On the Algebraizability of Annotated Logics
نویسندگان
چکیده
Annotated logics were introduced by V. S. Subrahmanian as logical foundations for computer programming. One of the difficulties of these systems from the logical point of view is that they are not structural, i.e., their consequence relations are not closed under substitutions. In this paper we give systems of annotated logics that are equivalent to those of Subrahmanian in the sense that everything provable in one type of system has a translation that is provable in the other. Moreover these new systems are structural. We prove that these systems are weakly congruential, namely, they have an infinite system of congruence 1-formulas. Moreover, we prove that an annotated logic is algebraizable (i.e., it has a finite system of congruence formulas,) if and only if the lattice of annotation constants is finite.
منابع مشابه
Possible-translations Algebraizability
The interest of investigating combinations of logics has a philosophical side, a purely logic-theoretical side and promising applicational interests. This paper concentrates on the logic-theoretical side and studies some general methods for combination and decomposition, taking into account that the general idea of combining logics requires methods not only for building new logics, but also for...
متن کاملAlgebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices
We study the algebraizability of the logics constructed using literal-paraconsistent and literal-paracomplete matrices described by Lewin and Mikenbergin[11] proving that theyare all algebraizable in the sense of Blok We study the algebraizability of the logics constructed using literal-paraconsistent and literal-paracomplete matrices described by Lewin and Mikenberg in [11], proving that they ...
متن کاملLeibniz filters and the strong version of a protoalgebraic logic
A filter of a sentential logic S is Leibniz when it is the smallest one among all the S-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic S+ defined by the class of all S-matrices whose filter is Leibniz, which is called the strong version of S , in the context of protoalgebraic logics with theorems. Topics studied include ...
متن کاملCompeting Logics and Healthcare; Comment on “(Re) Making the Procrustean Bed? Standardization and Customization as Competing Logics in Healthcare”
This paper offers a short commentary on the editorial by Mannion and Exworthy. The paper highlights the positive insights offered by their analysis into the tensions between the competing institutional logics of standardization and customization in healthcare, in part manifested in the conflict between managers and professionals, and endorses the plea of the authors for further research in this...
متن کاملOn theorem proving in annotated logics
Annotated logics are a class of paraconsistent logics[?] that have been used to provide the semantical foundations of various reasoning systems which may contain useful inconsistent or imprecise information. They were initially proposed by Subrahmanian based on a specific set, viz. [0, 1] ∪ {>}, of truth values[?], and subsequently studied from the viewpoints of foundation and logic programming...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Studia Logica
دوره 59 شماره
صفحات -
تاریخ انتشار 1997