Hypothetical revision and matter-of-fact supposition

TL;DR

This paper explores how non-Archimedean conditional probability models supposition and indicative conditionals, comparing it with classical belief revision methods and discussing applications in decision theory, causal models, and non-monotonic logic.

Contribution

It introduces an axiomatic framework for qualitative change of view via non-Archimedean probability, linking it to existing belief revision theories and exploring diverse applications.

Findings

Non-Archimedean probability effectively models supposition.

The framework aligns with and extends AGM and UPDATE models.

Applications demonstrate its relevance in decision theory, causal reasoning, and logic.

Abstract

The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals). The notion of qualitative change of view that thus arises is axiomatized and compared with standard notions like AGM and UPDATE. Applications in the following fields are discussed: (1) theory of games and decisions, (2) causal models, (3) non-monotonic logic.