How is predicate logic represented in Prolog?

Question

may be a strange and broad question and not a 100% programming question, but I hope this is ok. I recently had a discussion about, that a lot of programs in Prolog don´t follow strict predicate logic (of Frege) but often are "object oriented" which I am trying to grasp.

I know that Prolog is based on first order predicate logic especially Horn Clauses and that they are a special form of modus ponens. A fact and a rule if they occur solo are simply clauses, but as soon as I add more than one occurrence they become a predicate.

How are the quantors of first order predicate logic represented and related to fact , rule , predicate or the Prolog concept in general? What does the functor express and what the arguments in relation to predicate logic. How is predicate logic and first order predicate logic reflected in Prolog and where does prolog leave their concepts? e.g. how would I define a point, a line and a vertical line in predicate logic and first order predicate logic.

How do I formulate this in predicate logic and first order predicate logic what is the semantic and logic difference between

vertical(line).
line(vertical).

Or a line and point in this example. Are point and line not predicate logic? For me it is " point(X) the set of all points" and when I pick a concrete point "there exists one point(110, 12)."

point(X,Y).
line(point(W,X), point(Y,Z)).

vertical(line(point(X,Y), point(X,Z))).
horizontal(line(point(X,Y), point(Z,Y))).

Any info helps! Many thanks, H

Answer 1

A chapter of Programming in Prolog by W.Clocksin and C.Mellish is devoted to explain the relation of Prolog with logic. Citing from there

If we wish to discuss how Prolog is related to logic, we must first establish what we mean by logic. Logic was originally devised as a way of representing the form of arguments, so that it would be possible to check in a formal way whether or not they are valid. Thus we can use logic to express propositions, the relations between propositions and how one can validly infer some propositions from others. The particular form of logic that we will be talking about here is called the Predicate Calculus. We will only be able to say a few words about it here. There are scores of good basic introductions to logic you can turn to for background reading.

If we wish to express propositions about the world, we must be able to describe the objects that are involved in them. In Predicate Calculus, we represent objects by terms. A term is of one of the following forms:

• A constant symbol. This is a symbol that stands for a single individual or concept. We can think of this as a Prolog atom, and we will use the Prolog syntax. So greek, agatha, and peace are constant symbols.
• A variable symbol. This is a symbol that we may want to stand for different individuals at different times. Variables are really only introduced in conjunction with quantifiers, which are discussed below. We can think of them as Prolog variables and will use the Prolog syntax. Thus X, Man, and Greek are variable symbols.
• A compound term. A compound term consists of a function symbol, together with an ordered set of terms as its arguments. The idea is that the compound term represents some individual that depends on the individuals represented by the arguments. The function symbol represents how the first depends on the second. For instance, we could have a function symbol standing for the notion of "distance" and two arguments. In this case, the compound term stands for the distance between the objects represented by the arguments. We can think of a compound term as a Prolog structure with the function symbol as the functor. We will write Predicate Calculus compound terms using the Prolog syntax, so that, for instance, wife(henry) might mean Henry's wife, distance(point1, X) might mean the distance between some particular point and some other place to be specified, and classes(mary, dayafter(W)) might mean the classes that Mary teaches on the day after some day W to be specified.

Thus in Predicate Calculus the ways of representing objects are just like the ways available in Prolog.

Seems not appropriate to put the entire chapter here... there is also a program, very explanatory, in appendix B, that performs an automatic translation of WFFs into clauses.

The book is very readable, just a pity it's not among the titles in Free Prolog Programming Books section.