The Dual Spatial Connectives of Separation Logic

Abstract

Separation logic has two spatial connectives ∗ and − ∗ . It is known that ∗ and − ∗ are not dual each other, like ‘and’ and ‘or’, ‘for all’ and ‘there exists’, ‘necessarily’ and ‘possibly’, etc. To define the dual connectives of ∗ and − ∗ there are two choices: one is to take ∗ and − ∗ as special logical connectives; another is to take ∗ and − ∗ as binary modalities. Correspondingly, the dual modalities of ∗ and − ∗ are represented as the dual connectives of ∗ and − ∗ , and as the dual modalities of ∗ and − ∗ , where the latter can be represented by unary modalities in the case that the formulas are defined in a special form.