# Category: Metalogic

WFF 'N PROOF
WFF 'N PROOF is a game of modern logic, developed to teach principles of symbolic logic. It was developed by Layman E. Allen in 1962 a former professor of Yale Law School and the University of Michiga
Metasyntactic variable
A metasyntactic variable is a specific word or set of words identified as a placeholder in computer science and specifically computer programming. These words are commonly found in source code and are
Meta-communication
Meta-communication is a secondary communication (including indirect cues) about how a piece of information is meant to be interpreted. It is based on the idea that the same message accompanied by diff
Syntax (logic)
In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructin
Łoś–Tarski preservation theorem
The Łoś–Tarski theorem is a theorem in model theory, a branch of mathematics, that states that the set of formulas preserved under taking substructures is exactly the set of universal formulas. The th
Axiom independence
An axiom P is independent if there are no other axioms Q such that Q implies P. In many cases independence is desired, either to reach the conclusion of a reduced set of axioms, or to be able to repla
Completeness (logic)
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.e. is one of its
Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statem
Metalogic
Metalogic is the study of the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Lo
Use–mention distinction
The use–mention distinction is a foundational concept of analytic philosophy, according to which it is necessary to make a distinction between using a word (or phrase) and mentioning it. Many philosop
Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part
Proof theory
Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as in
Decidability (logic)
In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Zeroth-order logic (propositional logic) is decidable, whereas first-order and
Symbol (formal)
A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some ti
Metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may referen
Metavariable
In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instan
Consistency
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic def
Equisatisfiability
In Mathematical logic (a subtopic within the field of formal logic), two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either
Effective method
In logic, mathematics and computer science, especially metalogic and computability theory, an effective method or effective procedure is a procedure for solving a problem by any intuitively 'effective
Formal system
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are th
Logical equivalence
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as , , , or , depen
Type–token distinction
The type–token distinction is the difference between naming a class (type) of objects and naming the individual instances (tokens) of that class. Since each type may be exemplified by multiple tokens,
Metalanguage
In logic and linguistics, a metalanguage is a language used to describe another language, often called the object language. Expressions in a metalanguage are often distinguished from those in the obje