Artificial Intelligence － Prolog Programming －

Artificial Intelligence－ Prolog Programming － Ryo Hatano JAIST Oct 16, 2012

About this Lecture • Today only • No report, no examination today • But midterm examination contains some quiz about Prolog • TA: Ryo Hatano, D1 student of Tojo lab r-hatano@jaist.ac.jp • Lecture matelials: https://www.jaist.ac.jp/~s1220010/

Objectives • Study about the basic usage of Prolog • Understand the basics of logic programming • Become able to study Prolog by yourself • Today, I’ll teach only introduction

Reference • I. Bratko, Prolog Programming for Artificial Intelligence • Shapiro et al, The Art of Prolog • P. Blackburn et al, Learn Prolog Now! • S. Russell et al, Artificial Intelligence A Modern Approach • I. Bratko, Prologへの入門 • 古川康一他, 帰納論理プログラミング • S. Russell 他, エージェントアプローチ人工知能 (easy) (contains advanced topics) (be available online) (chap. 9 contains some background info) (わかりやすい) (短くまとまっている) (8章が背景に詳しい) You can find some books about Prolog in JAIST Library or online via Google.

What is the Prolog ? • PROgrammation en LOGique • Programming language which based on predicate logic • The implementation is a kind of automated proving system • It specializes in logical processing and knowledge representation • It suitable for the problems to handle relation between some objects • Symbol processing is better

Simple Planning System • There is a person in a room • He wants to catch a banana hanging from a ceiling • He have to find a way to the banana Definition of predicates for solving move(state(Before), command, state(After)). state(X, Y, BOX, Has). canget(state):- ←Recursion rule The problem can solve using only these predicates！

Monkey & Banana problem (details, for reference) state(atdoor, onfloor, atwindow, hasnot) walk(atdoor, P2) state(P2, onfloor, atwindow, hasnot) climb(onfloor, onbox) P2 = atwindow state(atwindow, onbox, atwindow, hasnot) Backtrack(onbox→onfloor) state(atwindow, onfloor, atwindow, hasnot) push(atwindow, P2’) state(P2’, onfloor, P2’, hasnot) climb state(P2’, onbox, P2’, hasnot) Grasp P2’ = middle Other backtracks are ommitted state(middle, onbox, middle, has)

Overview of the Prolog • Using of the Prolog environment • start, stop, load, execution • Many Syntaxes • Basics • Data structure, operators and recursion • Evaluation process • Advanced • list, cut, syntax sugar, user defined operator, extra logical predicates, set predicates, failure driven loop Today’s Topics and some samples

Overview of the Prolog (cont, for reference) • Theoretical Backgrounds • History • Formal Semantics of Prolog • Warren Abstract Machine • Herbrand’s Theorem • Evaluation Algorithms • Advanced topics • Meta programming (Higher order programming, Meta interpreter) • Grammar parsing with DCG (Definition Clauses Grammar) • Theorem proving and its application with user defined axiomatic system • Other Logic programming (Inductive logic programming, Probabilistic logic programming) • etc…

About the Prolog environment • Implementation • SICStus Prolog • SWI Prolog • GNU Prolog • Development environment • Prolog mode of Emacs • PDT of Eclipse • Text editor+ Prolog interpreter Not free, performance is good, but not easy to use Free, easy to use, recommend Note: some built-in libraries are not same

Basic Usage of the Prolog Environment • Using interpreter • You can control the prolog system interactively • First we load the program first. Then input a query after outputs of “?-”. Example ←load program by short notation ?- [sample_1e.pl]. % sample_1e.pl compiled 0.00 sec, 1,004 bytes ?- foo(bar). true. ?- foo(X). X = bar; X = baz ?- halt. ←load then compile ←query which input by user ←If other answer exists, input “;” then search next answer

Basic usage of the Prolog Environment (cont.) • Start • %prolog [-l] [filename] • Exit • halt. • Ctrl + ‘d’ • Interrupt and termination • Ctrl + ‘c’ then ‘a’ • File load • chdir(‘dir_path’). Change the current directory (ex.‘c:\\test’) • consult[‘file_name’]. or[‘file_name’]. Execute the file load • File reload • make. Reload the edited file • Trace • trace. It shows all steps of evaluation. “notrace” is for exit. In OS shell, -l is option for loading a prolog program (See also: official manual)

