introduction to prolog programming in logicnxg01/aicourse/lecture 5.pdf2008-09-18 introduction to...

2008-09-18

Introduction to Artificial Intelligence, Prolog (c) Peter Funk 1

Crash Course in Prolog Artificial Intelligence ��

MHD

Introduction to PROLOG PROgramming in LOGic

 Prolog-program are declarative and consist of properties, relations and rules.

 Lisp and Prolog are the most common programming languages for symbolic AI.

 Good to ”explore” and ”prototype programming".

 Prolog are based on Horn-clauses, a subset of first order predicate logic.

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Important to know about Prolog

n  Basics in Prolog: facts, lists [], meta-logical predicates, accumulator, tail-recursion, (DCG), generate-and-test, search.

n  Connection to other areas: Relational data-baser, Expert systems, Formal and automata-theory, (Natural language processing).

n  To think declarative.

Traditional Programming

Imperative programming: §  An abstraction of the Turing machine (a

program is instructions to a Turing machine).

§  Have an ”operational semantic” in terms of what the Turing machine has to perform.

§  Is context dependent (what operations have been made before).

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Logic programs

n  A description in a suitable logical notation describing a part of the real world or a fictive world.

n  Description of al needed to solve a task:

->relations between objects in a world (people, numbers, lists, trees, …).

Logic and Programming

A logic has 4 parts · syntax (describing logical formulas) · semantic (exact meaning) · a number of axioms (e.g. Tautologies: [a] = [a|[]] } · inference rules (e.g. modus ponens, “if a so b”)

Logics: First order logic, predicate logic, typed

logic, temporal logic (events, intervals, …), modal logic (probability, maybe, true in all worlds,…)

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Prolog & Logic today: n Prolog is used for prototypes n Some larger commercial systems (links to .exe and

users often not aware that system is in Prolog). n Compilation and Interpretation systems (Erlang used

at Ericsson is initially written in Prolog, used to program telephone exchanges).

n Graphic packets, fast execution, database acces, e.g mySQL, good interfaces to other programming languages (calls to/from e.g. C++/Java/PHP).

n Used in natural language processing, interpretation, translation etc.

n Good interfaces to web applications, web pages can use prolog (exv. LPA-Prolog – html – php - mySQL).

Status today for Logic and Logic programming:

n formal verification of safety critical systems (landnings wheels in air plains, train signals, medical hardware, etc).

n Hardware design (TTL-logic circuit, true=1=5 volt, false=0=0 volt), predicate logic, temporal logic, modal logic

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Future for Prolog? n  Knowledge representation (SDL, XML,

Relation databases -> Knowledge bases, natural language), temporal logic.

n  Safety critical systems need proof of their correctness n  Air plane, transportation, telecommunication,

medicine, etc (programs i C are very difficult to prove !).

n  Prolog is developed: n  Constraint Logic Programming (CLP): n  parallel-execution n  Agent programming n  web programming

Declarative description ~ Imperative Example for declarative description

Find all grand children of a certain person X. Declarative description

A grand child of X is a child of one of X’s children Imperative description

In order to find on grand child of X, first find one child of X, and then find a child of this child.

Imperative description II To find a grand child of X, first find a parent of one child, then check if the parent is a child of X.

• Logic: ∀ X ∀ Y (∃ Z

(child(X, Z) and child(Z, Y)) → grandchild(X, Y)). Prolog: grandchild (X,Y) :- child(X,Z), child(Z,Y).

read(person); for i := 1 to max_child do if child[i,1] = person then for j := 1 to max_child do if child[j,1] = child[i,2] then writeln(child[j,2]); fi od fi od

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Declarative and imperative languages

Imperative language

Declarative language

Philosophy Apply instructions of how to solve the problem

Apply descriptions of what the problem is

Program

A sequence of commands

A set of assertions

Example

Basic, C, C++, Ada, Java, Perl, php, Phyton, …

Prolog, ML, Scheme, Gödel, mercury, Oz, (SQL), …

Strength Fast and specialized program

General, readable and possibility of correct program

Different Language paradigms n  imperative languages are concrete and

enforcing, i.e., a given execution order. ”high level instructions to a processor”.

declarative program: n  Nothing about how it should be executed

(true in ”pure Prolog”). n  Describe only the problem and the

information of the problem. n  Origin in logic and how humans make

logical reasoning.

