What is the difference between a predicate symbol and a function symbol in predicate logic?
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There are a lot of questions and answers on what the difference a predicate and a function in predicate logic is on this website, but there is no question/answer on what the difference between a predicate symbol and a function symbol is.
logic predicate-logic
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
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add a comment |
$begingroup$
There are a lot of questions and answers on what the difference a predicate and a function in predicate logic is on this website, but there is no question/answer on what the difference between a predicate symbol and a function symbol is.
logic predicate-logic
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
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2
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There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
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– Henning Makholm
Mar 7 '17 at 22:30
1
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A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
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– Graham Kemp
Mar 7 '17 at 23:36
add a comment |
$begingroup$
There are a lot of questions and answers on what the difference a predicate and a function in predicate logic is on this website, but there is no question/answer on what the difference between a predicate symbol and a function symbol is.
logic predicate-logic
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
$endgroup$
There are a lot of questions and answers on what the difference a predicate and a function in predicate logic is on this website, but there is no question/answer on what the difference between a predicate symbol and a function symbol is.
logic predicate-logic
logic predicate-logic
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
asked Mar 7 '17 at 22:21
J. DormerJ. Dormer
183
183
2
$begingroup$
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
$endgroup$
– Henning Makholm
Mar 7 '17 at 22:30
1
$begingroup$
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
$endgroup$
– Graham Kemp
Mar 7 '17 at 23:36
add a comment |
2
$begingroup$
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
$endgroup$
– Henning Makholm
Mar 7 '17 at 22:30
1
$begingroup$
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
$endgroup$
– Graham Kemp
Mar 7 '17 at 23:36
2
2
$begingroup$
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
$endgroup$
– Henning Makholm
Mar 7 '17 at 22:30
$begingroup$
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
$endgroup$
– Henning Makholm
Mar 7 '17 at 22:30
1
1
$begingroup$
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
$endgroup$
– Graham Kemp
Mar 7 '17 at 23:36
$begingroup$
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
$endgroup$
– Graham Kemp
Mar 7 '17 at 23:36
add a comment |
2 Answers
2
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votes
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Predicate logic distinguishes between terms (formal expressions denoting elements of the domain of discourse, e.g., addition of numbers in arithmetic) and predicates (formal expressions denoting relations amongst elements in domain of discourse, e.g., the less-than relation in arithmetic).
A predicate symbol is an operator that combines terms and produces a predicate. E.g., in arithmetic $=$, $<$ and $>$ are predicate symbols.
A function symbol is an operator that combines terms and produces a new term. E.g., in arithmetic $+$ and $times$ are function symbols.
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
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add a comment |
$begingroup$
Once we interpret the symbols:
A function applied to one or more objects gives you another object, while a predicate applied to one or more objects gives you a claim
For example, under the standard interpretation for the language of arithmetic:
$1+2$ gives you the object $3$ (and $1+2$ is not a claim)
$1<2$ gives you the claim that $1$ is smaller than $2$ (and $1<2$ is not an object from the domain)
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
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add a comment |
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2 Answers
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2 Answers
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$begingroup$
Predicate logic distinguishes between terms (formal expressions denoting elements of the domain of discourse, e.g., addition of numbers in arithmetic) and predicates (formal expressions denoting relations amongst elements in domain of discourse, e.g., the less-than relation in arithmetic).
A predicate symbol is an operator that combines terms and produces a predicate. E.g., in arithmetic $=$, $<$ and $>$ are predicate symbols.
A function symbol is an operator that combines terms and produces a new term. E.g., in arithmetic $+$ and $times$ are function symbols.
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
$endgroup$
add a comment |
$begingroup$
Predicate logic distinguishes between terms (formal expressions denoting elements of the domain of discourse, e.g., addition of numbers in arithmetic) and predicates (formal expressions denoting relations amongst elements in domain of discourse, e.g., the less-than relation in arithmetic).
A predicate symbol is an operator that combines terms and produces a predicate. E.g., in arithmetic $=$, $<$ and $>$ are predicate symbols.
A function symbol is an operator that combines terms and produces a new term. E.g., in arithmetic $+$ and $times$ are function symbols.
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
$endgroup$
add a comment |
$begingroup$
Predicate logic distinguishes between terms (formal expressions denoting elements of the domain of discourse, e.g., addition of numbers in arithmetic) and predicates (formal expressions denoting relations amongst elements in domain of discourse, e.g., the less-than relation in arithmetic).
A predicate symbol is an operator that combines terms and produces a predicate. E.g., in arithmetic $=$, $<$ and $>$ are predicate symbols.
A function symbol is an operator that combines terms and produces a new term. E.g., in arithmetic $+$ and $times$ are function symbols.
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
$endgroup$
Predicate logic distinguishes between terms (formal expressions denoting elements of the domain of discourse, e.g., addition of numbers in arithmetic) and predicates (formal expressions denoting relations amongst elements in domain of discourse, e.g., the less-than relation in arithmetic).
A predicate symbol is an operator that combines terms and produces a predicate. E.g., in arithmetic $=$, $<$ and $>$ are predicate symbols.
A function symbol is an operator that combines terms and produces a new term. E.g., in arithmetic $+$ and $times$ are function symbols.
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
edited Dec 3 '18 at 18:28
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
answered Mar 7 '17 at 22:33
Rob ArthanRob Arthan
29.2k42966
29.2k42966
add a comment |
add a comment |
$begingroup$
Once we interpret the symbols:
A function applied to one or more objects gives you another object, while a predicate applied to one or more objects gives you a claim
For example, under the standard interpretation for the language of arithmetic:
$1+2$ gives you the object $3$ (and $1+2$ is not a claim)
$1<2$ gives you the claim that $1$ is smaller than $2$ (and $1<2$ is not an object from the domain)
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
$endgroup$
add a comment |
$begingroup$
Once we interpret the symbols:
A function applied to one or more objects gives you another object, while a predicate applied to one or more objects gives you a claim
For example, under the standard interpretation for the language of arithmetic:
$1+2$ gives you the object $3$ (and $1+2$ is not a claim)
$1<2$ gives you the claim that $1$ is smaller than $2$ (and $1<2$ is not an object from the domain)
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
$endgroup$
add a comment |
$begingroup$
Once we interpret the symbols:
A function applied to one or more objects gives you another object, while a predicate applied to one or more objects gives you a claim
For example, under the standard interpretation for the language of arithmetic:
$1+2$ gives you the object $3$ (and $1+2$ is not a claim)
$1<2$ gives you the claim that $1$ is smaller than $2$ (and $1<2$ is not an object from the domain)
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
$endgroup$
Once we interpret the symbols:
A function applied to one or more objects gives you another object, while a predicate applied to one or more objects gives you a claim
For example, under the standard interpretation for the language of arithmetic:
$1+2$ gives you the object $3$ (and $1+2$ is not a claim)
$1<2$ gives you the claim that $1$ is smaller than $2$ (and $1<2$ is not an object from the domain)
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
answered Mar 7 '17 at 23:02
Bram28Bram28
61.5k44793
61.5k44793
add a comment |
add a comment |
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There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
$endgroup$
– Henning Makholm
Mar 7 '17 at 22:30
1
$begingroup$
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
$endgroup$
– Graham Kemp
Mar 7 '17 at 23:36