Syntax of the Prolog program Data structures Clauses Head:- Body. Predicate(Term, Term, …, Term) VariableConstantFunction + Operators • Arithmetic, Comparison, Substitution, User defined • Unification, Control of backtrack • Comment + Some technics (ex. Recursion)

Comment • One line comment • From “%”to end of the line • Multi line comment • From “/*” to “*/” Write the comment in the source code and give the readability. It is important habit in software engineering. Example in Prolog programs /* Multi line comment */ foo(bar) %comment to end of the line

Clauses • Prolog program consists of the set of “Horn clauses” • Horn clause is clause which has zero or one positive conclusion • Prologsystem has 3 types of clauses • Facts, Rules, Goals(Query) Example in predicate logic These formula are expressed to the form of Prolog In the real program Program clauses

Example of Program Program • Notation of clauses in Prolog Head:- Body. % All of these are horn clauses！ vegetable(carrot). fruit(apple). vegetable(tomato). fruit(tomato). plant(X) :- vegetable(X). plant(X) :- fruit(X). plant(X) :- fruit(X), vegetable(X). Fact clauses Rule clauses Interpreter ?- plant(X). ← Goal clauses(query) Write the period end of the each clauses It is equivalent to implication operator “→” in predicate logic. But the direction is opposite(Body→Head).

Fact clauses • The clause express about the facts • Clauses has empty body (condition) • ⇔ Head (conclusion) only. • It contains predicates and constants which value is always true Empty value means “true” in Prolog system Explain about predicates is later Example of Prolog program vegetable(carrot). %Carrot is a kind of vegetables fruit(apple). %Apple is a kind of fruits vegetable(tomato). fruit(tomato). %Tomato is a kind of fruits and vegetables Equivalent form of predicate formula

Rule clauses • The clauses express about rules • The clause has head and non empty body • It offers the function of Modus Ponens like implication operator • True/False value is depends on the contents of the body Example in Prolog programs plant(X) :- vegetable(X). plant(X) :- fruit(X). plant(X) :- vegetable(X), fruit(X). Comma “,” means “and” condition. Semi colon “;” means “or” condition. If there are some same heads of fact and rule clauses, it means “or” condition Equivalent form of predicate formula Important notations are “．”, “，” and “:-”.

Goal clauses • The clause express about query • The clause has only body • It consists of at least one goal • There are 2 types of queries • Yes/No type, What type Example in interpreter(“Yes/No”type of query) ←Query which ask the fact exists ?- vegetable(carrot). true. ←System answers Yes or No Example in interpreter(“What” type of query) ←Query which contains valiable ?- vegetable(X). X = carrot. ←System answers the value of variable If the answer doesn’t exists, system answers error. Equivalent form of predicate formula Prolog system tries to find the answer of this arrow.

Data structures • All data objects treats as “term” in Prolog system • There are 3 types of terms • Constant • Variable • Function(= It is the complex data structure which consists of some elements)

carrot. miss_mary. 1234. ======>. ‘Mr. Tom’. 日本語の定数. ←Some atoms already used by system such as “:-” ←If you need constants which starts with upper case, “‘” is suitable ←This is exceptional case. It depends on environment Atoms • There are 3 types of atoms • Character string which starts with lower case or number • Special character string+, -, *, /, <, >, =, :, ., &, _, ~ • Quoted string Example of constants There are some special constants such as “true”, “end_of_file”. It depends on environment.

Variables • There are 2 types of variables • Normal variables which starts with upper case or under score • Anonymous variables which only express in under score • Temporary name of variables which appears only one time in the clause • When it appear, it allocates different number by the system • Anonymous variables in query ignores when answer Example of variables X Result _Arg1 hoge( _ , X):- ... ←Anonymous variable excludes from evaluation Memory allocates when variables evaluated

Function • Structural data which has some elements • Functor(Term1, Term2, …) • The naming rule is same as constants • The number of arguments calls “arity” • Function only refers other terms. It doesn’t have truth value. Another name is “Compound term” Example of function fruit(apple). plant(eatable(X)):- fruit(X). ←Function and predicate are not same Functor Term Predicate Interpreter ?- plant(Func). Func = eatable(apple). ←It only directs other terms. “eatable(apple)” is not returns true.

