On Independence and Compound and Iterated Conditionals

Gilio, Angelo; Over, David; Pfeifer, Niki; Sanfilippo, Giuseppe

Abstract

Understanding the logic of uncertain conditionals is a key problem in the new paradigm psychology of reasoning and related fields. We investigate conjunctions of conditionals, iterated conditionals, and independence within the theory of logical operations on conditionals, where compound conditionals are suitably defined as conditional random quantities. We show how conjunctions of conditionals and conditionals which feature conditionals in the antecedent and the consequent can be rationally interpreted. In particular, we study the behavior of such objects under different logical constraints, by also considering a kind of “independence” property. Unlike alternative approaches, in our framework we avoid counterintuitive consequences, which is necessary for understanding, or improving, human and artificial rationality in general.

Citation

Gilio, A., Over, D., Pfeifer, N., & Sanfilippo, G. (2024). On Independence and Compound and Iterated Conditionals. In Human and Artificial Rationalities: Second International Conference, HAR 2023, Paris, France, September 19–22, 2023, Proceedings (159-177). https://doi.org/10.1007/978-3-031-55245-8_11

• Conference Name: Human and Artificial Rationalities (HAR 2023)
• Conference Location: Paris, France
• Start Date: Sep 19, 2023
• End Date: Sep 22, 2023
• Acceptance Date: Jun 1, 2023
• Online Publication Date: Mar 15, 2024
• Publication Date: 2024
• Deposit Date: Jun 14, 2024
• Publisher: Springer Nature
• Pages: 159-177
• Series Title: Lecture Notes in Computer Science
• Series Number: 14522
• Series ISSN: 0302-9743
• Book Title: Human and Artificial Rationalities: Second International Conference, HAR 2023, Paris, France, September 19–22, 2023, Proceedings
• ISBN: 9783031552441
• DOI: https://doi.org/10.1007/978-3-031-55245-8_11
• Public URL: https://durham-repository.worktribe.com/output/2483330