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1
Mathematical
Toggle Mathematical subsection
1.1
Logical
1.2
In theoretical computer science (Formal language)
2
Other formal systems
3
See also
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List of formal systems
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From Wikipedia, the free encyclopedia
This is a list of
formal systems
, also known as logical calculi.
Mathematical
[
edit
]
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
[
edit
]
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
)
[
edit
]
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
[
edit
]
Formal ethics
– Formal logical system
See also
[
edit
]
Formal system
– Mathematical model for deduction or proof systems
Computability:Formal models
Model of computation
– Mathematical model describing how an output of a function is computed given an input
Calculus (disambiguation)
v
t
e
Mathematical logic
General
Axiom
list
Cardinality
First-order logic
Formal proof
Formal semantics
Foundations of mathematics
Information theory
Lemma
Logical consequence
Model
Theorem
Theory
Type theory
Theorems (
list
)
and
paradoxes
Gödel's completeness
and
incompleteness theorems
Tarski's undefinability
Banach–Tarski paradox
Cantor's
theorem,
paradox
and
diagonal argument
Compactness
Halting problem
Lindström's
Löwenheim–Skolem
Russell's paradox
Logics
Traditional
Classical logic
Logical truth
Tautology
Proposition
Inference
Logical equivalence
Consistency
Equiconsistency
Argument
Soundness
Validity
Syllogism
Square of opposition
Venn diagram
Propositional
Boolean algebra
Boolean functions
Logical connectives
Propositional calculus
Propositional formula
Truth tables
Many-valued logic
3
finite
∞
Predicate
First-order
list
Second-order
Monadic
Higher-order
Fixed-point
Free
Quantifiers
Predicate
Monadic predicate calculus
Set theory
Set
hereditary
Class
(
Ur-
)
Element
Ordinal number
Extensionality
Forcing
Relation
equivalence
partition
Set operations:
intersection
union
complement
Cartesian product
power set
identities
Types of
sets
Countable
Uncountable
Empty
Inhabited
Singleton
Finite
Infinite
Transitive
Ultrafilter
Recursive
Fuzzy
Universal
Universe
constructible
Grothendieck
Von Neumann
Maps
and
cardinality
Function
/
Map
domain
codomain
image
In
/
Sur
/
Bi
-jection
Schröder–Bernstein theorem
Isomorphism
Gödel numbering
Enumeration
Large cardinal
inaccessible
Aleph number
Operation
binary
Set theories
Zermelo–Fraenkel
axiom of choice
continuum hypothesis
General
Kripke–Platek
Morse–Kelley
Naive
New Foundations
Tarski–Grothendieck
Von Neumann–Bernays–Gödel
Ackermann
Constructive
Formal systems
(
list
),
language
and
syntax
Alphabet
Arity
Automata
Axiom schema
Expression
ground
Extension
by definition
conservative
Relation
Formation rule
Grammar
Formula
atomic
closed
ground
open
Free/bound variable
Language
Metalanguage
Logical connective
¬
∨
∧
→
↔
=
Predicate
functional
variable
propositional variable
Proof
Quantifier
∃
!
∀
rank
Sentence
atomic
spectrum
Signature
String
Substitution
Symbol
function
logical/constant
non-logical
variable
Term
Theory
list
Example
axiomatic
systems
(
list
)
of
true arithmetic
:
Peano
second-order
elementary function
primitive recursive
Robinson
Skolem
of the
real numbers
Tarski's axiomatization
of
Boolean algebras
canonical
minimal axioms
of
geometry
:
Euclidean
:
Elements
Hilbert's
Tarski's
non-Euclidean
Principia Mathematica
Proof theory
Formal proof
Natural deduction
Logical consequence
Rule of inference
Sequent calculus
Theorem
Systems
axiomatic
deductive
Hilbert
list
Complete theory
Independence
(
from ZFC
)
Proof of impossibility
Ordinal analysis
Reverse mathematics
Self-verifying theories
Model theory
Interpretation
function
of models
Model
atomic
equivalence
finite
prime
saturated
spectrum
submodel
Non-standard model
of
non-standard arithmetic
Diagram
elementary
Categorical theory
Model complete theory
Satisfiability
Semantics of logic
Strength
Theories of truth
semantic
Tarski's
Kripke's
T-schema
Transfer principle
Truth predicate
Truth value
Type
Ultraproduct
Validity
Computability theory
Church encoding
Church–Turing thesis
Computably enumerable
Computable function
Computable set
Decision problem
decidable
undecidable
P
NP
P versus NP problem
Kolmogorov complexity
Lambda calculus
Primitive recursive function
Recursion
Recursive set
Turing machine
Type theory
Related
Abstract logic
Algebraic logic
Automated theorem proving
Category theory
Concrete
/
Abstract category
Category of sets
History of logic
History of mathematical logic
timeline
Logicism
Mathematical object
Philosophy of mathematics
Supertask
Mathematics portal
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