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.