Predicate vs Functions in First order logic

Question

I have been so confused lately regarding difference between predicate and function in first order logic.

My understanding so far is,

Predicate is to show a comparison or showing a relation between two objects such as,

President(Obama, America)

Functions are to specify what a particular object is such as,

Human(Obama)

Now am I heading on right track to differentiate these two terms or I am completely wrong and need a brief explanation, I would like to have opinion from expert to clarify my knowledge(or approve my understanding). Thanks in advance

Krio

Answer 1

A predicate is a function that returns true or false.

Answer 2

Function symbols, which map individuals to individuals – father-of(Mary) = John – color-of(Sky) = Blue • Predicate symbols, which map individuals to truth values – greater(5,3) – green(Grass) – color(Grass, Green)

Answer 3

Predicate is confirmation for a particular property an objects or relation between objects. that is telling that property exists for that object. if you are given a formula P for president of America then

P(Obama,America)=true.

it tells you you are right and that property of Obama being President of America is true and that relation of Obama being president of America is true but

P(Putin,America)=false.

tells Putin being Americas president is false thus telling you that an object or objects holds or does not hold a particular property or relation. As for functions returns the value associated with a specific property of an object like America's President , Ann's mother etc. You give them a value and they will return a value.Like let P be a function that returns the president of country passed as arguments

P(America)=Obama.

P(Russia)=Putin.

Answer 4

From what I understand

Function returns a value that is in the domain, mapping n elements to a single member of the domain.

Predicate confirms whether the relation you are trying to make is true or not according to the axioms and inference rules you are following in your system.

Answer 5

Functions are relations in which there is only one value for a given input.

source : AIMA (Artificial Intelligent A Modern Approach Book)

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