Jake Arft-Guatelli L&S Arts & Humanities
Exploring Duality in Modal Logic
Duality is a well documented property of operators in classical logic and in algebra. To give an example from natural language, “it’s not the case that it might be raining” sounds equivalent to “it must not be raining”. Generalized work surrounding duality in algebraic settings has only been explored relatively recently, but duality of classical operators for possibility and necessity can be traced back to Aristotle. My project explores the historical, natural language, and computational motivations for modal duality. I plan to depart from the existing literature in focusing on the motivations for and results of explicitly rejecting modal duality, while past authors have largely focused on generalizations of a framework accepting duals or single motivations for duality. I consider and expand upon the philosophical and logical reasons to drop duality e.g. in intuitionistic logic, for agentive modals, and in recent logics underlying computational frameworks. My overall aim is to further understand reasons for dropping duality in modal logic and explore the effects on the underlying algebraic structure.