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Logic History 400 fK The first foundation was built by Aristoteles (axiom, premise,

conclusion “Alla valar är däggdjur" osv). 1930 Subject stabilized [Gödel, Church, Russel, etc.]. (Predicate logic

complete kartlagt Church-Turing-sentence => predicate logic == calculable funktions)

1960 Automatic Theorem Proving & AI. 1965  Resolution and unification [Robinson]. Resolution: an effective

conclusion drawing but rules must be written in a special form. 1972  The first Prolog-implementation [Colmerauer]. 1974  Logic programming (SLD-resolution) [Kowalski] (Algoritm = logic +

control, let computers decide how the problem should be solved, i.e., execution ord).

1977  Negation (SLDNF-resolution) [Clark]. (SLDNF completed negative assertion “A penguin can not fly").

1978  Edinburgh Prolog [Warren] (most common syntax today). 1981  Japanese announce its 5:e-generation project: robotic, AI, etc, with

logic programming (”main result”: increased use of computers in Japan with Kanji, romaji).

1995 – Constraint Logic Programming (CLP), Agent Programming (logic bubblor), …

Some Important Notes (Logic)

n  Predicate name is a name standing for both property and relation. green(grass). child(kai,mia)

n  Predicate name is followed by arguments. Arity gives the number of arguments of the

predicate. n  Arity= 0: satslogik (no argument) n  Arity= 1:property n  Arity= 2: relation

n  Arguments are called terms. A term can be constant, variable or a structure.

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Del 2: Test Prolog n  Free Prolog for Education (Linux/Mac/

Windows): http://www.swi-prolog.org/ Small space ( 4 Meg). Many Prolog introductions on web, search with

www.google.com for Prolog tutorial introduction

Prolog is different

n  Prolog has no global variables. n  No variable assignment statements n  No iterative constructions (e. g. loop) n  No ”if … then” format n  Recursion is central in Prolog

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Concept in Prolog n  True or false, a Prolog expression can only

accept two values, true or false n  Two arguments can be equal or different.

Equality can be obtained by binding free variables. lecturer(peter) = lecturer(X).

n  Search, Prolog is based on searching, Prolog tries to find a solution and test different ways.

n  Backtracking, if search fails, Prolog goes back and tests alternative ways (depth first).

Property Written as man(adam). man(kalle). man(lasse). woman(lisa). woman(eva).

RELATIONs written as: parent(adam,peter). % adam is parent of peter parent(eva,kalle). parent(eva,lisa). parent(lisa,lasse). parent(kalle, knut). Rest text after % is

comment

% Complete always with a point.

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Definition of Rule

Every rule has a head – name which defines the relation.

Every rule has a body – self definition of the relation. Definitions of father and mother are as follows:

”If M is a woman and M is parent of C then M is mother of C”: mother(M,C):- woman(M), parent(M,C).

”If F is a man and F is parent of C then F is father of C”: father(F,C):- man(F), parent(F,C).

”,” means logic ”AND”, both man och parent must be true in order for father to be true.

”:-” means logic implikation, ← but this is not available on keyboard, so prolog has adopted :-

Prolog Interpretations n  Facts and rules are written in file which have

ending .pl n  Dropp the file on the prolog icon or load prolog file

(se manual). Ask Prolog I there are any women.

| ?- woman(X). X = lisa ? ; X = eva ? ; no | ?-

typing ”;” after a answer asks prolog for more alternative answers.

Prolog Prompt: Prolog always prompts ”?-”. After the prompt you can enter your question.

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If we only whish to know if ther is a women. | ?- woman(_). yes | ?- child(_). no

Prolog is based on ”negation as failure”, all prolog does not know is false (will talk more about this later).

