cplint is a suite of programs for reasoning with ICL [13], LPADs [22, 23] and CP-logic programs [20, 21]. It contains programs both for inference and learning.
cplint is distributed in source code in the source code development tree of Yap. It includes Prolog and C files. Download it by following the instruction in http://www.ncc.up.pt/ vsc/Yap/downloads.html .
cplint requires CUDD . You can download CUDD from ftp://vlsi.colorado.edu/pub/cudd-2.4.2.tar.gz .
Compile CUDD:
Install Yap together with cplint: when compiling Yap following the instruction of the INSTALL file in the root of the Yap folder, use
where DIR is the directory where CUDD is, i.e., the directory ending with
cudd-2.4.2. Under Windows, you have to use Cygwin (CUDD does not compile
under MinGW), so
After having performed make install you can do make installcheck that will execute a suite of tests of the various programs. If no error is reported you have a working installation of cplint.
LPAD and CP-logic programs consist of a set of annotated disjunctive clauses. Disjunction in the head is represented with a semicolon and atoms in the head are separated from probabilities by a colon. For the rest, the usual syntax of Prolog is used. For example, the CP-logic clause
No parentheses are necessary. The pi are numeric expressions. It is up to the user to ensure that the numeric expressions are legal, i.e. that they sum up to less than one.
If the clause has an empty body, it can be represented like this
If the clause has a single head with probability 1, the annotation can be omitted and the clause takes the form of a normal prolog clause, i.e.
stands for
The coin example of [23] is represented as (see file coin.cpl)
The first clause states that if we toss a coin that is not biased it has equal probability of landing heads and tails. The second states that if the coin is biased it has a slightly higher probability of landing heads. The third states that the coin is fair with probability 0.9 and biased with probability 0.1 and the last clause states that we toss a coin with certainty.
Moreover, the bodies of rules can contain the built-in predicates:
The bodies can also contain the following library predicates:
plus the predicate
that, given a list of numbers, computes its arithmetic mean.
The syntax of ICL program is the one used by the AILog 2 system.
cplint contains various modules for answering queries.
These modules answer queries using using goal-oriented procedures:
It was proved correct [15] with respect to the semantics of LPADs for range restricted acyclic programs [1] without function symbols.
It is also able to deal with extensions of LPADs and CP-logic: the clause bodies can contain setof and bagof, the probabilities in the head may be depend on variables in the body and it is possible to specify a uniform distribution in the head with reference to a setof or bagof operator. These extended features have been introduced in order to represent CLP(BN) [19] programs and PRM models [12]: setof and bagof allow to express dependency of an attribute from an aggregate function of another attribute, as in CLP(BN) and PRM, while the possibility of specifying a uniform distribution allows the use of the reference uncertainty feature of PRM.
These modules answer queries using the definition of the semantics of LPADs and CP-logic:
The LPAD or CP-logic program must be stored in a text file with extension .cpl. Suppose you have stored the example above in file coin.cpl. In order to answer queries from this program, you have to run Yap, load one of the modules (such as for example lpad.pl) by issuing the command
at the command prompt. Then you must parse the source file coin.cpl with the command
if coin.cpl is in the current directory, or
if coin.cpl is in a different directory. At this point you can pose query to the program by using the predicate s/2 (for solve) that takes as its first argument a conjunction of goals in the form of a list and returns the computed probability as its second argument. For example, the probability of the conjunction head(coin),biased(coin) can be asked with the query
For computing the probability of a conjunction given another conjunction you can use the predicate sc/3 (for solve conditional) that take takes as input the query conjunction as its first argument, the evidence conjunction as its second argument and returns the probability in its third argument. For example, the probability of the query heads(coin) given the evidence biased(coin) can be asked with the query
After having parsed a program, in order to read in a new program you must restart Yap when using semlpadsld.pl and semlpad.pl. With the other modules, you can directly parse a new program.
When using lpad.pl, the system can print the message “Uunsound program” in the case in which an instance with a three valued well founded model is found. Moreover, it can print the message “It requires the choice of a head atom from a non ground head”: in this case, in order to answer the query, all the groundings of the culprit clause must be generated, which may be impossible for programs with function symbols.
When using semcpl.pl, you can print the execution process by using the command print. after p(file). Moreover, you can build an execution process given a context by issuing the command parse(file). and then build(context). where context is a list of atoms that are true in the context. semcpl.pl can print “Invalid program” in the case in which no execution process exists.
When using cpl.pl you can print a partial execution model including all the clauses involved in the query issued with print. cpl.pl can print the messages “Uunsound program”, “It requires the choice of a head atom from a non ground head” and “Invalid program”.
For approx/deepit.pl and approx/deepdyn.pl the command
takes as input a list of goals GoalsList and returns a lower bound on the probability ProbLow, an upper bound on the probability ProbUp, the CPU time spent on performing resolution ResTime and the CPU time spent on handling BDDs BddTime.
