This paper focuses on the equational class S„ of Brouwerian algebras and the equational class L„ of Heyting algebras generated by an »-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in Sn and L„ are characterized. Finally, free prod...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

Information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. The document processor, matching function and query analyzer are the main components of an information retrieval system. Document retrieval system is fundamentally based on: Boolean, vector-space, probabilistic, and language models. In this paper, a new methodology for mat...

Information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. The document processor, matching function and query analyzer are the main components of an information retrieval system. Document retrieval system is fundamentally based on: Boolean, vector-space, probabilistic, and language models. In this paper, a new methodology for mat...

There are two main results concerning the nature of constructive extensions of the countable atomless Boolean algebra, say 28 a, which appear in [1]. These results are (I) if <& is a constructive extension of 23a, then each element of # is recursive open and regular, and (II) the characterization of the simple constructive extensions 28JJJ) as those for which U is recursive open and regular. We...

In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to maximize the number (or the total weight, for the weighted case) of satisfied constraints. This problem is NP-hard in general, and, therefore, it is natural t...

The algebra of logic developed by Boole was not Boolean algebra. In this article we give a natural framework that allows one to easily reconstruct his algebra and see the difficulties it created for his successors. It is well known that modern Boolean algebra is connected with the work of George Boole [1815–1864], namely with his two books on a mathematical treatment of logic: • The Mathematica...

The common-sense view of reality is expressed logically in Boolean subset logic (each element is either definitely in or not in a subset, i.e., either definitely has or does not have a property). But quantum mechanics does not agree with this "properties all the way down" picture of microreality. Are there other coherent alternative views of reality? A logic of partitions, dual to the Boolean l...