A Note on the Use of Sum in the Logic of Proofs

The Logic of Proofs~LP, introduced by Artemov, encodes the same reasoning as the modal logic~S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application~$\cdot$, positive introspection~!, and sum~+) are sufficient to mimic provability concealed in S4~modality. While the first two operations go back to G{\"o}del, the exact role of~+ remained somewhat unclear. In particular, it was not known whether the other two operations are sufficient by themselves. We provide a positive answer to this question under a very weak restriction on the axiomatization of LP.

Right ventricular rupture after lateral thoracotomy for removal of rib-associated telangiectatic osteosarcoma in a dog

OBJECTIVE: To describe a case of a focal right ventricular rupture following removal of a rib-associated telangiectatic osteosarcoma (TOS) in a dog. CASE SUMMARY: A 2-year-old spayed female mixed-breed dog, weighing 20 kg, was presented in compensated hypovolemic shock due to active bleeding into the thoracic cavity. The dog was stabilized with appropriate fluid administration. Subsequent computed tomographic examination revealed a large mineralized mass originating from the body of a rib and displacing the heart. Two days after surgical removal of this mass, focal right ventricular rupture occurred and the dog died. The mass was later identified as a TOS. NEW OR UNIQUE INFORMATION PROVIDED: Although hemothorax secondary to TOS has been described previously, this report describes for the first time, spontaneous focal right ventricular rupture as a rare complication of thoracotomy and rib resection for the removal of a rib-associated, intrathoracic TOS.

Chronic intervertebral disk herniation associated with fused vertebrae treated by vertebral lateral corpectomy in a cat

A 10-year-old Domestic Shorthair cat was admitted for chronic ambulatory paraparesis and a spinal malformation. The clinical examination revealed paraparesis accentuated on the left side. Thoracolumbar radiographs revealed a spinal malformation with a narrowed intervertebral space between L1 and L2, and a dorsal fusion at the level of L2-L3 with a common dorsal process. Magnetic resonance imaging (MRI) revealed an intervertebral disk herniation with a ventral compression of the spinal cord at the level of L1/2. A standard vertebral lateral corpectomy with a foraminotomy was performed with a good outcome.

State of the science on controversial topics: missing maxillary lateral incisors - a report of the Angle Society of Europe 2012 meeting

BACKGROUND The optimal long-term management of the congenitally missing maxillary lateral incisor continues to cause controversy within the specialty. The Angle Society of Europe meeting 2012 dedicated a day to address some of the current controversies relating to the management of these missing lateral incisors. FINDINGS The format of the day consisted of morning presentations and afternoon breakout sessions to discuss a variety of questions related to the management of missing lateral incisors. CONCLUSIONS The consensus viewpoint from this day was that the care of patients with congenitally missing lateral incisors is best achieved through a multi-disciplinary approach. The current evidence base is weak, and further well-designed, prospective trials are needed.

Illusions of fusions: assessing cervical vertebral fusion on lateral cephalograms, multidetector computed tomographs, and cone-beam computed tomographs

INTRODUCTION The aims of this study were to compare lateral cephalograms with other radiologic methods for diagnosing suspected fusions of the cervical spine and to validate the assessment of congenital fusions and osteoarthritic changes against the anatomic truth. METHODS Four cadaver heads were selected with fusion of vertebrae C2 and C3 seen on a lateral cephalogram. Multidetector computed tomography (MDCT) and cone-beam computed tomography (CBCT) were performed and assessed by 5 general radiologists and 5 oral radiologists, respectively. Vertebrae C2 and C3 were examined for osseous fusions, and the left and right facet joints were diagnosed for osteoarthritis. Subsequently, the C2 and C3 were macerated and appraised by a pathologist. Descriptive analysis was performed, and interrater agreements between and within the groups were computed. RESULTS All macerated specimens showed osteoarthritic findings of varying degrees, but no congenital bony fusion. All observers agreed that no fusion was found on MDCT or CBCT. They disagreed on the prevalence of osteoarthritic deformities (general radiologists/MDCT, 100%; oral radiologists/CBCT, 93.3%) and joint space assessment in the facet joints (kappa = 0.452). The agreement within the rater groups differed considerably (general radiologists/MDCT, kappa = 0.612; oral radiologists/CBCT, kappa = 0.240). CONCLUSIONS Lateral cephalograms do not provide dependable data to assess the cervical spine for fusions and cause false-positive detections. Both MDCT interpreted by general radiologists and CBCT interpreted by oral radiologists are reliable methods to exclude potential fusions. Degenerative osteoarthritic changes are diagnosed more accurately and consistently by general radiologists evaluating MDCT.

