Polyteam Semantics

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define "Polyteam Semantics" in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatisation for the associated implication problem. We also characterise the expressive power of poly-dependence logic by properties of polyteams that are downward closed and definable in existential second-order logic (ESO). The analogous result is shown to hold for poly-independence logic and all ESO-definable properties.Peer reviewe

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

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

Probabilistic Team Semantics

Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this framework to a Tarskian two-sorted logic. We also show that very simple quantifier-free formulae of our logic give rise to backslashmathrm NP NP -hard model checking problems.Peer reviewe

Purely ropivacaine-based TEA vs single TAP block in pain management after elective laparoscopic colon surgery within an upgraded institutional ERAS program

Publisher Copyright: © 2021, The Author(s).Background: The aim of this study was to compare thoracic epidural analgesia (TEA) with transversus abdominis plane (TAP) block in post-operative pain management after laparoscopic colon surgery. Methods: One hundred thirty-six patients undergoing laparoscopic colon resection randomly received either TEA or TAP with ropivacaine only. The primary endpoint was opioid requirement up to 48 h postoperatively. Intensity of pain, time to onset of bowel function, time to mobilization, postoperative complications, length of hospital stay, and patients’ satisfaction with pain management were also assessed. Results: We observed a significant decrease in opioid consumption on the day of surgery with TEA compared with TAP block (30 mg vs 14 mg, p < 0.001). On the first two postoperative days (POD), the balance shifted to opioid consumption being smaller in the TAP group: on POD 1 (15.2 mg vs 10.6 mg; p = 0.086) and on POD 2 (9.2 mg vs 4.6 mg; p = 0.021). There were no differences in postoperative nausea/vomiting or time to first postoperative bowel movement between the groups. No direct blockade-related complications were observed and the length of stay was similar between TEA and TAP groups. Conclusion: TEA is more efficient for acute postoperative pain than TAP block on day of surgery, but not on the first two PODs. No differences in pain management-related complications were detected.Peer reviewe

Systematic review of analgesics and dexamethasone for post-tonsillectomy pain in adults

Background: Intense pain can last several days after tonsillectomy. It is often undertreated and improved analgesic strategies that can be safely used at home are needed. Methods: We conducted a systematic review and meta-analysis on the effectiveness of systemic medications used for post-tonsillectomy pain in adult and adolescent (13 yr old) patients. Studies were identified from PubMed, the Cochrane Library, and by hand searching reference lists from studies and review articles. Randomised, double-blind, placebo-controlled studies reporting on pain intensity or use of rescue analgesia were included. Results: Twenty-nine randomised controlled trials representing 1816 subjects met the inclusion criteria. Follow-up time was Conclusions: Single analgesics and dexamethasone provide only a weak to moderate effect for post-tonsillectomy pain on the day of operation and thus a multimodal analgesic strategy is recommended. Short follow-up times and clinical heterogeneity of studies limit the usefulness of results.Peer reviewe

Complexity Thresholds in Inclusion Logic

Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are relatively well understood. Inclusion logic is similar to these team-based logical formalisms with the exception that it corresponds to deterministic polynomial time in ordered models. In this article we examine connections between syntactical fragments of inclusion logic and different complexity classes in terms of two computational problems: maximal subteam membership and the model checking problem for a fixed inclusion logic formula. We show that very simple quantifier-free formulae with one or two inclusion atoms generate instances of these problems that are complete for (non-deterministic) logarithmic space and polynomial time. Furthermore, we present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models

Undefinability in Inquisitive Logic with Tensor

Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.Peer reviewe

Young starless cores embedded in the magnetically dominated Pipe Nebula

The Pipe Nebula is a massive, nearby dark molecular cloud with a low star-formation efficiency which makes it a good laboratory to study the very early stages of the star formation process. The Pipe Nebula is largely filamentary, and appears to be threaded by a uniform magnetic field at scales of few parsecs, perpendicular to its main axis. The field is only locally perturbed in a few regions, such as the only active cluster forming core B59. The aim of this study is to investigate primordial conditions in low-mass pre-stellar cores and how they relate to the local magnetic field in the cloud. We used the IRAM 30-m telescope to carry out a continuum and molecular survey at 3 and 1 mm of early- and late-time molecules toward four selected starless cores inside the Pipe Nebula. We found that the dust continuum emission maps trace better the densest regions than previous 2MASS extinction maps, while 2MASS extinction maps trace better the diffuse gas. The properties of the cores derived from dust emission show average radii of ~0.09 pc, densities of ~1.3x10^5 cm^-3, and core masses of ~2.5 M_sun. Our results confirm that the Pipe Nebula starless cores studied are in a very early evolutionary stage, and present a very young chemistry with different properties that allow us to propose an evolutionary sequence. All of the cores present early-time molecular emission, with CS detections toward all the sample. Two of them, Cores 40 and 109, present strong late-time molecular emission. There seems to be a correlation between the chemical evolutionary stage of the cores and the local magnetic properties that suggests that the evolution of the cores is ruled by a local competition between the magnetic energy and other mechanisms, such as turbulence.Comment: Accepted for publication in ApJ. 15 pages, 5 figures, 9 table