Coalgebraic Fuzzy geometric logic
This work addresses theoretical foundations for fuzzy logic and coalgebra, likely incremental for researchers in mathematical logic and category theory.
The paper developed a framework for coalgebraic fuzzy geometric logic by adding modal operators to fuzzy geometric logic using coalgebra methods, and introduced models based on fuzzy topological spaces and bisimulations.
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric logic. To define the modal operators, we introduce a notion of fuzzy-open predicate lifting. Based on coalgebras for an endofunctor $T$ on the category $\textbf{Fuzzy-Top}$ of fuzzy topological spaces and fuzzy continuous maps, we build models for the coalgebraic fuzzy geometric logic. Bisimulations for the defined models are discussed in this work.