Questions and Answers — a Category Arising in Linear Logic , Complexity Theory , and Set Theory

POWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES

Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...

تئوری پیچیدگی و رویکرد کلاژیسم در سیستم های ژئومورفیک

Complexity Theory and Collagist Approach in Geomorphic Systems Introduction Now, scientists know the world as complex systems that predict consequences of it is so difficult. In this situation, the systems operated by rotation manner in which chaos is order and discipline leads to chaos. Nowadays, simple idea of ​​how the world work change and convert to complex and paradoxical idea. This i...

Kolmogorov Complexity and Information Theory. With an Interpretation in Terms of Questions and Answers

Beyond first order logic: From number of structures to structure of numbers: Part II

We study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. We discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. This second part continues to study the question of catecoricitytrans...