If You're Happy, Then You Know It: The Logic of Happiness... and Sadness

TL;DR

This paper develops a formal semantics for happiness and sadness modalities in imperfect information settings, demonstrating their independence and providing a complete axiomatization of their properties.

Contribution

It introduces a novel formal semantics for happiness and sadness modalities and proves their non-definability through each other.

Findings

Happiness and sadness modalities are not definable from each other.

A sound and complete axiomatization of these modalities is provided.

The semantics applies to imperfect information settings.

Abstract

The article proposes a formal semantics of happiness and sadness modalities in imperfect information setting. It shows that these modalities are not definable through each other and gives a sound and complete axiomatization of their properties.