Metalogic

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 object language by the use of italics, quotation marks, or writing on a separate line. The structure of sentences and phrases in a metalanguage can be described by a metasyntax. For example, to say that the word "noun" can be used as a noun in a sentence, one could write "noun" is a .

any well-defined system of abstract thought based on the model of mathematics

fundamental concept in logic

branch of mathematical logic

concept in logic

Metalogic is 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. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.

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 different meta-communication can mean something entirely different, including its opposite, as in irony. The term was brought to prominence by Gregory Bateson to refer to "communication about communication", which he expanded to: "all exchanged cues and propositions about (a) codification and (b) relationship between the communicators".

property of theories that have computable membership

finite sequence of symbols from a given alphabet that is part of a formal language

distinction that separates a concept from the objects which are particular instances of the concept

fundamental concept in metalogic, and the term may be used without qualification with differing meanings depending on the context within mathematical logic

placeholder term used in computer science

rules used for constructing or transforming the symbols of a formal language

in analytic philosophy, a distinction between using a word or phrase and mentioning it

problem-solving procedures with certain characteristics

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 reference concepts that are present in the metatheory but not the object theory.

basic element of strings in a formal language

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 both formulae are satisfiable or neither is. The truth values of two equisatisfiable formulae may nevertheless disagree for a particular assignment of variables. As a result, equisatisfiability differs from logical equivalence, since two equivalent formulae always have the same models, whereas equisatisfiable ones need only share satisfiability status. More formally, the equisatisfiability meta fo