in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...

A (general) preferential entailment is defined by a “preference relation” among “states”. States can be either interpretations or sets of interpretations, or “copies” of interpretations or of sets of interpretations, although it is known that the second kind and the fourth one produce the same notion. Circumscription is a special case of the simplest kind, where the states are interpretations. ...

In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...

The technical problem addressed in this paper is, given two rule systems for consequence relations X and Y, how to construct Y-approximations of a given X-relation. While an upper Yapproximation can be easily constructed if all Yrules are Horn, the construction of lower Yapproximations is less straightforward. We address the problem by defining the notion of coclosure under co-Horn rules, that ...

Twelve years ago, various notions of preferential entailment have been introduced. The main reference is a paper by Kraus, Lehmann and Magidor (KLM), one of the main competitor being a more general version defined by Makinson (MAK). These two versions have already been compared, but it is time to revisit these comparisons. Here are our main results: (1) These two notions are equivalent, provide...

We show that, in the nite propositional case, traditional circumscrip-tions can be fully described only from the formulas which can never come as a result of the given circumscription (the \inaccessible formulas"). Some work has already been done on the subject. Siegel and Forget have introduced the general notion of X-logic, and they have considered the case of nite proposi-tional circumscript...

In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...

China's ruling Nationalist government saw the Second World War as an opportunity to shape postwar world in favour. However, existing studies have often focused on plans territorial arrangements East Asia. This article examines how China imagined and attempted improve status of Chinese diaspora host countries. During war, envisaged removal discriminatory treatment against planned advocate racial...

This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation ≺. They are equivalent to Shoham’s so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After ...

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...