Toward a probability theory for product logic: states, integral representation and reasoning

The aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure. Furthermore, the relation between states and measures is shown to be one-one. In addition, we study geometrical properties of the convex set of states and show that extremal states, i.e., the extremal points of the state space, are the same as the truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal logic for probabilistic reasoning on product logic events and prove soundness and completeness with respect to probabilistic spaces, where the algebra is a free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur

Projectivity in (bounded) integral residuated lattices

In this paper we study projective algebras in varieties of (bounded) commutative integral residuated lattices from an algebraic (as opposed to categorical) point of view. In particular we use a well-established construction in residuated lattices: the ordinal sum. Its interaction with divisibility makes our results have a better scope in varieties of divisibile commutative integral residuated lattices, and it allows us to show that many such varieties have the property that every finitely presented algebra is projective. In particular, we obtain results on (Stonean) Heyting algebras, certain varieties of hoops, and product algebras. Moreover, we study varieties with a Boolean retraction term, showing for instance that in a variety with a Boolean retraction term all finite Boolean algebras are projective. Finally, we connect our results with the theory of Unification

Structural and universal completeness in algebra and logic

In this work we study the notions of structural and universal completeness both from the algebraic and logical point of view. In particular, we provide new algebraic characterizations of quasivarieties that are actively and passively universally complete, and passively structurally complete. We apply these general results to varieties of bounded lattices and to quasivarieties related to substructural logics. In particular we show that a substructural logic satisfying weakening is passively structurally complete if and only if every classical contradiction is explosive in it. Moreover, we fully characterize the passively structurally complete varieties of MTL-algebras, i.e., bounded commutative integral residuated lattices generated by chains.Comment: This is a preprin

Gluing residuated lattices

We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction (also known as ordinal sum for residuated structures), where algebras that intersect only in the top element are glued together, we first consider the gluing on a congruence filter, and then add a lattice ideal as well. We characterize such constructions in terms of (possibly partial) operators acting on (possibly partial) residuated structures. As particular examples of gluing constructions, we obtain the non-commutative version of some rotation constructions, and an interesting variety of semilinear residuated lattices that are 2-potent. This study also serves as a first attempt toward the study of amalgamation of non-commutative residuated lattices, by constructing an amalgam in the special case where the common subalgebra in the V-formation is either a special (congruence) filter or the union of a filter and an ideal.Comment: This is a preprint. The final version of this work appears in Orde

Neuronal Premotor Networks Involved in Eyelid Responses: Retrograde Transneuronal Tracing with Rabies Virus from the Orbicularis Oculi Muscle in the Rat

Retrograde transneuronal tracing with rabies virus from the right orbicularis oculi muscle was used to identify neural networks underlying spontaneous, reflex, and learned blinks. The kinetics of viral transfer was studied at sequential 12 hr intervals between 3 and 5 d after inoculation. Rabies virus immunolabeling was combined with the immunohistochemical detection of choline acetyltransferase expression in brainstem motoneurons or Fluoro-Ruby injections in the rubrospinal tract. Virus uptake involved exclusively orbicularis oculi motoneurons in the dorsolateral division of the facial nucleus. At 3-3.5 d, transneuronal transfer involved premotor interneurons of trigeminal, auditory, and vestibular reflex pathways (in medullary and pontine reticular formation, trigeminal nuclei, periolivary and ventral cochlear nuclei, and medial vestibular nuclei), motor pathways (dorsolateral quadrant of contralateral red nucleus and pararubral area), deep cerebellar nuclei (lateral portion of interpositus nucleus and dorsolateral hump ipsilaterally), limbic relays (parabrachial and Kölliker-Fuse nuclei), and oculomotor structures involved in eye-eyelid coordination (oculomotor nucleus, supraoculomotor area, and interstitial nucleus of Cajal). At 4 d, higher order neurons were revealed in trigeminal, auditory, vestibular, and deep cerebellar nuclei (medial, interpositus, and lateral), oculomotor and visual-related structures (Darkschewitsch, nucleus of the posterior commissure, deep layers of superior colliculus, and pretectal area), lateral hypothalamus, and cerebral cortex (particularly in parietal areas). At 4.5 and 5 d the labeling of higher order neurons occurred in hypothalamus, cerebral cortex, and blink-related areas of cerebellar cortex. These results provide a comprehensive picture of the premotor networks mediating reflex, voluntary, and limbic-related eyelid responses and highlight potential sites of motor learning in eyelid classical conditioning

