-
metalogic concerns the
truths that may be
derived about the
languages and
systems that are used to
express truths. The
basic objects of
metalogical study...
-
proving in first-order logic. First-order
logic also
satisfies several metalogical theorems that make it
amenable to
analysis in
proof theory, such as the...
- In
logic and mathematics, second-order
logic is an
extension of first-order logic,
which itself is an
extension of
propositional logic. Second-order logic...
- more
general use of a
metalogic or
metalanguage to
describe and
reason about another language,
called the
object language.
Metalogic programming allows object-level...
- and 1400 AD. In
mathematics and logic,
effective is used to
describe metalogical methods that fit the
criteria of an
effective procedure. In
group theory...
-
texts ⇔ is used with this meaning,
while ≡ is used for the higher-level
metalogical notion of
logical equivalence,
according to
which two
formulas are logically...
-
counterpart of Gödel's
incompleteness theorem of
metalogic, as well as Löb's theorem, and
other metalogical results in
terms of belief. To
demonstrate the...
- \lor ,\neg ]} . This
theorem is a
convenient way to
derive many
useful metalogical results in
propositional logic, such as, trivially, the
result that the...
- {\displaystyle P\vdash (P\lor Q)}
where ⊢ {\displaystyle \vdash } is a
metalogical symbol meaning that P ∨ Q {\displaystyle P\lor Q} is a
syntactic consequence...
- Q)\Leftrightarrow (Q\land P)}
where " ⇔ {\displaystyle \Leftrightarrow } " is a
metalogical symbol representing "can be
replaced in a
proof with". Commutativity...
