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. Dormer
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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. Dormer
183
2
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
– Henning Makholm
Mar 7 '17 at 22:30
1
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
– Graham Kemp
Mar 7 '17 at 23:36
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
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. Dormer
183
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. Dormer
183
asked Mar 7 '17 at 22:21
J. Dormer
183
asked Mar 7 '17 at 22:21
J. Dormer
183
asked Mar 7 '17 at 22:21
J. Dormer
183
asked Mar 7 '17 at 22:21
J. Dormer
183
183
2
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
– Henning Makholm
Mar 7 '17 at 22:30
1
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
– Graham Kemp
Mar 7 '17 at 23:36
add a comment |
2
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
– Henning Makholm
Mar 7 '17 at 22:30
1
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
– Graham Kemp
Mar 7 '17 at 23:36
2
2
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
– Henning Makholm
Mar 7 '17 at 22:30
There's no difference in the symbols themselves. The difference is in what you have decided to use them for.
– Henning Makholm
Mar 7 '17 at 22:30
1
1
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
– Graham Kemp
Mar 7 '17 at 23:36
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
– Graham Kemp
Mar 7 '17 at 23:36
add a comment |
2 Answers
2
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oldest
votes
up vote
5
down vote
accepted
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 Arthan
28.7k42865
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up vote
4
down vote
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
Bram28
58.8k44185
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
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 Arthan
28.7k42865
add a comment |
up vote
5
down vote
accepted
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 Arthan
28.7k42865
add a comment |
up vote
5
down vote
accepted
up vote
5
down vote
accepted
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 Arthan
28.7k42865
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 Arthan
28.7k42865
edited Dec 3 at 18:28
answered Mar 7 '17 at 22:33
Rob Arthan
28.7k42865
answered Mar 7 '17 at 22:33
Rob Arthan
28.7k42865
answered Mar 7 '17 at 22:33
Rob Arthan
28.7k42865
28.7k42865
add a comment |
add a comment |
up vote
4
down vote
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
Bram28
58.8k44185
add a comment |
up vote
4
down vote
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
Bram28
58.8k44185
add a comment |
up vote
4
down vote
up vote
4
down vote
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
Bram28
58.8k44185
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
Bram28
58.8k44185
answered Mar 7 '17 at 23:02
Bram28
58.8k44185
answered Mar 7 '17 at 23:02
Bram28
58.8k44185
answered Mar 7 '17 at 23:02
Bram28
58.8k44185
58.8k44185
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.
– Henning Makholm
Mar 7 '17 at 22:30
1
A predicate is a function that maps entities/terms to truth-values/claims rather than to other terms.
– Graham Kemp
Mar 7 '17 at 23:36