Metatheorem

Metatheorem

A metatheorem is a theorem that describes or proves something about a formal system or a set of theorems, rather than being a theorem within that system or set. It is a higher-level theorem that provides insight into the properties or behavior of the system or set as a whole. Examples of metatheorems include the principle of duality and the consistency of a formal system with its interpretation.From: Modern Digital Design and Switching Theory [2017], Software Engineering Mathematics [1988]

Formal Systems

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Published in Janet Woodcock, Software Engineering Mathematics, 1988

Janet Woodcock

interpretations will have this property. The consistency of a formal system with its interpretation is an example of a metatheorem, as it states something about the system rather than being just a string of symbols within it. In the rest of this book we will only be interested in consistent interpretations of formal systems.

A New Metatheorem and Subdirect Product Theorem for L-Subgroups

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Published in Fuzzy Information and Engineering, 2018

Naseem Ajmal, Iffat Jahan

Let be two expressions in where H and K are subsets of G and the operation is the natural extension of the binary operation given by . In view of Lemma 3.6 and by the isomorphism chi from to , we have Thus As L is a complete dense chain, the natural extension is commutative. So the metatheorem applies and this equality holds for corresponding L-class also. That is Therefore .

Axiomatic and dual systems for constructive necessity, a formally verified equivalence

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Published in Journal of Applied Non-Classical Logics, 2019

Lourdes del Carmen González-Huesca, Favio E. Miranda-Perea, P. Selene Linares-Arévalo

This problem has been discussed since long time ago. To ensure the validity of the deduction theorem, one usually needs to restrict the definition of derivation or to generalise the statement of this important metatheorem. See for example the works of Zeman (1973, chapter 12) and Perzanowski (1973) (see also the survey Porte, 1982 and Fitting, 2007 for semantical deduction theorems). In this work, we prefer to follow the more recent Hakli and Negri (2012): to validate the deduction theorem we only need to give a precise definition of derivability from assumptions in an axiomatic framework.

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Formal Systems

A New Metatheorem and Subdirect Product Theorem for L-Subgroups

Axiomatic and dual systems for constructive necessity, a formally verified equivalence