Abstract Parametric Classes and Abstract Data Types defined by Classical and Constructive Logical Methods

AbstractWe introduce a methodology to treat abstract data types (ADT), abstract parametric classes (APC) and subclasses, together with appropriate inheritance properties, by means of first order theories. The notion of a first order theory axiomatizing an ADT is based on the notion of isoinitial model and has been proposed by the authors in previous papers (Bertoni et al. (1979), Bertoni et al. (1983), Bertoni et al. (1984)). A theory formalizing an APC is seen, in this paper, as a theory T incompletely axiomatizing an ADT. Given a class C of ADT's, the class formalized by T can be seen (under suitable soundness conditions on T) as the class of the instances of T over C. An instantiation of T by an ADT I of C completes T into a T′ formalizing an ADT I′, which extends I and inherits the properties of the APC T.We use both classical and constructive methods in the following sense: on the one hand, the semantics is based on classical model theory; on the other hand, the soundness of a consistent axiomatization can be analyzed by purely syntactical methods, in terms of provability within suitable constructive systems.A theory T formalizing an APC (or an ADT) is not given by a list of axioms, but by a suitable "APC-expression", which explicitly or implicitly (but effectively ) defines the axioms of T. We have APC-expressions to define APC's, to extend already defined APC's and to instantiate APC's (into ADT's or subclasses). We allow also "recurrence APC-expressions". At the end of the paper we give some examples showing how the proposed methodology works

On Uniformly Constructive and Semiconstructive Formal Systems

We propose a formalization of two notions of uniformly constructive formal system, we call uniform e-constructivity and uniform r-constructivity. On an intuitive ground, the first (extended) notion concerns formal systems characterized by calculi with the following properties: any proof of a formula such as A {vee} B (of a formula such as xA(x)) contains sufficient information to build up a proof of A or a proof of B (respectively, a proof of A(t) for some term t). On the other hand, the second (restricted) notion takes into account the same properties only for A {vee} B, xA(x) and t closed. Our treatment allows us to analyze both "weak" systems (containing only purely logical principles or, at most, weak mathematical axioms) and "powerful" ones (comparable with Intuitionistic Arithmetic or extensions of it), and exceeds the class of intuitionistic systems, as well as the class of systems for which normalization or cut-elimination theorems can be stated; moreover, it allows us to tackle systems to which the variants of recursive realizability interpretation most known in literature are not applicable. We also introduce a weaker notion of uniformly semiconstructive formal system, requiring classical logic to complete the "constructive content" involved in its proofs. We give examples of uniformly constructive and uniformly semiconstructive systems. Finally, we provide an example of a system which is not uniformly constructive (more than this, not uniformly semiconstructive), yet satisfying the disjunction property and the explicit definability property

Significance of IgM antibody to hepatitis C virus in patients with chronic hepatitis C

We assessed the correlation between the positivity for serum IgM antibody to hepatitis C virus and the activity of liver disease in patients with chronic hepatitis C virus infection. Serum samples were taken from 10 antibody to hepatitis C virus‐positive asymptomatic patients with normal serum ALT levels, from 14 untreated patients with clinically and histologically proven chronic hepatitis C and from 26 patients with clinically and histologically proven chronic hepatitis C assigned to receive recombinant interferon α‐2a (6 million IU three times a week for 6 mo). Each serum specimen was tested for IgM antibody to hepatitis C virus‐associated C 100‐3 antigen by enzyme‐linked immunosorbent assay. Patients were observed for at least 12 mo. All 10 patients with normal ALT values tested negative for IgM antibody to hepatitis C virus. In contrast, 33 of 40 (82%) patients with chronic hepatitis C had IgM antibody to hepatitis C virus, and a positive correlation was seen between the ALT level and the level of IgM antibody to hepatitis C virus (r = 0.803, p < 0.001). During interferon treatment, ALT levels declined into the normal range in 18 of 26 treated patients (69%) and remained normal after stopping treatment in 8 patients (31%). In untreated patients, in treated patients who did not respond to interferon treatment and in responder patients who relapsed, no significant changes in IgM antibody to hepatitis C virus levels were seen during the study period. In contrast, IgM antibody to hepatitis C virus became undetectable by the end of interferon treatment in seven of eight patients with a sustained response. In conclusion, we found a positive correlation between the presence of serum IgM antibody to hepatitis C virus and the activity of the hepatitis C‐induced liver disease. In patients with chronic hepatitis C showing a response to α‐interferon treatment, the disappearance of IgM antibody to hepatitis C virus predicted that the response would be sustained. (HEPATOLOGY 1992;15:998–1001). Copyright © 1992 American Association for the Study of Liver Disease

Serological and histological aspects of hepatitis C virus infection in alcoholic patients

The recent cloning of the genome of hepatitis C virus (HCV) has allowed the detection of antibodies to HCV (anti-HCV) in human serum. The presence of serum antibodies to HCV often indicates active infection with HCV. We have assessed the serological and histological features in a group of alcoholic patients with chronic liver disease and have evaluated the possible etiologic rote of HCV infection in the development of liver damage. Serum samples and liver biopsy specimens were obtained from 41 consecutive patients, all having a definite history of alcohol abuse and evidence of chronic hypertransaminasemia. Fifteen patients (37%) were positive for anti-HCV by ELISA, and 13 (86.6%) of them were also positive by RIBA. Eleven of these patients had histologic features of chronic active hepatitis (CAH), a lesion which is not known to be induced by excessive alcohol intake. No other possible causes of CAH were found, and CAH was not present in any of the anti-HCV negative patients. In patients with CAH, mean AST to ALT ratio was less than 1 (0.6), a finding which is characteristic of viral rather than alcoholic chronic liver disease. In conclusion, our study suggests that sporadic hepatitis C virus infection plays an etiologic role in the development of chronic active liver disease in a subgroup of alcoholic patients. © 1991

A pilot study of combination therapy with ribavirin plus interferon alfa for interferon alfa-resistant chronic hepatitis C

Background/Aims: In chronic hepatitis C, interferon alfa (IFN-α) therapy fails to achieve a sustained response in approximately 75% of patients. Similarly, ribavirin induces only a transient response. The aim of this study was to evaluate whether ribavirin and IFN-α in combination could be effective in IFN-α-resistant chronic hepatitis C. Methods: Twenty patients with chronic hepatitis C resistant to a previous course of IFN-α were randomly assigned to receive either ribavirin combined with IFN-α or IFN-α alone for 6 months. Results: Serum alanine aminotransferase levels decreased significantly during therapy in both treatment groups, but after therapy, the levels remained significantly decreased only in the combination therapy group. Nine months after treatment, sustained normalization of aminotransferase levels, associated with sustained loss of serum hepatitis C virus RNA, was observed in 40% of the patients in the combination therapy group but in none of the patients treated with IFN-α alone (P < 0.05). The sustained response was accompanied by reduced hepatic necroinflammatory activity on biopsy. Conclusions: These findings suggest that ribavirin plus IFN-α combination therapy is able to induce a sustained biochemical and virological response in a significant proportion of patients with IFN-α-resistant chronic hepatitis C. © 1994