# Modeling biconditionals: Equivalence in an uncertain world

- Koji Sawa,
*Japan Women’s University, Kawasaki, Kanagawa, Japan*
- Junki Yokokawa,
*Tokyo Denki university, hatoyama, saitama, japan*
- Tatsuji Takahashi,
*Tokyo Denki university, hatoyama, saitama, japan*

## Abstract

For almost a half century, it has been known that participants
consider the truth value of “if p then q,” in a
“defective” way, as true when p and q are both true, false when p is
true but q is false, but uncertain whenever p is false. Recently, researchers has
given this truth table a new normative status, under the theory of subjective
probability by de Finetti, as of conditional event, q|p. On the basis of ample
evidence that P(if p then q)=P(q|p), we study biconditionals, “if p then q,
and if q then p.” Here we show the psychological priority of biconditional
event to material equivalence. Additionally, we discuss the logical background of
(bi-)conditional event and three types of uncertainty. Two are ones in the domain
and codomain of the truth-function, and the other is connected to the
indefiniteness of a world or the frame problem.

Back to Table of Contents