Progol - Output from Animals example

The following is a trace of Progol learning different rules to discriminate animals. The trace was generated at verbosity level 1, which makes Progol slightly more talkative than is usual. It shows various intermediate steps in theory construction, enclosed within "[" and "]". In the search, this trace shows every clause tried by Progol. Each clause is preceded by 4 numbers. These are, in turn,

f = Number of positive examples covered -
    Number of negative examples covered -
    Number of literals in body of clause -
    Optimistic estimate of literals needed
p = Number of positive examples covered
n = Number of negative examples covered
h = Optimistic estimate of literals needed

Below Progol reads in the file animals.pl. It notes all mode declarations and adds background knowledge and positive and negative examples to its clause base. Have a look at the file animals.pl. A mode declaration is a query aimed at the Prolog interpreter within Progol. Prolog queries have a `:-' at the beginning and a `?' at the end to differentiate them from from aserted statements. Thus

  :- modeb(1,has_milk(+animal))?

is a mode declaration describing the form of a literal which can be used in a Progol hypothesised clause (see more about mode declarations below). A positive example is a statement such as

  class(dog,mammal).

A negative example is a statement such as

  :- class(trout,mammal).

Background knowledge is described as arbitrary pieces of Prolog code. For instance,

  has_eggs(trout).

is a statement in the background knowledge. Progol generalises any predicates associated with `modeh' (head mode) declarations. In this case, the predicate class/2. The statement

  :- modeh(1,class(+animal,#class))?

says that generalisations must all have the form

  class(A,#) :- ...

where A is an input variable of type animal/1 and # is a constant of type class/1. The bodies of generalisations will be constructed using `modeb' (body mode) declarations. For instance the declaration

  :- modeb(1,has_milk(+animal))?

allows the generalisation

  class(A,mammal) :- has_milk(A).

In the following Progol first learns constraints such as

  :- class(A,mammal), class(A,fish).

which says the no mammal is a fish and conversely no fish is a mammal. This clause is stored within Progol as

  false :- class(A,mammal), class(A,fish).

This is a generalisation of the negative example

  :- class(trout,mammal).

Following this, general rules are learned for distingishing the class of animals. For instance,

  class(A,bird) :- has_covering(A,feathers).

Progol finishes by printing the new definition of class/2. Note that snakes are treated as exceptions since all other reptiles have 4 legs.

BEGINNING OF PROGOL TRACE

sparc007_{{24}}? progol animals
CProgol Version 4.1

[:- set(c,3)? - Time taken 0.00s]
[:- modeh(1,class(+animal,#class))? - Time taken 0.00s]
[:- modeb(1,has_milk(+animal))? - Time taken 0.00s]
[:- modeb(1,has_gills(+animal))? - Time taken 0.00s]
[:- modeb(1,has_covering(+animal,#covering))? - Time taken 0.00s]
[:- modeb(1,has_legs(+animal,#nat))? - Time taken 0.00s]
[:- modeb(1,homeothermic(+animal))? - Time taken 0.00s]
[:- modeb(1,has_eggs(+animal))? - Time taken 0.00s]
[:- modeb(100,habitat(+animal,#habitat))? - Time taken 0.00s]
[:- modeh(1,false)? - Time taken 0.00s]
[:- modeb(1,class(+animal,#class))? - Time taken 0.00s]
[Generalising :- class(trout,mammal).]
[Most specific clause is]
:- class(A,mammal), class(A,fish), has_gills(A), has_covering(A,
	scales), has_legs(A,0), has_eggs(A), habitat(A,water).
[C:40,42,1,0 :- class(A,mammal).]
[C:5,7,0,0 :- class(A,mammal), class(A,fish).]
[C:39,42,1,0 :- class(A,mammal), has_legs(A,0).]
[C:39,42,1,0 :- class(A,mammal), has_eggs(A).]
[C:39,42,1,0 :- class(A,mammal), habitat(A,water).]
[C:38,42,1,0 :- class(A,mammal), has_eggs(A), habitat(A,water).]
[C:38,42,1,0 :- class(A,mammal), has_legs(A,0), habitat(A,water).]
[7 explored search nodes]
[f=5,p=7,n=0,h=0]
[Result of search is]
:- class(A,mammal), class(A,fish).
[7 redundant clauses retracted]

[Generalising :- class(lizard,mammal).]
[Most specific clause is]
:- class(A,mammal), class(A,reptile), has_covering(A,scales),
	has_legs(A,4), has_eggs(A), habitat(A,land).
[C:34,36,1,0 :- class(A,mammal).]
[C:6,8,0,0 :- class(A,mammal), class(A,reptile).]
[C:33,36,1,0 :- class(A,mammal), has_legs(A,4).]
[C:33,36,1,0 :- class(A,mammal), has_eggs(A).]
[C:33,36,1,0 :- class(A,mammal), habitat(A,land).]
[C:32,36,1,0 :- class(A,mammal), has_legs(A,4), habitat(A,land).]
[6 explored search nodes]
[f=6,p=8,n=0,h=0]
[Result of search is]
:- class(A,mammal), class(A,reptile).
[8 redundant clauses retracted]

[Generalising :- class(eagle,mammal).]
[Most specific clause is]
:- class(A,mammal), class(A,bird), has_covering(A,feathers), 
	has_legs(A,2), homeothermic(A), has_eggs(A), habitat(A,
	land), habitat(A,air).
[C:27,29,1,0 :- class(A,mammal).]
[C:5,7,0,0 :- class(A,mammal), class(A,bird).]
[C:26,29,1,0 :- class(A,mammal), has_legs(A,2).]
[C:26,29,1,0 :- class(A,mammal), homeothermic(A).]
[C:26,29,1,0 :- class(A,mammal), has_eggs(A).]
[C:26,29,1,0 :- class(A,mammal), habitat(A,land).]
[C:26,29,1,0 :- class(A,mammal), habitat(A,air).]
[C:25,29,1,0 :- class(A,mammal), has_legs(A,2), homeothermic(A).]
[C:25,29,1,0 :- class(A,mammal), has_legs(A,2), has_eggs(A).]
[C:25,29,1,0 :- class(A,mammal), has_legs(A,2), habitat(A,air).]
[C:25,29,1,0 :- class(A,mammal), homeothermic(A), has_eggs(A).]
[C:25,29,1,0 :- class(A,mammal), homeothermic(A), habitat(A,land).]
[C:25,29,1,0 :- class(A,mammal), homeothermic(A), habitat(A,air).]
[13 explored search nodes]
[f=5,p=7,n=0,h=0]
[Result of search is]
:- class(A,mammal), class(A,bird).
[7 redundant clauses retracted]

[Generalising :- class(lizard,fish).]
[Most specific clause is]
:- class(A,fish), class(A,reptile), has_covering(A,scales), has_legs(A,
	4), has_eggs(A), habitat(A,land).
[C:21,23,1,0 :- class(A,fish).]
[C:5,7,0,0 :- class(A,fish), class(A,reptile).]
[C:20,23,1,0 :- class(A,fish), has_covering(A,scales).]
[C:20,23,1,0 :- class(A,fish), has_eggs(A).]
[C:19,23,1,0 :- class(A,fish), has_covering(A,scales), has_eggs(A).]
[5 explored search nodes]
[f=5,p=7,n=0,h=0]
[Result of search is]
:- class(A,fish), class(A,reptile).
[7 redundant clauses retracted]

[Generalising :- class(eagle,fish).]
[Most specific clause is]
:- class(A,fish), class(A,bird), has_covering(A,feathers), has_legs(A,
	2), homeothermic(A), has_eggs(A), habitat(A,land), habitat(A,
	air).
[C:15,17,1,0 :- class(A,fish).]
[C:4,6,0,0 :- class(A,fish), class(A,bird).]
[C:14,17,1,0 :- class(A,fish), has_eggs(A).]
[3 explored search nodes]
[f=4,p=6,n=0,h=0]
[Result of search is]
:- class(A,fish), class(A,bird).
[6 redundant clauses retracted]

[Generalising :- class(eagle,reptile).]
[Most specific clause is]
:- class(A,reptile), class(A,bird), has_covering(A,feathers),
	has_legs(A,2), homeothermic(A), has_eggs(A), habitat(A,
	land), habitat(A,air).
[C:10,12,1,0 :- class(A,reptile).]
[C:5,7,0,0 :- class(A,reptile), class(A,bird).]
[C:9,12,1,0 :- class(A,reptile), has_eggs(A).]
[C:9,12,1,0 :- class(A,reptile), habitat(A,land).]
[C:8,12,1,0 :- class(A,reptile), has_eggs(A), habitat(A,land).]
[5 explored search nodes]
[f=5,p=7,n=0,h=0]
[Result of search is]
:- class(A,reptile), class(A,bird).
[7 redundant clauses retracted]

