A first-order logic for multi-algebras

Jānis Cīrulis

We present a complete first-order proof system for complex algebras of multi-algebras of a fixed signature, which is based on a language whose single primitive relation is singular inclusion, i.e., restricted set inclusion with the domain consisting only of one-element sets. This proof system is then adapted for multi-algebras by relativizing both free and bounded variables in formulas to singletons.