requirements for a fully irrigated crop. In response to this problem irrigation strategies were developed to assist farmers. Field investigations focused on the performance of water winch and furrow irrigation systems, which make up 91 percent of the irrigated area in the district. As most of these application systems have insufficient capacity to meet crop demands, opportunities to schedule irrigations were limited to start up after rain. Improvements in irrigation system performance were found to provide the greatest potential to increase sugarcane yield under conditions of limited water. Investigations identified that irrigation performance could be significantly improved through relatively minor adjustment. Timing of irrigation start up after rain influenced how much water could be applied to the field. Even with relatively low allocations delayed start up strategies could lead to a situation where water was left over at the end of the season