Theory (mathematical logic)
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually a deductive system is understood from context. An element of a theory is then called...
Cracking The Problem Of River Growth
MIT researchers find that a similar principle predicts the growth of fractures and rivers. A general mathematical theory that predicts how cracks spread through materials like glass and ice can also p...
Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition ...
Completeness
Complete may refer to:
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic te...
First-order logic
First-order logic is a formal system used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantificatio...
First-order logic - Wikipedia
Structure (mathematical logic)
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. Universal algebra studies structures that ...
List of rules of inference
This is a list of rules of inference, logical laws that relate to mathematical formulae.
Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise t...
Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where subst...
Free variables and bound variables - Wikipedia
Sequent calculus
Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautol...
Sequent calculus - Wikipedia
Formal languages
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols that may be constrained by rules that are specific to it.The alphabet of a formal language is the se...
Automated theorem proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Autom...
Automated theorem proving - Wikipedia
Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and a stronger semantics. Higher-order logics with ...
Infinitary logic
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In...
Lindström's theorem
In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the strongest logic (satisfying certain conditions, e...
Method of analytic tableaux
In proof theory, the semantic tableau ([ta'blo]; singular: tableau; plural: tableaux), also called truth tree, is a decision procedure for sentential and related logics, and a proof procedure for form...
Method of analytic tableaux - Wikipedia
Empty domain
In first-order logic the empty domain is the empty set having no members. In traditional and classical logic domains are restrictedly non-empty in order that certain theorems be valid. Interpretations...
List of first-order theories
In mathematical logic, a first-order theory is given by a set of axioms in somelanguage. This entry lists some of the more common examples used in model theory and some of their properties.
For ev...
Satisfiability
In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true. A fo...
Second order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and ...
Intended interpretation
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic te...
Signature (logic)
In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the operations that characterize an alge...
Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic. The objects of study...
Universal algebra
Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.For instance, rather than...