The prolog history with it’s roots in Edinburgh and Scotland makes Whiskey (distillated beer put in an ok barrel 3 years or more) examples common.

Write this in a textfile with the ending “.pl” ;

whisky(bowmore). whisky(glenlivet). region(bowmore, islay). region(glenlivet, highland). age(bowmore, 12).

Is there a whisky from Islay and how old is the whisky? | ?- region(W, islay), age(W, A). A = 12, W = bowmore ? ; no | ?-

W is instantiates to (binds to) bowmore.

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whisky(bowmore). region(bowmore, islay). age(bowmore, 12).

Is there a whisky older than 8 years? | ?- whisky(W), age(W, A), A>8. A = 12, W = bowmore ? ; no | ?-

Structure 3 different ways to write the same facts: taste(oban, 16, taste, peat, medium, smoky, medium, body,

medium). taste(oban, 12, [peat, medium], [smoky, medium], [body,

medium]). taste(oban, 12, [[peat, medium], [smoky, medium], [body,

medium] ]). taste(oban, 10, taste(peat(medium), smoky(medium), body

(medium))). Warning, it is easy to misunderstand structures in

Prolog, there are no functions in Prolog!

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taste(oban, 10, taste(peat(me), smoky(me), body(me))).

| ?- taste(W, _, S). S = taste(peat(me), smoky(me), body(me)), W = oban ? ; no | ?-

taste(oban, 10, taste(peat(me), smoky(me), body(me))).

| ?- taste(W, _, taste(peat(T), _,_)). T = me, W = oban ? ; no | ?-

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Mer REGLER whisky(bowmore). region(bowmore, islay). age(bowmore, 12). taste(bowmore,12, taste(peat(me), smoky(me),

body(me)).

man(peter). % All men M and whisky W is true that… % M likes W. likes(M, W) :- man(M), whisky(W).

What does Peter like? | ?- likes(peter, X). X = bowmore ? ; no | ?- \+ likes(peter,bowmore). no

whisky(bowmore). region(bowmore, islay). aalder(bowmore, 12). taste(bowmore,12, taste(peat(me), smoky(me), full(me)). man(peter). likes(M, W) :- man(M), whisky(W).

Negation, ”it is not true”, is written”\+”

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Task

1) Add the fact that Kalle has a daughter Mia. 2) Write a clause that defines the relation cuisine,

e.g. answering who Mia is cuisine with. Extra: 3a) write a clause that defines grand mother. 3b)

Use this rule to show that Eva is Lasses grand mother. Preferable use a relation mother with two arguments (to show a predicate’s number of arguments the notation is “mother/2”).

man(adam). man(kalle). man(lasse). woman(lisa). woman(eva). woman(mia). parent(adam,lasse). % adam är förälder till lasse parent(eva,kalle). parent(eva,lisa). parent(lisa,lasse). parent

(kalle,knut). father(F,C):- man(F), parent(F,C). mother(M,C):- woman(M), parent(M,C).

Idea to answer (there are many different ways to solve it)

cousin(K1, K2):- parent(P1, K1), parent(P2, K2), sibling(P1,P2).

sibling(S1,S2):-

parent(X,S1), parent(X,S2), S1 \== S2. % S1 and S2 can not be the same person,

% you can not be a sibling with yourself J

Test i Prolog ?- kusin(X,Y). X = lasse Y = knut ; no

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Lists n  [ ] : an empty list n  [1, 2, abba] : a lista with 3 elements n  [[11, 12, 13], [21, 22, 23], [31, 32, 33]] :

a 3x3 matrix (a list with 3 rows where every row has 3 columns).

Lists Head of a list, tail of a list, analogy with

CAR and CDR in LISP These two lists are identical! ?- [a,b,c] = [a|[b,c]]. Yes ?- [a,b,c] = [Head|Tail]. Head=a Tail=[b,c] | ?-

Gives the head and the tail

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Some basic clauses: member % Clause member % X is member in a list if it is the first element in

the list, e.g is a member of [a,b,c] member(X, [X|Tail]). member(a,[a|[b,c]]).

