List of formal systems

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

Mathematical

 * Functional calculus, a way to apply various types of functions to operators
 * Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices
 * 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

Logical

 * Predicate calculus, specifies the rules of inference governing the logic of predicates
 * Propositional calculus, specifies the rules of inference governing the logic of propositions

In theoretical computer science (Formal language)

 * Modal μ-calculus, a common temporal logic used by formal verification methods such as model checking
 * Lambda calculus, a formulation of the theory of reflexive functions that has deep connections to computational theory
 * Kappa calculus, a reformulation of the first-order fragment of typed lambda calculus
 * Rho calculus, introduced as a general means to uniformly integrate rewriting into lambda calculus
 * Process calculus, a set of approaches to formulating formal models of concurrent systems
 * Ambient calculus, a family of models for concurrent systems based on the concept of agent mobility
 * Join calculus, a theoretical model for the design of distributed programming languages
 * π-calculus, a formulation of the theory of concurrent, communicating processes, that was invented by Robin Milner
 * Relational calculus, a calculus for the relational data model
 * Domain relational calculus
 * Tuple calculus, inspired the SQL language
 * Refinement calculus, a way of refining models of programs into efficient programs

Other formal systems


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