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







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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




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    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


















3












$begingroup$


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







share|cite|improve this question









$endgroup$








  • 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
















3












3








3





$begingroup$


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







share|cite|improve this question









$endgroup$




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






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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
















  • 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












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.






share|cite|improve this answer











$endgroup$





















    4












    $begingroup$

    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)






    share|cite|improve this answer









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      2 Answers
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      active

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      2 Answers
      2






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      5












      $begingroup$

      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.






      share|cite|improve this answer











      $endgroup$


















        5












        $begingroup$

        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.






        share|cite|improve this answer











        $endgroup$
















          5












          5








          5





          $begingroup$

          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.






          share|cite|improve this answer











          $endgroup$



          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.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Dec 3 '18 at 18:28

























          answered Mar 7 '17 at 22:33









          Rob ArthanRob Arthan

          29.2k42966




          29.2k42966























              4












              $begingroup$

              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)






              share|cite|improve this answer









              $endgroup$


















                4












                $begingroup$

                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)






                share|cite|improve this answer









                $endgroup$
















                  4












                  4








                  4





                  $begingroup$

                  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)






                  share|cite|improve this answer









                  $endgroup$



                  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)







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Mar 7 '17 at 23:02









                  Bram28Bram28

                  61.5k44793




                  61.5k44793






























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