Mathematical logic

In computability theory Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ : Bk → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function.

In digital circuit theory, combinational logic (sometimes also referred to as time-independent logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only.

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".

In mathematics, a finitary relation has a finite number of "places".

First-order logic is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) is a set of production rules for strings in a formal language.

Foundations of mathematics is the study of the logical and philosophical basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.

Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.

Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs.

Intuitionistic logic, sometimes more generally called constructive logic, is a system of symbolic logic that differs from classical logic by replacing the traditional concept of truth with the concept of constructive provability.

Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal.

In logic, the law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought.

In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values.

In mathematics, a proof is a deductive argument for a mathematical statement.

In logic, necessity and sufficiency are implicational relationships between statements.

For example, in arithmetic, it allows the expression of the statement that every natural number has a successor.

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

A Venn diagram (also called a set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets.

Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930).

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters.

In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.

Metamathematics is the study of mathematics itself using mathematical methods.

In mathematics, a proof by infinite descent is a particular kind of proof by contradiction that relies on the least integer principle.

In mathematical logic, a truth function is a function from a set of truth values to truth values.

An enumeration is a complete, ordered listing of all the items in a collection.

In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.

Grundlagen der Mathematik (English: Foundations of Mathematics) is a two-volume work by David Hilbert and Paul Bernays.

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations, and relations that are defined on it.

In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.

This list of mathematical symbols by subject shows a selection of the most common symbols that are used in modern mathematical notation within formulas, grouped by mathematical topic.

A proof of impossibility, also known as negative proof, proof of an impossibility theorem, or negative result, is a proof demonstrating that a particular problem cannot be solved, or cannot be solved in general.