:- class(A,mammal), class(A,fish).
:- class(A,mammal), class(A,reptile).
:- class(A,mammal), class(A,bird).
:- class(A,fish), class(A,reptile).
:- class(A,fish), class(A,bird).
:- class(A,reptile), class(A,bird).
[Total number of clauses = 6]

[Time taken 1.228s]
[Generalising class(dog,mammal).]
[Most specific clause is]
class(A,mammal) :- has_milk(A), has_covering(A,hair), has_legs(A,
	4), homeothermic(A), habitat(A,land).
[C:1,4,3,0 class(A,mammal).]
[C:3,4,0,0 class(A,mammal) :- has_milk(A).]
[2 explored search nodes]
[f=3,p=4,n=0,h=0]
[Result of search is]
class(A,mammal) :- has_milk(A).
[4 redundant clauses retracted]

[Generalising class(trout,fish).]
[Most specific clause is]
class(A,fish) :- has_gills(A), has_covering(A,scales), has_legs(A,
	0), has_eggs(A), habitat(A,water).
[C:1,4,3,0 class(A,fish).]
[C:3,4,0,0 class(A,fish) :- has_gills(A).]
[2 explored search nodes]
[f=3,p=4,n=0,h=0]
[Result of search is]
class(A,fish) :- has_gills(A).
[4 redundant clauses retracted]

[Generalising class(lizard,reptile).]
[Most specific clause is]
class(A,reptile) :- has_covering(A,scales), has_legs(A,4), has_eggs(A),
	habitat(A,land).
[C:2,5,3,0 class(A,reptile).]
[C:3,5,1,0 class(A,reptile) :- has_covering(A,scales).]
[C:2,4,0,0 class(A,reptile) :- has_covering(A,scales), has_legs(A,4).]
[C:2,5,1,0 class(A,reptile) :- has_covering(A,scales), has_eggs(A).]
[C:2,4,1,0 class(A,reptile) :- has_legs(A,4).]
[C:1,5,3,0 class(A,reptile) :- has_eggs(A).]
[C:1,4,2,0 class(A,reptile) :- habitat(A,land).]
[7 explored search nodes]
[f=2,p=4,n=0,h=0]
[Result of search is]
class(A,reptile) :- has_covering(A,scales), has_legs(A,4).
[4 redundant clauses retracted]

[Generalising class(snake,reptile).]
[Most specific clause is]
class(A,reptile) :- has_covering(A,scales), has_legs(A,0), has_eggs(A),
	habitat(A,land).
[C:-1,2,3,0 class(A,reptile).]
[C:0,2,1,0 class(A,reptile) :- has_covering(A,scales).]
[2 explored search nodes]
[f=1,p=7,n=6,h=0]
[No compression]

[Generalising class(eagle,bird).]
[Most specific clause is]
class(A,bird) :- has_covering(A,feathers), has_legs(A,2), homeothermic(A),
	has_eggs(A), habitat(A,land), habitat(A,air).
[C:0,3,3,0 class(A,bird).]
[C:2,3,0,0 class(A,bird) :- has_covering(A,feathers).]
[2 explored search nodes]
[f=2,p=3,n=0,h=0]
[Result of search is]
class(A,bird) :- has_covering(A,feathers).
[3 redundant clauses retracted]

class(snake,reptile).
class(A,mammal) :- has_milk(A).
class(A,fish) :- has_gills(A).
class(A,bird) :- has_covering(A,feathers).
class(A,reptile) :- has_covering(A,scales), has_legs(A,4).
[Total number of clauses = 5]

[Time taken 0.332s]

END OF PROGOL TRACE

The final output from Progol are the following clauses:

	class(snake,reptile).
	class(A,mammal) :- has_milk(A).
	class(A,fish) :- has_gills(A).
	class(A,bird) :- has_covering(A,feathers).
	class(A,reptile) :- has_covering(A,scales), has_legs(A,4).

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