Function (cont.) • The data structure consider as tree • When all elements of some trees are same, they treat as same data It depends on matching operation Example of tree structurefather(parent(X, Y), male(X)) father The root of tree calls to Principal functor parent male X X Y

Predicates • Structural data which express relation between terms • Predicate symbol(Term1, Term2, …) • The naming rule is same as constants • Predicate symbols and terms constructs atomic formula. It has truth value. Example of predicates fruit(carrot). plant(X):- fruit(X). father(X):- parent(X, Y), male(X). ←It can contains some variables and constants. Predicate symbol Terms

Predicate (cont.) • Distinguish the same predicate or not is by predicate symbol and arity • Short notation “predicate symbol/arity” has used Example plant(X) :- vegetable(X). plant(Y) :- vegetable(Y), fruit(Y). Body and variable name are same, but each predicate Treat as same byplant/1 Note: The problem of distinguish predicates and tree structure of functions are not same.

Arithmetic operator • X + Y Addition • X - Y Subtraction • X * Y Multiplication • X / Y Division • X // Y Quotient of the natural number division • X mod Y Remainder of the natural number division • X is Y Y substitute to X(Y need to be bind) Example of arithmetic formula ?- Result is 2 + 3. Result = 5. ?- Result = 2 + 3. Result = 2 + 3 ←example of correct arithmetic operation and substitution ←it is not correct. “＝” is not arithmetic operation. So it is not evaluated. In general, the arithmetic operator writes in infix notation

Comparison operators • X > Y X is greater thanY • X < Y X is less thanY • X >= Y X is greater than or equal toY • X =< Y X is less than or equal toY • X =:= Y (Arithmetic formula) value of X andY are equals • X =\= Y (Arithmetic formula) value of X andY are not equals • X == Y Terms X and Y are equals • X \== Y Terms X andY are not equals

Unification • X = Y Matching X and Y, then if it matches true otherwise false Example of unification ?-date(_Day, _Month, 2012) = date(9, april, _Year). _Day = 9 _Month = april _Year = 2012 ←it returns most general solution Matching of the Prolog is near to predicate logic

Recursion • The evaluation process calls itself • The rule which calls itself in the body • Usually, it uses as loop • The condition (address of variables and values) of each predicates are saved on memory When returns, the process take the values from memory Example of recursion factorial(0, 1). factorial(N, Result):- N2 is N – 1, factorial(N2, Result2), Result is N * Result2. ←Stop condition. It needs to write above recursion.

Outline of the evaluation process • Prolog system is a kind of automated theorem proving system • It mainly consists of 4 technics • Depth first backward search • Unification • Backtracks • Closed world assumption

Depth first backward search Source code Interpreter %Definition of facts fruit(apple). fruit(tomato). vegetable(tomato). %Definition of rules plant(X) :- fruit(X). plant(X) :- vegetable(X). ?- trace. true. ?- plant(X). Call: (6) plant(_G466) ? creep Call: (7) fruit(_G466) ? creep Exit: (7) fruit(apple) ? creep Exit: (6) plant(apple) ? creep X = apple Search tree plant It searches from query to defined facts by depth first fruit vegetable apple tomato tomato

Unification Source code Interpreter %Definition of facts fruit(apple). fruit(tomato). vegetable(tomato). %Definition of rules plant(X) :- fruit(X). plant(X) :- vegetable(X). ?- trace. true. ?- plant(X). Call: (6) plant(_G466) ? creep Call: (7) fruit(_G466) ? creep Exit: (7) fruit(apple) ? creep Exit: (6) plant(apple) ? creep X = apple Search tree plant It matches variables and terms. The scope is only same clause. X= apple fruit vegetable apple tomato tomato

Backtracks Source code Interpreter %Definition of facts fruit(apple). fruit(tomato). vegetable(tomato). %Definition of rules plant(X) :- fruit(X). plant(X) :- vegetable(X). X = apple ; Redo: (7) fruit(_G466) ? creep Exit: (7) fruit(tomato) ? creep Exit: (6) plant(tomato) ? creep X = tomato Search tree plant It backs to former branch then search other answers. fruit vegetable apple tomato tomato

Closed world assumption Source code Interpreter %Definition of facts fruit(apple). fruit(tomato). vegetable(tomato). %Definition of rules plant(X) :- fruit(X). plant(X) :- vegetable(X). ?- plant(X). X = apple ; X = tomato ; X = tomato ; X = tomato. ?- ←Waiting for next query Search tree There are no more things substitute to X. In the prolog, there are assumption which Means not defining things are all false. Therefore, the result of this example is false. plant fruit vegetable apple tomato tomato It is called closed world assumption No more choices

Artificial Intelligence － Prolog Programming －