Mirqāt The Ascent of Logic

Contemporary · a field of logic

Algebraic Logic

Logic recast as algebra: Boolean, cylindric, and relation algebras, the algebraic shadow that every logic casts.

The problem
Can every logic be studied as an algebra, so that logical questions become equational ones?
The turning point
Stone’s representation theorem: every Boolean algebra is an algebra of sets, bridging logic, algebra, and topology.
An open question
How far does algebraization extend to modal, substructural, and quantum logics, and what does it leave out?

The Canon

  • Henkin, Monk & Tarski Cylindric Algebras

To study it

  • Hirsch & Hodkinson Relation Algebras by Games
  • Németi Algebraic Logic