Abstract
The fuzzy and algebraic treatment of the hyperstructured logical variables and complex logical expressions are centric in inference methodologies of many contemporary disciplines such as cognitive informatics, cognitive computing, computational linguistics, cognitive semantics, causal inferences, computing with words, cognitive robotics, and computational intelligence. This paper presents a denotational mathematics of fuzzy logical algebra and a formal theory for cognitive inference systems. Fuzzy logical propositions are formally modeled based on fuzzy logical expressions and variables. An algebraic structure of extended fuzzy logic is created by a set of algebraic operators on formal fuzzy propositions. Fuzzy logical algebra provides a denotational mathematical means for algebraic manipulations of fuzzy logical expressions. A set of insightful and interesting properties of fuzzy logical algebra is revealed.
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