Knowledge Spaces and the Completeness of Learning Strategies

We propose a theory of learning aimed to formalize some ideas underlying Coquand's game semantics and Krivine's realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite positive and negative information that guides a learning strategy. We use a leading example to illustrate how non-constructive proofs lead to continuous and effective learning strategies over knowledge spaces, and prove that our learning semantics is sound and complete w.r.t. classical truth, as it is the case for Coquand's and Krivine's approaches

Toward the interpretation of non-constructive reasoning as non-monotonic learning

AbstractWe study an abstract representation of the learning process, which we call learning sequence, aiming at a constructive interpretation of classical logical proofs, that we see as learning strategies, coming from Coquand’s game theoretic interpretation of classical logic. Inspired by Gold’s notion of limiting recursion and by the Limit-Computable Mathematics by Hayashi, we investigate the idea of learning in the limit in the general case, where both guess retraction and resumption are allowed. The main contribution is the characterization of the limits of non-monotonic learning sequences in terms of the extension relation between guesses

Knowledge Spaces and the Completeness of Learning Strategies

We propose a theory of learning aimed to formalize some ideas underlying Coquand\u27s game semantics and Krivine\u27s realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite positive and negative information that guides a learning strategy. We use a leading example to illustrate how non-constructive proofs lead to continuous and effective learning strategies over knowledge spaces, and prove that our learning semantics is sound and complete w.r.t. classical truth, as it is the case for Coquand\u27s and Krivine\u27s approaches

Non-monotonic Pre-fixed Points and Learning

Comment: In Proceedings FICS 2013, arXiv:1308.589

Interactive Learning-Based Realizability for Heyting Arithmetic with EM1

We apply to the semantics of Arithmetic the idea of ``finite approximation'' used to provide computational interpretations of Herbrand's Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for $\vee, \exists$) over a suitable structure \StructureN for the language of natural numbers and maps of G\"odel's system \SystemT. We introduce a new Realizability semantics we call ``Interactive learning-based Realizability'', for Heyting Arithmetic plus \EM_1 (Excluded middle axiom restricted to $\Sigma^0_1$ formulas). Individuals of \StructureN evolve with time, and realizers may ``interact'' with them, by influencing their evolution. We build our semantics over Avigad's fixed point result, but the same semantics may be defined over different constructive interpretations of classical arithmetic (Berardi and de' Liguoro use continuations). Our notion of realizability extends intuitionistic realizability and differs from it only in the atomic case: we interpret atomic realizers as ``learning agents''

Systemic immune-inflammation index predicts the clinical outcome in patients with metastatic renal cell cancer treated with sunitinib.

Background: In this retrospective analysis, we explored the prognostic and predictive value of the systemic immune-inflammation index (SII), based on lymphocyte, neutrophil, and platelet counts, at baseline and changes at week 6 during first-line sunitinib in patients with metastatic renal cell cancer (RCC).Results: Patients were stratified into high SII (? 730) and low SII (< 730) groups. SII was associated with objective response, p < 0.0001. The median PFS was 6.3 months (95% CI 5.5–8.9) in patients with SII ? 730 and 18.7 months (95% CI 14.7–22.8) in those with SII < 730, p < 0.0001. The median OS was 43.6 months (95% CI 35.3–52.1) in patients with SII < 730, and 13.5 months (95% CI 9.8–18.5) in those with SII ? 730, p < 0.0001. In multivariate analysis, performance status, IMDC score and SII were able to predict OS (HR = 3.29, HR = 1.71 and HR = 1.79, respectively).Materials and Methods: We included 335 consecutive RCC patients treated with first-line sunitinib. The X-tile 3.6.1 software (Yale University, New Haven, CT) was used for bioinformatic analysis of the data to determine the cutoff value of SII. Progression-free survival (PFS), overall survival (OS) and their 95% confidence interval (95% CI) were estimated by Kaplan-Meier method and compared with logrank test. The impact of SII conversion at week 6 of treatment on PFS and OS was evaluated by Cox regression analyses.Conclusions: The SII and its changes during treatment represent a powerful prognostic indicator of clinical outcome in patients with metastatic RCC

Cabozantinib After a Previous Immune Checkpoint Inhibitor in Metastatic Renal Cell Carcinoma: A Retrospective Multi-Institutional Analysis

Background: Angiogenesis has been recognized as the most important factor for tumor invasion, proliferation, and progression in metastatic renal cell carcinoma (mRCC). However, few clinical data are available regarding the efficacy of cabozantinib following immunotherapy. Objective: To describe the outcome of cabozantinib in patients previously treated with immunotherapy. Patients and methods: Patients with mRCC who received cabozantinib immediately after nivolumab were included. The primary endpoint was to assess the outcome in terms of efficacy and activity. Results: Eighty-four mRCC patients met the criteria to be included in the final analysis. After a median follow-up of 9.4 months, median overall survival was 17.3 months. According to the IMDC criteria, the rates of patients alive at 12 months in the good, intermediate, and poor prognostic groups were 100%, 74%, and 33%, respectively (p < 0.001). The median progression-free survival (PFS) was 11.5 months (95% CI 8.3-14.7); no difference was found based on duration of previous first-line therapy or nivolumab PFS. The overall response rate was 52%, stable disease was found as the best response in 25.3% and progressive disease in 22.7% of patients. Among the 35 patients with progressive disease on nivolumab, 26 (74.3%) patients showed complete/partial response or stable disease with cabozantinib as best response after nivolumab. The major limitations of this study are the retrospective nature and the short follow-up. Conclusions: Cabozantinib was shown to be effective and active in patients previously receiving immune checkpoint inhibitors. Therefore, cabozantinib can be considered a valid therapeutic option for previously treated mRCC patients, irrespective of the type and duration of prior therapies

Revisional Surgery After One Anastomosis/Minigastric Bypass: an Italian Multi-institutional Survey

Background: Efficacy and safety of OAGB/MGB (one anastomosis/mini gastric bypass) have been well documented both as primary and as revisional procedures. However, even after OAGB/MGB, revisional surgery is unavoidable in patients with surgical complications or insufficient weight loss. Methods: A questionnaire asking for the total number and demographics of primary and revisional OAGB/MGBs performed between January 2006 and July 2020 was e-mailed to all S.I.C. OB centres of excellence (annual caseload > 100; 5-year follow-up > 50%). Each bariatric centre was asked to provide gender, age, preoperative body mass index (BMI) and obesity-related comorbidities, previous history of abdominal or bariatric surgery, indication for surgical revision of OAGB/MGB, type of revisional procedure, pre- and post-revisional BMI, peri- and post-operative complications, last follow-up (FU). Results: Twenty-three bariatric centres (54.8%) responded to our survey reporting a total number of 8676 primary OAGB/MGBS and a follow-up of 62.42 ± 52.22 months. A total of 181 (2.08%) patients underwent revisional surgery: 82 (0.94%) were suffering from intractable DGER (duodeno-gastric-esophageal reflux), 42 (0.48%) were reoperated for weight regain, 16 (0.18%) had excessive weight loss and malnutrition, 12 (0.13%) had a marginal ulcer perforation, 10 (0.11%) had a gastro-gastric fistula, 20 (0.23%) had other causes of revision. Roux-en-Y gastric bypass (RYGB) was the most performed revisional procedure (109; 54%), followed by bilio-pancreatic limb elongation (19; 9.4%) and normal anatomy restoration (19; 9.4%). Conclusions: Our findings demonstrate that there is acceptable revisional rate after OAGB/MGB and conversion to RYGB represents the most frequent choice