On Gabbay's temporal fixed point operator

AbstractWe discuss the temporal logic “USF”, involving Until, Since and the fixed point operator ϑ of Gabbay, with semantics over the natural numbers. We show that any formula not involving Until is equivalent to one without nested fixed point operators. We then prove that USF has expressive power matching that of the monadic second-order logic S1S. The proof shows that any USF-formula is equivalent to one with at most two nested fixed point operators — i.e., no branch of its formation tree has more than two ϑ's. We then axiomatise USF and prove that it is decidable, with PSPACE-complete satisfiability problem. Finally, we discuss an application of these results to the executable temporal logic system “MetateM”

Non-representable relation algebras from vector spaces

Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018)

Non-representable relation algebras from vector spaces

Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018)

The k-variable property is stronger than H-dimension k

Accepted versio

FINITE H-DIMENSION DOES NOT IMPLY EXPRESSIVE COMPLETENESS

Accepted versio

Relation algebras from cylindric algebras, II

Accepted versio

Pathways to care for critically ill or injured children: A cohort study from first presentation to healthcare services through to admission to intensive care or death

Purpose Critically ill or injured children require prompt identification, rapid referral and quality emergency management. We undertook a study to evaluate the care pathway of critically ill or injured children to identify preventable failures in the care provided. METHODS: A year-long cohort study of critically ill and injured children was performed in Cape Town, South Africa, from first presentation to healthcare services until paediatric intensive care unit (PICU) admission or emergency department death, using expert panel review of medical records and caregiver interview. Main outcomes were expert assessment of overall quality of care; avoidability of severity of illness and PICU admission or death and the identification of modifiable factors. RESULTS: The study enrolled 282 children, 252 emergency PICU admissions, and 30 deaths. Global quality of care was graded good in 10% of cases, with half having at least one major impact modifiable factor. Key modifiable factors related to access to care and identification of the critically ill, assessment of severity, inadequate resuscitation, and delays in decision making and referral. Children were transferred with median time from first presentation to PICU admission of 12.3 hours. There was potentially avoidable severity of illness in 185 (74%) of children, and death prior to PICU admission was avoidable in 17/30 (56.7%) of children. CONCLUSIONS: The study presents a novel methodology, examining quality of care across an entire system, and highlighting the complexity of the pathway and the modifiable events amenable to interventions, that could reduce mortality and morbidity, and optimize utilization of scarce critical care resources; as well as demonstrating the importance of continuity and quality of care

Decidable fragments of first-order temporal logics

Accepted versio

Pilot evaluation of the psychometric properties of a self-medication Risk Assessment Tool among elderly patients in a community setting

<p>Abstract</p> <p>Background</p> <p>Although community pharmacists in the United Kingdom are expected to assess elderly patients' needs for additional support in managing their medicines, there is limited data on potentially useful assessment tools. We sought to evaluate a 13-item assessment instrument among community dwelling elderly patients, 65 years and above. The instrument is composed of a cognitive risk sub-scale of 6 items and a physical risk sub-scale of 7 items.</p> <p>Findings</p> <p>The instrument was administered to elderly patients in a survey performed in a community to the west of Glasgow, Scotland. The survey recruited 37 participants, 31 from 4 community pharmacies and 6 patients whose medication management tasks were managed by the West Glasgow Community Health and Care Partnership (managed patients). Community pharmacists independently rated 29 of the 37 participants' comprehension of, and dexterity in handling their medicines. We assessed scale reliability, convergent validity and criterion validity. In sub-analyses, we assessed differences in scores between the managed patients and those recruited from the community pharmacies, and between multi-compartment compliance aid users and non-users. The instrument showed satisfactory internal consistency (Cronbach's alpha of 0.792 for 13-item scale). There was significant strong negative correlation between the cognitive risk sub-scores and community pharmacists' assessment of comprehension (ρ = -0.546, p = 0.0038); and physical risk sub-scores and community pharmacists' assessment of dexterity (ρ = -0.491, p = 0.0093). The Area Under the Receiver Operator Characteristic Curve (AUC ± SE; 95%CI) showed that the instrument had good discriminatory capacity (0.86 ± 0.07; 0.68, 0.96). The best cut-off (sensitivity, specificity) was ≥4 (65%, 100%). In the sub-analyses, managed patients had significantly higher cognitive risk sub-scores (6.5 versus 4.0, p = 0.0461) compared to non-managed patients. There was a significant difference in total risk score (4 versus 2, p = 0.0135) and cognitive risk sub-score (4 versus 1.5, p = 0.0029) between users and non-users of multi-compartment compliance aids.</p> <p>Conclusions</p> <p>This instrument shows potential for use in identifying elderly patients who may have problems managing their own medicines in the community setting. However, more robust validity and reliability assessments are needed prior to introduction of the tool into routine practice.</p