Information about Extension (predicate Logic)
The extension of a predicate is the set of true propositions that can be formed by substituting a term for each of its free variables.
For example, consider the predicate "d2 is the weekday following d1". Its extension is the set
{Monday is the weekday following Sunday, Tuesday is the weekday following Monday, Wednesday is the weekday following Tuesday, Thursday is the weekday following Wednesday, Friday is the weekday following Thursday, Saturday is the weekday following Friday, Sunday is the weekday following Saturday}
By examining this extension we can conclude, under the Closed World Assumption and the principle of bivalence, that "Tuesday is the weekday following Saturday" (for example) is false.
Note that some predicates have different extensions in different situations. For example, that of "a is the mother of b" changes over time, whenever somebody is born. However, that of "x < y" (in the domain of numbers) can be safely assumed to have the same extension in all situations--in particular, at all times.
For example, consider the predicate "d2 is the weekday following d1". Its extension is the set
{Monday is the weekday following Sunday, Tuesday is the weekday following Monday, Wednesday is the weekday following Tuesday, Thursday is the weekday following Wednesday, Friday is the weekday following Thursday, Saturday is the weekday following Friday, Sunday is the weekday following Saturday}
By examining this extension we can conclude, under the Closed World Assumption and the principle of bivalence, that "Tuesday is the weekday following Saturday" (for example) is false.
Note that some predicates have different extensions in different situations. For example, that of "a is the mother of b" changes over time, whenever somebody is born. However, that of "x < y" (in the domain of numbers) can be safely assumed to have the same extension in all situations--in particular, at all times.
The closed world assumption is the presumption that what is not currently known to be true is false. The same name also refer to a logical formalization of this assumption by Raymond Reiter.
..... Click the link for more information.
..... Click the link for more information.
In logic, the semantic principle of bivalence states that every proposition takes exactly one of two truth values (e.g. truth or falsehood). The laws of bivalence, excluded middle, and non-contradiction are related, but they refer to the calculus of logic, not its
..... Click the link for more information.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
