In logic, a metatheorem is a statement about theorems or about some axiomatic theory. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... The term statement can have several meanings: In programming, a statement is an instruction to execute something that will not return a value. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ...

Examples

Security Property as a Metatheorem

In security protocol analysis using formal methods, a security protocol specification can be seen as a theory and the refinement of this theory would correspond to a theory extension, for instance the addition of new axioms regarding adversary capabilities such as algebraic manipulation of cryptographic terms. These analysis results are usually counter-intuitive and difficult to accomplish without the help of formal methods because a security property is a metatheorem about the security system: it states that the adversary is not able to deduce certain facts (for instance, a session key) from the underlying theory, and adding new adversary capabilities can invalidate the security (see properties below). The concrete implementation of a security protocol is always a refinement of its theory, and therefore an implementation is always suscetible to vulnerabilities that are not present in the security protocol abstract theory. Such vulnerabilities correspond to the invalidation of the metatheorem of the security property. A cryptographic protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods. ... In computer science, formal methods refers to mathematically based techniques for the specification, development and verification of software and hardware systems. ... In engineering and manufacturing, the term specification has the following meanings: Technical requirement A specification is a set of requirements. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ... This article does not cite its references or sources. ... A session key is a key used for encrypting one message or a group of messages in a communication session. ...

Properties

• Metatheorems are not preserved by theory extensions (e.g. after adding new axioms to some theory, the metatheorem may not hold anymore.)

This article does not cite its references or sources. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ...

See also

• Theorem
• Metamathematics

A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... In general, metamathematics or meta-mathematics is reflection about mathematics seen as an entity/object in human consciousness and culture. ...

References

• http://mathworld.wolfram.com/Metatheorem.html