-
languages and
systems that are used to
express truths. The
basic objects of
metalogical study are
formal languages,
formal systems, and
their interpretations...
-
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...
-
languages and
systems that are used to
express truths. The
basic objects of
metalogical study are
formal languages,
formal systems, and
their interpretations...
- is the
disjunction logic operator (OR), ⟺ {\displaystyle \iff } is a
metalogical symbol meaning "can be
replaced in a
logical proof with",
often read...
- R)\Leftrightarrow (P\to (Q\to R))}
Where " ⇔ {\displaystyle \Leftrightarrow } " is a
metalogical symbol representing "can be
replaced in a
proof with." In
strict terminology...
- more
general use of a
metalogic or
metalanguage to
describe and
reason about another language,
called the
object language.
Metalogic programming allows object-level...
- Q)\Leftrightarrow (Q\land P)}
where " ⇔ {\displaystyle \Leftrightarrow } " is a
metalogical symbol representing "can be
replaced in a
proof with". Commutativity...
-
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...
-
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...
