Functions - first-order logic:

Functions can be thought of as exceptional predicates, wherever we think of all but one of the arguments as input and the output as final argument. Thus such each set of things such kind of classed are as the input to a function, there is exactly one output to just that they are related by the function. To compose it obvious that we are dealing with specify a function, we can need an equality sign. So, for example, if we wanted to say that the cost of an omelette at the Red Lion pub is five pounds, the normal way to express it in first-order logic would probably be:

cost_of(omelette, red_lion, five_pounds)

However, because we know this is a function, we can make this clearer:

Because we know that there is only one output for every set of inputs to a function, we tolerate ourselves to use an abbreviation when it would make things clearer. That is, we can talk about the output from a function without explicitly writing it down, so to rather replacing it with the left hand side of the equation. So, it can be easily understand by example, if we wanted to tell that the price of omelettes at the Red Lion is less than the price of pancakes at the House Of Pancakes, then we would normally write something like this: