Algebraic semantics for one-variable lattice-valued logics

The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic semantics for these logics have been obtained: most notably, for the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and intuitionistic logic, respectively. Outside the setting of first-order intermediate logics, however, a general approach is lacking. This paper provides the basis for such an approach in the setting of first-order lattice-valued logics, where formulas are interpreted in algebraic structures with a lattice reduct. In particular, axiomatizations are obtained for modal counterparts of one-variable fragments of a broad family of these logics by generalizing a functional representation theorem of Bezhanishvili and Harding for monadic Heyting algebras. An alternative proof-theoretic proof is also provided for one-variable fragments of first-order substructural logics that have a cut-free sequent calculus and admit a certain bounded interpolation property

One-variable fragments of first-order logics

The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases -- notably, the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and intuitionistic logic -- but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in this paper for the one-variable fragment of a semantically-defined first-order logic -- spanning families of intermediate, substructural, many-valued, and modal logics -- to admit a natural axiomatization. More precisely, such an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has the superamalgamation property, building on a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property.Comment: arXiv admin note: text overlap with arXiv:2209.0856

Discovery of Shocked Molecular Clouds Associated with the Shell-type Supernova Remnant RX J0046.5-7308 in the Small Magellanic Cloud

RX J0046.5−7308 is a shell-type supernova remnant (SNR) in the Small Magellanic Cloud (SMC). We carried out new 12CO(J = 1–0, 3–2) observations toward the SNR using Mopra and the Atacama Submillimeter Telescope Experiment. We found eight molecular clouds (A–H) along the X-ray shell of the SNR. The typical cloud size and mass are ∼10–15 pc and ∼1000–3000 M☉, respectively. The X-ray shell is slightly deformed and has the brightest peak in the southwestern shell where two molecular clouds A and B are located. The four molecular clouds A, B, F, and G have high intensity ratios of 12CO(J = 3–2)/12CO(J = 1–0) > 1.2, which are not attributable to any identified internal infrared sources or high-mass stars. The H I cavity and its expanding motion are found toward the SNR, which are likely created by strong stellar winds from a massive progenitor. We suggest that the molecular clouds A–D, F, and G and H I clouds within the wind-blown cavity at VLSR = 117.1–122.5 km s−1 are associated with the SNR. The X-ray spectroscopy reveals the dynamical age of - + 26000 2000 1000 yr and the progenitor mass of 30 M☉, which is also consistent with the proposed scenario. We determine physical conditions of the giant molecular cloud LIRS 36A using the large velocity gradient analysis with archival data sets of the Atacama Large Millimeter/submillimeter Array; the kinematic temperature is - + 72 37 50 K and the number density of molecular hydrogen is - + 1500 300 600 cm−3 . The next generation of γ-ray observations will allow us to study the pion-decay γ-rays from the molecular clouds in the SMC SNR.This study was financially supported by Grants-in-Aid for Scientific Research (KAKENHI) of the Japanese Society for the Promotion of Science (JSPS, grant Nos. 16K17664, 18J01417, 19K14758). H.S. was supported by “Building of Consortia for the Development of Human Resources in Science and Technology” of Ministry of Education, Culture, Sports, Science and Technology (MEXT, grant No. 01-M1-0305). H.M. was supported by World Premier International Research Center Initiative (WPI). K. Tokuda was supported by NAOJ ALMA Scientific Research (grant No. 2016-03B). H.S. was also supported by the ALMA Japan Research Grant of NAOJ Chile Observatory (grant Nos. NAOJ-ALMA-201 and NAOJALMA-208)

Algebraic semantics for one-variable lattice-valued logics

The one-variable fragment of any first-order logic may be considered as a modal logic, where the universal and existential quantifiers are replaced by a box and diamond modality, respectively. In several cases, axiomatizations of algebraic semantics for these logics have been obtained: most notably, for the modal counterparts S5 and MIPC of the one-variable fragments of first-order classical logic and intuitionistic logic, respectively. Outside the setting of first-order intermediate logics, however, a general approach is lacking. This paper provides the basis for such an approach in the setting of first-order lattice-valued logics, where formulas are interpreted in algebraic structures with a lattice reduct. In particular, axiomatizations are obtained for modal counterparts of one-variable fragments of a broad family of these logics by generalizing a functional representation theorem of Bezhanishvili and Harding for monadic Heyting algebras. An alternative proof-theoretic proof is also provided for one-variable fragments of first-order substructural logics that have a cut-free sequent calculus and admit a certain bounded interpolation property

Prevalence and appropriateness of indwelling urinary catheters in Japanese hospital wards: a multicenter point prevalence study

Abstract Background Indwelling urinary catheters are commonly used in hospitalized patients, which can lead to the development of urinary catheter complications, including catheter-associated urinary tract infection (CAUTI). Limited reports on the appropriateness of urinary catheter use exist in Japan. This study investigated the prevalence and appropriateness of indwelling urinary catheters, and the incidence of CAUTI in non-intensive care unit (non-ICU) wards in Japanese hospitals. Methods This prospective observational study was conducted in 7 non-ICU wards from 6 hospitals in Japan from October 2017 to June 2018. At each hospital the study teams evaluated urinary catheter prevalence through in-person bedside evaluation for at least 5 days of each week for 3 months. Catheter associated urinary tract infection (CAUTI) incidence and appropriateness of catheter use was collected via chart review. Results We assessed 710 catheter-days over 5528 patient-days. The mean prevalence of indwelling urinary catheter use in participating wards was 13% (range: 5% to 19%), while the mean incidence of CAUTI was 9.86 per 1000 catheter-days (range: 0 to 33.90). Approximately 66% of the urinary catheter days assessed had an appropriate indication for use (range: 17% to 81%). A physician's order for catheter placement was present in only 10% of catheterized patients. Conclusion This multicenter study provides epidemiological information about the appropriate use of urinary catheters in Japanese non-ICU wards. A multimodal intervention may help improve the appropriate use of urinary catheters.http://deepblue.lib.umich.edu/bitstream/2027.42/173458/1/12879_2022_Article_7162.pd

Discovery of shocked molecular clouds associated with the shell-type supernova remnant RX J0046.5-7308 in the Small Magellanic Cloud

RX J0046.5-7308 is a shell-type supernova remnant (SNR) in the Small Magellanic Cloud (SMC). We carried out new 12CO(J = 1-0, 3-2) observations toward the SNR using Mopra and the Atacama Submillimeter Telescope Experiment. We found eight molecular clouds (A-H) along the X-ray shell of the SNR. The typical cloud size and mass are ∼10-15 pc and ∼1000-3000 M , respectively. The X-ray shell is slightly deformed and has the brightest peak in the southwestern shell where two molecular clouds A and B are located. The four molecular clouds A, B, F, and G have high intensity ratios of 12CO(J = 3-2)/12CO(J = 1-0) > 1.2, which are not attributable to any identified internal infrared sources or high-mass stars. The H i cavity and its expanding motion are found toward the SNR, which are likely created by strong stellar winds from a massive progenitor. We suggest that the molecular clouds A-D, F, and G and H i clouds within the wind-blown cavity at V LSR = 117.1-122.5 km s-1 are associated with the SNR. The X-ray spectroscopy reveals the dynamical age of yr and the progenitor mass of ≳30 M , which is also consistent with the proposed scenario. We determine physical conditions of the giant molecular cloud LIRS 36A using the large velocity gradient analysis with archival data sets of the Atacama Large Millimeter/submillimeter Array; the kinematic temperature is K and the number density of molecular hydrogen is cm-3. The next generation of γ-ray observations will allow us to study the pion-decay γ-rays from the molecular clouds in the SMC SNR