List of formal systems

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

Mathematical[edit]

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

Formal ethics – formal logical system for describing and evaluating the "form" as opposed to the "content" of ethical principles

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