MV-algebras freely generated by finite Kleene algebras

If V and W are varieties of algebras such that any V-algebra A has a reduct U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on objects, and identically on homomorphisms. This functor U always has a left adjoint F: W->V by general considerations. One calls F(B) the V-algebra freely generated by the W-algebra B. Two problems arise naturally in this broad setting. The description problem is to describe the structure of the V-algebra F(B) as explicitly as possible in terms of the structure of the W-algebra B. The recognition problem is to find conditions on the structure of a given V-algebra A that are necessary and sufficient for the existence of a W-algebra B such that F(B) is isomorphic to A. Building on and extending previous work on MV-algebras freely generated by finite distributive lattices, in this paper we provide solutions to the description and recognition problems in case V is the variety of MV-algebras, W is the variety of Kleene algebras, and B is finitely generated--equivalently, finite. The proofs rely heavily on the Davey-Werner natural duality for Kleene algebras, on the representation of finitely presented MV-algebras by compact rational polyhedra, and on the theory of bases of MV-algebras.Comment: 27 pages, 8 figures. Submitted to Algebra Universali

Hyperstates of Involutive MTL-Algebras that Satisfy (2x)2=2(x2)(2x)^2 = 2(x^2)

States of MV-algebras have been the object of intensive study and attempts of generalizations. The aim of this contribution is to provide a preliminary investigation for states of prelinear semihoops and hyperstates of algebras in the variety generated by perfect and involutive MTL-algebras (IBP0-algebras for short). Grounding on a recent result showing that IBP0-algebras can be constructed from a Boolean algebra, a prelinear semihoop and a suitably defined operator between them, our first investigation on states of prelinear semihoops will support and justify the notion of hyperstate for IBP0- algebras and will actually show that each such map can be represented by a probability measure on its Boolean skeleton, and a state on a suitably defined abelian l-group.Comment: 12 page

Development of a Nomogram Predicting the Risk of Persistence/Recurrence of Cervical Dysplasia

Background: Cervical dysplasia persistence/recurrence has a great impact on women's health and quality of life. In this study, we investigated whether a prognostic nomogram may improve risk assessment after primary conization. Methods: This is a retrospective multi-institutional study based on charts of consecutive patients undergoing conization between 1 January 2010 and 31 December 2014. A nomogram assessing the importance of different variables was built. A cohort of patients treated between 1 January 2015 and 30 June 2016 was used to validate the nomogram. Results: A total of 2966 patients undergoing primary conization were analyzed. The median (range) patient age was 40 (18-89) years. At 5-year of follow-up, 6% of patients (175/2966) had developed a persistent/recurrent cervical dysplasia. Median (range) recurrence-free survival was 18 (5-52) months. Diagnosis of CIN3, presence of HR-HPV types, positive endocervical margins, HPV persistence, and the omission of HPV vaccination after conization increased significantly and independently of the risk of developing cervical dysplasia persistence/recurrence. A nomogram weighting the impact of all variables was built with a C-Index of 0.809. A dataset of 549 patients was used to validate the nomogram, with a C-index of 0.809. Conclusions: The present nomogram represents a useful tool for counseling women about their risk of persistence/recurrence after primary conization. HPV vaccination after conization is associated with a reduced risk of CIN2+

Characteristics and patterns of care of endometrial cancer before and during COVID-19 pandemic

Objective: Coronavirus disease 2019 (COVID-19) outbreak has correlated with the disruption of screening activities and diagnostic assessments. Endometrial cancer (EC) is one of the most common gynecological malignancies and it is often detected at an early stage, because it frequently produces symptoms. Here, we aim to investigate the impact of COVID-19 outbreak on patterns of presentation and treatment of EC patients. Methods: This is a retrospective study involving 54 centers in Italy. We evaluated patterns of presentation and treatment of EC patients before (period 1: March 1, 2019 to February 29, 2020) and during (period 2: April 1, 2020 to March 31, 2021) the COVID-19 outbreak. Results: Medical records of 5,164 EC patients have been retrieved: 2,718 and 2,446 women treated in period 1 and period 2, respectively. Surgery was the mainstay of treatment in both periods (p=0.356). Nodal assessment was omitted in 689 (27.3%) and 484 (21.2%) patients treated in period 1 and 2, respectively (p<0.001). While, the prevalence of patients undergoing sentinel node mapping (with or without backup lymphadenectomy) has increased during the COVID-19 pandemic (46.7% in period 1 vs. 52.8% in period 2; p<0.001). Overall, 1,280 (50.4%) and 1,021 (44.7%) patients had no adjuvant therapy in period 1 and 2, respectively (p<0.001). Adjuvant therapy use has increased during COVID-19 pandemic (p<0.001). Conclusion: Our data suggest that the COVID-19 pandemic had a significant impact on the characteristics and patterns of care of EC patients. These findings highlight the need to implement healthcare services during the pandemic

Practice patterns and 90-day treatment-related morbidity in early-stage cervical cancer

To evaluate the impact of the Laparoscopic Approach to Cervical Cancer (LACC) Trial on patterns of care and surgery-related morbidity in early-stage cervical cancer

Uniform Description of Calculi for All t-norm Logics

A t-norm logic \u2112* is the logic of a standard algebra [0, 1]* = ([0, 1], *, \u2192*, 0), * being a continuous t-norm and \u2192* its residuum. The notion of canonical t-algebra introduced by Hanikov\ue1 [12] and Esteva-Godo-Montagna [9], the sets-as-signs approach to many-valued tableau systems by H\ue4hnle [10], and finite-valued reduction techniques [2, 3] allow to describe in a uniform way co-NP calculi for all t-norm logics

Geometric and proof-theoretic issues in Lukasiewicz propositional logics

Dottorato di ricerca in logica matematica ed informatica teorica. 10. ciclo. Relatori F. Montagna e D. MundiciConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal