Questions in Logic — ESSLLI 22

Course description
Logic is concerned with relations among sentences, such as entailment and consistency, logical operations on sentences, and how sentences can be arranged into valid arguments. Traditionally, however, logic has focused on a special class of sentences, namely, statements, which can be true or false. The course makes a case for extending logic beyond statements to encompass also questions, and describes how such an extension can be achieved in the framework of inquisitive logic. We will see that once logic is generalized to questions, important logical notions such as answerhood and dependency emerge as facets of the fundamental notion of entailment, and can thereby be analyzed using the logician’s toolkit. After motivating the enterprise and introducing the conceptual foundations of the framework, we will look at how classical propositional and predicate logic can be enriched with questions and study the meta-theoretic properties of the resulting logics.

Course material

Inquisitive Logic book


Familiarity with classical propositional and predicate logic is presupposed. Familiarity with intensional semantics is convenient but not presupposed.

Course outline

Class 1: Foundations
We motivate the enterprise and introduce the key ideas of inquisitive logic, in particular the semantic notion of support and the generalizations of entailment and implication. 
Material: Sections 2.1-2.5 of the book. Slides.
Class 2: inquisitive propositional logic
We show how classical propositional logic can be enriched with questions. We illustrate the resulting system with examples and look at the logical properties of propositional statements and questions.
Material: Chapter 3 of the book. Slides.
Class 3: inferences with propositional questions
We discuss the role of questions in proofs, and the significance of supposing or concluding a question in an argument.We illustrate these points by introducing a complete natural deduction system for inquisitive propositional logic and looking at proofs in this system.
Material: Chapter 4 of the book. Slides.
Class 4: inquisitive predicate logic
We discuss how questions can be added to first-order predicate logic. We illustrate the broad spectrum of question types expressible in this framework and discuss the logical properties of first-order statements and questions. In this setting, some classical themes of intensional semantics come into play, such as modes of reference and intensional identity.
Material: Sections 5.1-5.5 of the book. Slides.
Class 5: Inferences with first-order questions
We discuss some recent results about the meta-theory of inquisitive predicate logic, and present complete natural deduction systems for some interesting fragments. We close by outlining a range of important open problems in this area.
Material: Sections 5.6-5.8 and Chapter 6 of the book. Slides.