Lecture 9b: Prolog Heshaam Faili hfaili@ece.ut.ac.ir University of Tehran The language of logic...

Lecture 9b: Prolog

Heshaam Failihfaili@ece.ut.ac.i

rUniversity of

Tehran

The language of logic

Concepts

Examples

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History

Kowalski: late 60’s Logician who showed logical proof can support computation.

Colmerauer: early 70’s Developed early version of Prolog for natural language processing, mainly multiple parses.

Warren: mid 70’s First version of Prolog that was efficient.

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Characteristics

Prolog approximates first-order logic. Every program is a set of Horn clauses. Inference is by resolution. Search is by backtracking with

unification. Basic data structure is term or tree. Variables are unknowns not locations. Prolog does not distinguish between

inputs and outputs. It solves relations/predicates.

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SWI-Prolog Notes Free! Down Loadable To load a file:

consult( ‘C:\\prolog\\test’). For help:

help(predicate-name). “ ; “ will give you next solution. ‘%’ comment listing(member) will give definition.

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Example

Facts: () likes(john,mary). likes(john,X). % Variables begin with

capital Queries

?- likes(X,Y). X=john, y=Mary. % hit “;” for more ?- likes(X,X). X=john.

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Example

Rules likes(john,X) :- likes(X,wine). % :- = if likes(john,X):- human(X), likes(X,john).

Note: variables are dummy. Standardized apart

Some Facts: likes(bill,wine). human(mary). human(sue).

Query: ? - likes(john,Y). Y = bill ; no.

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Family

father(a,b). father(e,d). mother(c,b). mother(d,f). parent(X,Y) :- father(X,Y). parent(X,Y) :- mother(X,Y). grandfather(X,Y):-

father(X,Z),parent(Z,Y).% Do your own for practice.

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Informal Summary

Program is facts + rules. (horn clauses).

Query = conjunct of predicates. First set of bindings for variables

that solve query are reported. If none, then Prolog returns no.

Use “;” to get other solutions. Can be viewed as constraint

satisfaction program.

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MapColoring

color(r). color(g). color(b). colormap(C1,C2,C3):-

color(C1),color(C2),color(C3), C1\==C2,C1\==C3, C2\==C3.

Query: colormap(X,Y,Z). X = r, Y= g, Z=b.

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Unification: (matching) terms

Two terms UNIFY if there is a common substitution for all variables which makes them identical.

f(g(X),Y) = f(Z,Z). % = cheap unification X = _G225, Y=g(_G225).

Look at parse tree for each term. variables match variable matches anything (set the binding) function symbols only match identical function

symbols.

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Satisfiability: uses unification

sat(true). % base case sat(not(false)). % base case sat(or(X,Y)):- sat(X). sat(or(X,Y)):-sat(Y). sat(and(X,Y)):-sat(X),sat(Y).

test1(X,Y):- sat(and(not(X),X)). test2(X,Y):- sat(and(X,not(Y))).

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List Operator [H |T]

[a,b,c] is a list in Prolog. [H|T] = [a,b,c] results in

H = a i.e. the head of list T = [b,c] i.e. the tail of the list.

membership definition member(H,[H|T]). % base case first.

Why? member(H,[_|T]) :- member(H,T). Use it.

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Member Tests

?- member(3,X). X = [3| _G109].

% _G.., system generated variable X= [_G11,3| _]. % etc.

?- member(X,Y). X = _G131, Y= [_G131|, _G321].

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Permutation & Insert

insert(X,L, [X|L]). insert(X,[H|T],[H|T1]):- insert(X,T,T1).

perm([],[]). perm([H|T],P):-

perm(T,T1),insert(H,T1,P).

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DFS

% solve(goal, solution Path)% s(state, successor-state)dfs(N,[N]) :- goal(N).dfs(N,[N|Sol1]):- s(N,N1), dfs(N1,Sol1).

s(a,b). s(a,c). s(b,d). s(b,e). s(c,f).s(c,g). s(d,h). s(e,i). s(e,j). s(f,k).goal(i). goal(f).

?- dfs(a,N). N = [a, b, e, i] ; N = [a, c, f] ;

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Cut !

P :- a, b. P :- c.

P :- a, !, b.P :- c.

P (ab)c

P (ab)(a c)

Use to ignore backtracking: performance issue

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MAX

MAX(X,Y,X) :- X>=Y.MAX(X,Y,Y).

?- MAX(3,2,X).

X=3 ; X = 2 !!!!!

MAX(X,Y,X) :- X>=Y, !.MAX(X,Y,Y).

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Factorial

factorial(0,1). factorial(N,F) :-

N>0, N1 is N-1, factorial(N1,F1), F is N * F1.

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Hanoi Tower move(1,X,Y,_) :-

write('Move top disk from '), write(X), write(' to '), write(Y), nl.

move(N,X,Y,Z) :- N>1, M is N-1, move(M,X,Z,Y), move(1,X,Y,_), move(M,Z,Y,X).

?- move(3,left,right,center). Move top disk from left to right Move top disk from left to center Move top disk from right to center Move top disk from left to right Move top disk from center to left Move top disk from center to right Move top disk from left to right yes

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More examples

http://www.csupomona.edu/~jrfisher/www/prolog_tutorial/contents.html

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Limitations

2nd order: Can’t ask what is relationship between heart and lungs?

Probabilities: What is likelihood of fire destroying Julian?

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