Outline of Class 33: Logic Programming in Prolog

Held: Wednesday, April 22, 1998

Administrivia

• The second exam is this Friday. It will cover general functional programming issues, as well as some details in Haskell and Scheme. I've prepared a short review sheet so that you can have a sense of what will be on the exam. Feel free to ask me questions about the exam in class today. Note also that I'm willing to discuss rescheduling for those of you who have too many other pressing commitments.
• A number of you handed in assignment five very late. Those assignments are at the bottom of my "to do" pile and probably won't be graded for some time.
• A few of you have asked for a "redo assignment" for assignment five. I'll try to have one ready for Friday.
• I encourage those of you who haven't read the Kane and Krukowski reports to do so. Learn about what people are recommending for Grinnell.
• On Friday, May 1, the department will be hosting a picnic at Merrill park. Sign up to have fun with the majors, nonmajors, faculty, and families. It's gotta be more fun than the MathLAN, right?
• Prolog can be found in /usr/local/bin/bp. Instructions can be found at http://clement.info.umoncton.ca/BinProlog/UNCOMPRESSED/doc/html/art.html

Predicate-Logic Programming

• How might we use the predicate logic as a programming language? We could state "theorems" and ask the system to prove the theorems based on the rules of predicate logic and the definitions contained within our program. In effect, we state our theorem as a question and ask the program to answer it.
  • For example: "Is Socrates mortal?" "Yes, because Socrates is a person and all people are mortal."
  • Similarly: "Are there any mortals?" "Yes, Socrates is a mortal because Socrates is a person and all people are mortal."
  • Similarly: "Is Socrates immortal?" "No, because Socrates is mortal (see above) and no mortal is immortal."
  • And "Is Lou Reed influential?" "Yes, because Lou Reed was a member of the Velvet Underground and R.E.M. were influenced by the Velvet Underground."
• How might we implement such a language? Well, there are two aspects, depending on the type of question that is being asked.
  • To prove a theorem about an atom. In this case, we might "plug" the atom in to the right hand side and then attempt to prove the right hand side.
  • To prove a theorem about a variable, we may need to "guess" instantiations and plug in.
  • Note that the first quickly becomes the second. For example, in proving that Lou Reed is influential, we need to identify a band that Lou Reed was/is a member of. Then, we need to determine whether that band is influential.
• It turns out that some aspects of such proofs are extremely difficult. In particular, it may be impossible to prove a negation.
• To simplify matters, we may want to write a disjunction of Horn clauses: clauses that define predicates in which consist of only an and of assertions (i.e., no nots, the only ors are used around our horn clauses).
• In such a system, we have a simpler nondeterministic proof strategy: pick a rule that defines a predicate and attempt to prove each component of the right hand side.
• Of course, that leads to the question of how to deal with the nondeterminism. We'll return to that question later.

Prolog

• Prolog was developed in the early 1970's to demonstrate that it is possible to "program" in predicate logic. The paper that introduced prolog was titled something like "Logic + Control = Program".
• When people speak of "logic programming" they often mean "Prolog programming".
  • This can lead to some interesting misunderstandings. If have friends who do "equational logic programming", programming based on the logic of equations. However, many people think that they do "Prolog + equations".
• Prolog includes some nonlogical components (we'll discuss some of them), some of which are there for the sake of efficiency.
  • Many Prolog programmers take advantage of knowledge of these nonlogical components.
• An interaction with a Prolog system consists of
  • Specifications of basic facts about objects and relationships ("The Velvet Underground was an influential band.", "Maureen Tucker was a member of the Velvet Underground")
  • Specifications of rules about objects and relationships ("All members of influential bands are influential.")
  • Ask questions about objects and relationships ("Is Lou Reed influential?" "Is Barry Manilow influential?" "Are there any influential musicians?")
• As this suggests, Prolog is particularly good at working with so-called "atomic" or "symbolic" values. That is, values whose meaning is determined by the program.
• Basic syntax:
  • atoms, predicates, and functions begin with lowercase letters. For example, lou_reed, influential, ....
  • variables begin with uppercase letters or underscore. For example, Musician.
  • the arguments to a predicate are parenthesized and separated by commas. influencedBy(Musician,lou_reed).
  • a period indicates the end of a fact or rule.
  • lists are surrounded by brackets; items in a list are separated by commas; the vertical bar acts like cons (more or less).
    • [] -- the empty list
    • [a,b,c] -- a list of three elements
    • [a|X] -- a list whose first element is a and whose remainder is the list X.
    • [a,b|X] -- a list whose first two elements are a and b and whose remainder is the list X.
• Prolog predicate definitions have the form

  P :- Q1,Q2,...,Qn.
  

where the P and Q's are all predicate applications.