% If not, then X needs to be in the tail. member(X, [First|Tail]) :- member (X, Tail). ---- | ?- member(1, [abba, 1, 3]). yes

Tail recursion= if the last predicate is the predicate itself. As efficient as a loop in C if execution time is an issue.

member member(X,L) :- L = [X|Rest]. member(X,L) :- L = [F|Rest], member(X, Rest). | ?- member(X, [abba, 1, 3]). X = abba ? ; X = 1 ? ; X = 3 ? ; no | ?-

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member | ?- member(1, [A, B]). A = 1 ? ; B = 1 ? ; no | ?-

Tricky, A and B are variables and may be anything, e.g. 1. So both the first elements may be ”1” and the second element in the list may be ”1”.

first, second, tail % First element in list. first(X, [X|_]). % Second element in list. second(X, [ _,X|_ ]). % Rest of list. tail(R, [ _|R]).

| ?- first(X, [kalle,lisa,mats]). X = kalle? ; no | ?- | ?- second(X, [kalle,lisa,mats]). X = lisa? ; no | ?- | ?- tail(X, [kalle,lisa,mats]). X = [lisa,mats]? ; no | ?-

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Aritmetic an others n  A condition is true or fals: <, >, >=, =<,

=:=, =\= (reduces left and right side ). n  is (exempel ?- X is 4 + 3) n  ==, \== (exact equal) n  = (unification, Prolog tries to bind all

unbound variables as far as possible. If Prolog succeeds it is called a successful unification).

n  +, -, *, /, sin, cos, tan

| ?- 2 =< 4. yes | ?- 2+2 =:= 4. yes | ?- 2+2 =:= 5. no | ?- 2+2 =\= sin(0), 0 + 0 =:= sin(0). yes

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Trace | ? - trace, X is sin(4/5), X>2. 1 1 Call: _59 is sin(4/5) ? <ENTER> 1 1 Exit: 0.71735609 is sin(4/5) ?

<ENTER> 2 1 Call: 0.71735609 > 2 ? <ENTER> 2 1 Fail: 0.71735609 > 2 ? <ENTER> 1 1 Redo: 0.71735609 is sin(4/5) ?

<ENTER> 1 1 Fail: _59 is sin(4/5) ? <ENTER>

”Redo” meens that Prolog interprer backtracks (backs one or more steps to try to find an other solution).

A is B. B is calculated and unified with the variable och

constant A. | ? - Area is 3.14 * 5 * 5. Area = 78.5 ? <ENTER> yes | ? - 4 is 4. yes | ? – X is 2 + M. ERROR | ? – M = 2, X is 2 + M. X = 4

• To calculate the right side of ”is” no unbound variables are

alowed

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Strictly equal ”==” | ?- V == Q. %variabel V is not strictly equal to Q % e.g. you may bind V with 1 and Q with 2 no | ?- V = 5, Q = 5, V == Q. %Now V and Q are strictly

equal yes | ?- 1+2 == 2+1. % structur 1+2 is not strictly 2 + 1 No | ?- 1+2 == 1+2. yes | ?- +(1,2) == 1+2. % structur 1+2 is strictly equal 2 +

1 yes

Unifying ’=’ Two predicats may be unified if and only if n  They have the same name n  They have the same amount of

arguments Arguments can be unified Two arguments may be unified if and only if n  Both are the same constant n  Both are structures...

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Unification ”=”

Two structures may be unified if and only if

n  They have the same constructor (namn, e.g. +, peat, ..)

n  They have the same number of arity (same number of parameters)

n  The parameters can be unified

Exampel on unifification -1 | ?- xx(left, 123, X) = xx(A,B,B). A = left, B = 123, X = 123 ? ; | ?- cbc = X. X = cbc ? | ?- +(5,5) = 5 + 5 yes Why does this example fail? | ?- X = 5 + 5, X = 10. no

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Example on unification 2 | ?- E = 1+2. E = 1+2 ? <ENTER> Yes (E has beed bound to the structure

