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

• 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.