An Exposition of Modal Logic

Abstract

In logic, modality is the intertwined reference of the actual, the possible, and the neces-sary, and a modal logic is a formal language composed to speak consistently about all three. After an introduction which contextualizes the pursuit of modal logic in an era of highly-developed mathematical logic, Chapter 1 undertakes the task of introducing modality into the syntax of modern propositional logic and examines the predicaments which ensue while interpreting modal statements and attempting to determine their validity. Chapter 2 is a de-tailed exposition of possible-worlds interpretations of modal logic, with special attention paid to answers regarding the validity of modal formulas which interpreting statements of modal logic as referring to possible worlds can provide. Chapter 3 turns to mathematics for alternative schemes of interpretation and explores semantics for modal logic drawn from the subfield of mathematics known as topology. Finally, Chapter 4 examines a variant of modal logic, geared towards a temporal reading of modality, called tense logic. In lieu of a conclusion, Chapter 4 returns to the possible-worlds semantics and the topological seman-tics of previous chapters and shows how each of these may be used to interpret tense-logical statements.