This is a list of formal systems, also known as logical calculi.

Mathematical

• Domain relational calculus, a calculus for the relational data model
• Functional calculus, a way to apply various types of functions to operators
• Join calculus, a theoretical model for distributed programming
• Lambda calculus, a formulation of the theory of reflexive functions that has deep connections to computational theory
• Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices
• Modal μ-calculus, a common temporal logic used by formal verification methods such as model checking
• Pi-calculus, a formulation of the theory of concurrent, communicating processes that was invented by Robin Milner
• Predicate calculus, specifies the rules of inference governing the logic of predicates
• Propositional calculus, specifies the rules of inference governing the logic of propositions
• Refinement calculus, a way of refining models of programs into efficient programs
• Rho calculus, introduced as a general means to uniformly integrate rewriting and lambda calculus
• Tuple calculus, a calculus for the relational data model, inspired the SQL language
• Umbral calculus, the combinatorics of certain operations on polynomials
• Vector calculus (also called vector analysis), comprising specialized notations for multivariable analysis of vectors in an inner-product space

Other formal systems

• Formal ethics – formal logical system for describing and evaluating the "form" as opposed to the "content" of ethical principlesPages displaying wikidata descriptions as a fallback

Music is a formal system too. Please have editors illuminate on this.