Far lateral lumbar disc extrusion: MRI findings and surgical treatment

This case report describes the magnetic resonance imaging (MRI) findings and the treatment of a far lateral extrusion of disc material at the sixth and seventh lumbar vertebrae (L6-L7) in a five-year-old male Alpine Dachsbracke dog referred to our hospital for investigation of the complaint of a one week progressive lameness in the left pelvic limb and poorly localized back pain. An extra-foraminal left lateral disc herniation impinging on the sixth lumbar nerve root was diagnosed by MRI examinations. Due to the far lateral position of the extruded disc material on MRI, surgical opening of the spinal canal was not necessary. Removal of the herniated soft disc material impinging on the L6 nerve root, and fenestration of the L6-L7 disc was performed laterally. To the author's knowledge 'far-lateral' disc herniation beyond the neuroforamen without any spinal canal contact has not been described in dogs until now. A complete recovery with no evidence of pain was achieved only after a couple of weeks after surgery. We acknowledge that it is possible that other pathological mechanisms may have contributed to clinical signs and to a delayed recovery.

Effect of lateral meniscectomy and osteochondral grafting of a lateral femoral condylar defect on contact mechanics: a cadaveric study in dogs

BACKGROUND Osteochondral autograft transfer (OAT) aims at restoring normal articular cartilage surface geometry and articular contact mechanics. To date, no studies have evaluated the contact mechanics of the canine stifle following OAT. Additionally, there are no studies that evaluated the role of the meniscus in contact mechanics following OAT in human or canine femorotibial joints. The objective of this study was to measure the changes in femorotibial contact areas (CA), mean contact pressure (MCP) and peak contact pressure (PCP) before and after osteochondral autograft transplantation (OAT) of a simulated lateral femoral condylar cartilage defect with an intact lateral meniscus and following lateral meniscectomy. RESULTS With an intact lateral meniscus, creation of an osteochondral defect caused a decrease in MCP and PCP by 11% and 30%, respectively, compared to the intact stifle (p < 0.01). With an intact meniscus, implanting an osteochondral graft restored MCP and PCP to 96% (p = 0.56) and 92% (p = 0.41) of the control values. Lateral meniscectomy with grafting decreased CA by 54% and increased PCP by 79% compared to the intact stifle (p < 0.01). CONCLUSIONS OAT restored contact pressures in stifles with a simulated lateral condylar defect when the meniscus was intact. The lateral meniscus has a significant role in maintaining normal contact pressures in both stifles with a defect or following OAT. Meniscectomy should be avoided when a femoral condylar defect is present and when performing OAT.

Lateral incisor agenesis, canine impaction and characteristics of supernumerary teeth in a South European male population

Objective: To assess the prevalence of lateral incisor agenesis impacted canines and supernumerary teeth in a young adult male population. Materials and Methods: The panoramic radiographs of 1745 military students (mean age: 18.6 ± 0.52 years) who attended the Center of Aviation Medicine of the Armed Forces of Greece during the period 1997-2011 were initially analyzed for lateral incisor agenesis by two observers. After exclusion of the known orthodontic cases, a subgroup of 1636 examinees (mean age: 18.6 ± 0.44 years) was evaluated for canine impaction and supernumerary teeth. Results: Twenty-eight missing lateral incisors were observed in 22 military students, indicating an incidence of 1.3% in the investigated population. No lateral incisor agenesis was detected in the mandibular arch. A prevalence rate of 0.8% was determined for canine impaction in the sample of young adults. The majority of impacted teeth (86.7%) were diagnosed in the maxillary arch. Thirty-five supernumerary teeth were observed in 24 examinees (prevalence rate: 1.5%). The ratio of supernumerary teeth located in the maxilla versus the mandible was 2.2:1. The most common type of supernumerary tooth was the upper distomolar. Conclusion: The prevalence of lateral incisor agenesis, canine impaction, and supernumerary teeth ranged from 0.8 to 1.5% in the sample of male Greek military students.

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.