• For example,

  influential(X) :- influencedBy(X,Y).
  

• The meaning of the general form is "for (all the variables in P), if there exist values for (all the other variables in the Q's) such that all the Q's hold, then P holds.
• Basic facts (e.g., coolDude(louReed).) do not require the :-.
• A Prolog program is a collection of definitions. Input is a question, such as "does this predicate hold on these values?" or "for what values does this predicate hold?"
• Prolog is often used for databases as the basic facts are effectively database entries and the predicate definitions are ways to reason with the basic entries.

A Simple Example: Information about Musicians

• How might we write a program that describes some information about modern "alternative" music?
• First, we might want to choose some appropriate predicates. The one's I've come up with are:
  • influential(Group_or_Musician): is a group or musician influential.
  • influenced(Alpha,Beta): the Alpha influence Beta. Note that the meaning and ordering are determined solely by my description (and, later, by definitions).
  • memberOf(Musician,Group): Musician is a member of Group.
  • deservesFame(Musician): Musician deserves fame (perhaps all do, but we'll come up with some rules that may help decide when).
  • gold(Group,Record): guess.
• We'll develop some of our own rules, but here are some to start with.
• A group or musician is influential if they influenced someone.

  influential(G_or_M) :- influenced(G_or_M, Someone).
  

• A musician is influential if he or she belongs to an influential group.

  influential(Musician) :- memberOf(Musician,Group), influential(Group).
  

• Note that I might also have defined this as:

  influential(Musician) :- influential(Group), memberOf(Musician,Group).
  

• This makes no difference logically, but may make some difference relative to Prolog's solution strategy. The first is probably better.
• When does someone deserve fame? Perhaps when they influenced a group that had a gold record. (See, logic is hard :-).

  deservesFame(M_or_G) :- influenced(M_or_G, Group), gold(Group, Record).
  

• A group deserves fame if they influenced someone who deserves fame.

  deservesFame(M_or_G) :- influenced(M_or_G, Group), deservesFame(Group).
  

• Again, ordering may make a difference in efficiency (both ordering of rules and ordering of right-hand-sides).
• The remaining predicates may be defined by "base facts". Here are a few.

  memberOf(lou_reed, velvet_underground).
  memberOf(maureen_tucker, velvet_underground).
  memberOf(john_cale, velvet_underground).
  memberOf(sterling_morrison, velvet_underground).
  memberOf(doug_yule, velvet_underground).
  memberOf(willie_alexander, velvet_underground).
  memberOf(michael_stipe, rem).
  memberOf(bob_stinson, replacments).
  influenced(velvet_underground, rem).
  influenced(velvet_underground, jonathan_richman).
  influenced(jonathan_richman, silos).
  influenced(velvet_underground, replacements).
  influenced(replacements, nirvana).
  gold(nirvana, nevermind).
  

• We can now ask questions.

  ?- influential(velvet_underground).
  yes
  ?- influential(maureen_tucker).
  yes
  ?- influential(michael_stipe).
  no
  ?- memberOf(X, velvet_underground).
  X=lou_reed;
  X=maureen_tucker;
  X=john_cale;
  X=sterling_morrison;
  X=doug_yule;
  X=willie_alexander;
  no
  ?- deservesFame(X).
  X=replacements;
  X=velvet_underground;
  no
  

• Note that when I wanted other answers, I typed a semicolon. This is somewhat equivalent to "what else can you prove?".
• Note also that some of our predicates may be oddly defined. For example, our rules don't allow us to prove that members of groups that deserve fame also deserve fame. We could add rules for deservesFame or we could add a recursive rule for influenced.
• Note also that careless use of our rules can lead to false conclusions. For example, while the Velvet Underground were clearly influential, Willie "Loco" Alexander is far from influential.