IISER MOHALI

Abstract: What is modal logic? What is its relation to formal reasoning on the one hand and to our everyday intuitions about reasoning across different situations on the other? This introductory lecture offers a gateway into the fascinating world of modal logic, a branch of formal logic that extends classical systems of modern symbolic logic to capture notions of necessity, possibility, and other modalities. The primary objective is to introduce the key concepts of modal reasoning, including the syntax and semantics of modal expressions, the role of possible worlds, and the philosophical motivations behind modal systems. While the lecture will briefly touch upon the broader landscape of modal logic—including epistemic, deontic, and temporal modalities—its primary focus will be on Alethic Modal Logic (AML), the branch of modal logic aimed at capturing the modes of truth. The discussion will center on the standard systems of AML – K, T, S4, and S5 – and how they each formalize different interpretations of necessity and possibility. By invoking a notion of truth that goes beyond the actual world and extends across possible worlds, the lecture aims to illuminate how alethic modalities (with their formal structures) are related to our understanding of necessity, possibility, and reality.