”1+2” which is equal to +(1,2) | ?- p(p(p(p(0)))) = p(p(X)). X = p(p(0)) ? ; no | ?-

Example on unification 3a

% predikatet lenght1 length1(0, [ ]). length1(N, [ F|R]) :- length1(N2, R), N = N2+1.

| ?- length1(X, [a,b,c]). X = 1+(1+(1+0)) ? ; no | ?-

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Example on unification 3b

% predicat: lenght1 length1(0, [ ]). length1(N, [ F|R]) :- length1(N2, R), N is N2+1.

| ?- length1(X, [a,b,c]). X = 3; no | ?-

Syntax n  Predicat: mamma, mMM, no_1_. n  Variables: W, W12, _12 n  Constanter: stefan, sTEFAN, ’Stefan’ n  Structurer: node(node(X,10,nil),12,nil). n  Lists: [], [1,2, [44, 55], 3], [a,n(1,2,3)] n  Arithmetik : +, -, *, /, sin, cos, tan, <, >,

>=, =<, =:=, =\=, ==, =, is

n  numbers: 0,…, 9, 123.31, 55.2e-3

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Closed world assumption (CWA)

Exempel: SJ says that there is a train from Stockholm at 8:07. But it is not mentioned that there is NO train at 8:10 or 8:15.

Since nothing is mentioned about a train leaving at 8:15 then there is most likely no train.

CWA: Things not mentioned are noDet som inte kan visas är inte sant.

Negation as Failure: NF: Everything the program can nDet som

Prologprogrammet inte kan härleda i ändlig tid är falskt.

Negation i Prolog

”Negation by failure” is written i prolog as ”\+” Exemple: ?- X = z, \+ member(X,[a,b,c]). yes ?- X = c, \+ member(X,[a,b,c]). no

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How does Prolog find all solutions n  Depth-first with backtracking: n  Once a leaf is reached the interpreter

backs up and takes the first found branch to the left.

n  Problem: infinite sub trees ⇒ program execution never ends.

SLD-tree for ← member(X, [a, b, c])."

Program: member(X, [X|_]). member(X, [_|T]) :- member(X, T).

← member(X, [a, b, c]).

← ← member(X, [b, c]). X/a ← ← member(X, [c]). X/b ← ← member(X, []). X/c

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Search in prolog

door(s,a). door(a,b). door(b,c). door(c,d). door(d,e). door(e,f). move(A,B):-door(A,B). % Is there a door between A and B then we can

reach B move(A,B):-door(A,X), move(X,B).

%is there a door between A and X % is it possible to get from X to B then we succeeded to go from A to B ?- move(s,f). Yes

a b c

d e f

s

Search, new door e-b door(s,a). door(a,b). door(b,c). door(c,d). door(d,e). door(e,b). %now risk for loop door(e,f).

move(A,B):-door(A,B). move(A,C):-door(A,X), move(X,C).

?- move(s,f). Stack overflow

a b c

d e f

s

move(A,B, _):-door(A,B). move(A,B,V):-door(A,X), \+ member(X, V), move(X,B, [X|V]). ?- move(s,f). Yes move2(A,B,V,P):-door(A,B), V = P. move2(A,B,V,P):-door(A,X), \+ member(X, V), move2(X,B, [X|V], P). ?- move2(s,f, [], P). P = [a,b,c,d,e,f]

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Metalogic predicat " Prolog contains a number of predicate that are not strictly first

order logic. You may also write programs able to change their own code (an important feature for AI)."

"

?- write(”hello world ”), writeln(5). hello world 5 n  var(X) – fails if X is bound to a constant.

Exempel:""

?- X = Y, var(X). yes"?- Z = hello, var(Z)."no"?- var(sol). no "• integer( X) - true ifX is bound to a number."• atomic(X) - true if X is bound to a constant.

This is all knowledge needed to write Prolog programs.

The rest is hard work, practice in

thinking descriptive and exercise your brain out of imperative programming

Read more Prolog tutorials on the

web!

introduction to prolog programming in logicnxg01/aicourse/lecture 5.pdf2008-09-18 introduction to...

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