Please answer the following question: Information: - In linguistics, a word is the smallest element that can be uttered in isolation with semantic or pragmatic content (with literal or practical meaning). This contrasts deeply with a morpheme, which is the smallest unit of meaning but will not necessarily stand on its own. A word may consist of a single morpheme (for example: "oh!, rock, red, quick, run, expect"), or several ("rocks, redness, quickly, running, unexpected"), whereas a morpheme may not be able to stand on its own as a word (in the words just mentioned, these are "-s, -ness, -ly, -ing, un-, -ed"). A complex word will typically include a root and one or more affixes ("rock-s, red-ness, quick-ly, run-ning, un-expect-ed"), or more than one root in a compound ("black-board, rat-race"). Words can be put together to build larger elements of language, such as phrases ("a red rock"), clauses ("I threw a rock"), and sentences ("He threw a rock too, but he missed"). - An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek "axima" 'that which is thought worthy or fit' or 'that which commends itself as evident.' - In proof theory , a structural rule is an inference rule that does not refer to any logical connective , but instead operates on the judgment or sequents directly . Structural rules often mimic intended meta - theoretic properties of the logic . Logics that deny one or more of the structural rules are classified as substructural logics . - Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those. - In logic, a logical connective (also called a logical operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences. - A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics. - 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 inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. - In neuropsychology, linguistics and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages can take different forms, such as speech, signing, or writing. They are distinguished from constructed and formal languages such as those used to program computers or to study logic. - 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 are models of theories in a formal language. A set of sentences in a formal language is called a theory; a model of a theory is a structure (e.g. an interpretation) that satisfies the sentences of that theory. What is the relationship between 'structural rule' and 'metamathematics'?
Answer:
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