A Concise Formalization of Partial Falsifiability, Water Logic, and Neither Nor Logic with Neutrosophic logic

This paper explores the application of neutrosophic logic to Partial Falsifiability, Water Logic, and Neither Nor Logic through a mathematical perspective. Neutrosophic logic, as an extension of classical logic, introduces truth, indeterminacy, and falsehood as independent components, offering a framework to handle uncertainty more effectively [34]. Partial Falsifiability refers to a hypothesis that can be partially refuted under certain conditions without being completely disproven [36]. Water Logic represents a flexible reasoning system that, like water, adapts and flows around obstacles rather than adhering to strict true/false dichotomies. Neither Nor Logic challenges binary choices, allowing for an indeterminate middle state to accommodate uncertainty and ambiguity(cf. [8]). By incorporating neutrosophic logic, this paper provides an initial mathematical examination of how these alternative logical systems can be formally expressed and analyzed.