Taking Pain Out of NGF: A “Painless” NGF Mutant, Linked to Hereditary Sensory Autonomic Neuropathy Type V, with Full Neurotrophic Activity

During adulthood, the neurotrophin Nerve Growth Factor (NGF) sensitizes nociceptors, thereby increasing the response to noxious stimuli. The relationship between NGF and pain is supported by genetic evidence: mutations in the NGF TrkA receptor in patients affected by an hereditary rare disease (Hereditary Sensory and Autonomic Neuropathy type IV, HSAN IV) determine a congenital form of severe pain insensitivity, with mental retardation, while a mutation in NGFB gene, leading to the aminoacid substitution R100W in mature NGF, determines a similar loss of pain perception, without overt cognitive neurological defects (HSAN V). The R100W mutation provokes a reduced processing of proNGF to mature NGF in cultured cells and a higher percentage of neurotrophin secreted is in the proNGF form. Moreover, using Surface Plasmon Resonance we showed that the R100W mutation does not affect NGF binding to TrkA, while it abolishes NGF binding to p75NTR receptors. However, it remains to be clarified whether the major impact of the mutation is on the biological function of proNGF or of mature NGF and to what extent the effects of the R100W mutation on the HSAN V clinical phenotype are developmental, or whether they reflect an impaired effectiveness of NGF to regulate and mediate nociceptive transmission in adult sensory neurons. Here we show that the R100 mutation selectively alters some of the signaling pathways activated downstream of TrkA NGF receptors. NGFR100 mutants maintain identical neurotrophic and neuroprotective properties in a variety of cell assays, while displaying a significantly reduced pain-inducing activity in vivo (n = 8–10 mice/group). We also show that proNGF has a significantly reduced nociceptive activity, with respect to NGF. Both sets of results jointly contribute to elucidating the mechanisms underlying the clinical HSAN V manifestations, and to clarifying which receptors and intracellular signaling cascades participate in the pain sensitizing action of NGF

Case Report: Spontaneous lung intercostal hernia series and literature review

Spontaneous lung intercostal hernia (SLIH) is a rare condition potentially carrying severe morbidity. About 120 cases have been described so far, with an apparently increasing number of reports in recent years. The main presenting findings are chest pain and bulging, with ecchymosis in the affected area, hemoptysis, respiratory distress, and signs of infection or incarceration being described as well. The gold standard treatment has not been established, and conservative management has been advocated as first-line treatment for asymptomatic patients. Here, we report a case series of five patients, and surgical repair was deemed necessary for four of them either at first evaluation or after failure of conservative management. One patient remains under surveillance and conservative management. We believe that SLIH surgical repair should be considered as first-line treatment for fit patients, due to the uncertainty of its mid- and long-term impact and described pejorative trend/defect enlargement. A proposed algorithm for SLIH management is also presented

Dirofilaria repens testicular infection in child, Italy

Testicular Dirofilaria repens infection was identified and confirmed by sequence analysis in a child in northeastern Italy. Because human dirofilariasis is emerging in southern and eastern Europe, this parasitic infection should be considered in the differential diagnosis of scrotal swelling in disease-endemic countries to avoid unnecessary interventions, such as orchiectomy

A unique case of foreign body aspiration and recurrent pneumothorax

Paediatric foreign body aspiration can be related to a high morbidity/mortality rate, especially in young children, and pneumothorax can be a severe associated issue. We describe a case of a 13-year-old girl with recurrent pneumothorax in bilateral bullous lung, twice previously treated at our institution by robotassisted bullectomy, and once again showing same signs and symptoms. At conventional thoracoscopy an inorganic foreign body was found to be located pointing upwards the apex. We believe this may have acted as a contributory cause in the persistence of the clinical picture, despite the surgical removal of the underlying pathology