For approx/bestk.pl the command
takes as input a list of goals GoalsList and returns a lower bound on the probability ProbLow, the CPU time spent on performing resolution ResTime and the CPU time spent on handling BDDs BddTime.
For approx/bestfirst.pl the command
takes as input a list of goals GoalsList and returns a lower bound on the probability ProbLow, an upper bound on the probability ProbUp, the number of BDDs generated by the algorithm Count, the CPU time spent on performing resolution ResTime and the CPU time spent on handling BDDs BddTime.
For approx/montecarlo.pl the command
takes as input a list of goals GoalsList and returns the number of samples taken Samples, the time required to solve the problem Time, the lower end of the confidence interval Lower, the estimated probability Prob and the upper end of the confidence interval Up.
For mcintyre.pl: the command
takes as input a conjunction of goals Goals and returns the number of samples taken Samples, the CPU time required to solve the problem CPUTime, the wall time required to solve the problem CPUTime, the lower end of the confidence interval Lower, the estimated probability Prob and the upper end of the confidence interval Up.
For approx/exact.pl the command
takes as input a conjunction of goals Goals and returns the probability Prob, the CPU time spent on performing resolution ResTime and the CPU time spent on handling BDDs BddTime.
The modules make use of a number of parameters in order to control their behavior. They that can be set with the command
from the Yap prompt after having loaded the module. The current value can be read with
from the Yap prompt. The available parameters are:
where the first element of each couple is the clause number of the input file (starting from 1). In the example above variable X0 corresponds to clause 2 with the substitutions X=2,X1=1, variable X1 corresponds to clause 2 with the substitutions X=1,X1=0 and variable X2 corresponds to clause 1 with the empty substitution. You can view the graph with graphviz using the command
The three semantic modules need to produce a grounding of the program in order to compute the semantics. They require an extra file with extension .uni (for universe) in the same directory where the .cpl file is.
There are two ways to specify how to ground a program. The first consists in providing the list of constants to which each variable can be instantiated. For example, in our case the current directory will contain a file coin.uni that is a Prolog file containing facts of the form
where var_list is a list of variables names (each must be included in single quotes) and const_list is a list of constants. The semantic modules generate the grounding by instantiating in all possible ways the variables of var_list with the constants of const_list. Note that the variables are identified by name, so a variable with the same name in two different clauses will be instantiated with the same constants.
The other way to specify how to ground a program consists in using mode and type information. For each predicate, the file .uni must contain a fact of the form
that specifies the number and types of each argument of the predicate. Then, the list of constants that are in the domain of each type ti must be specified with a fact of the form
The file .uni can contain both universe and mode declaration, the ones to be used depend on the value of the parameter grounding: with value variables, the universe declarations are used, with value modes the mode declarations are used.
With semcpl.pl only mode declarations can be used.
In this section we will present the extensions to the syntax of LPADs and CP-logic programs that lpadsld can handle.
When using lpadsld.pl, the bodies can contain the predicates setof/3 and bagof/3 with the same meaning as in Prolog. Existential quantifiers are allowed in both, so for example the query
returns all the instantiations of Z such that there exists an instantiation of X and Y for which foo(X,Y,Z) is true.
An example of the use of setof and bagof is in the file female.cpl:
The disjunctive rule expresses the probability of a person of unknown sex of being male or female depending on the number of males and females that are known. This is an example of the use of expressions in the probabilities in the head that depend on variables in the body. The probabilities are well defined because they always sum to 1 (unless P is 0).
Another use of setof and bagof is to have an attribute depend on an aggregate function of another attribute, similarly to what is done in PRM and CLP(BN).
So, in the classical school example (available in student.cpl) you can find the following clauses:
where registr_stu(R,S) expresses that registration R refers to student S and registr_gr(R,G) expresses that registration R reports grade G which is a natural number. The two clauses express a dependency of the rank of the student from the average of her grades.
Another extension can be used with lpadsld.pl in order to be able to represent reference uncertainty of PRMs. Reference uncertainty means that the link structure of a relational model is not fixed but is uncertain: this is represented by having the instance referenced in a relationship be chosen uniformly from a set. For example, consider a domain modeling scientific papers: you have a single entity, paper, and a relationship, cites, between paper and itself that connects the citing paper to the cited paper. To represent the fact that the cited paper and the citing paper are selected uniformly from certain sets, the following clauses can be used (see file paper_ref_simple.cpl):
The first clauses states that the paper P cited in a citation C is selected uniformly from the set of all papers with topic theory. The second clauses expresses that the citing paper is selected uniformly from the papers with topic ai.
These clauses make use of the predicate
in the head, where Atom must contain Variable. The meaning is the following: the set of all the atoms obtained by instantiating Variable of Atom with a term taken from List is generated and the head is obtained by having a disjunct for each instantiation with probability 1∕N where N is the length of List.
A more elaborate example is present in file paper_ref.cpl:
where the cited paper depends on the topic of the citing paper. In particular, if the topic is theory, the cited paper is selected uniformly from the papers about theory with probability 0.9 and from the papers about ai with probability 0.1. if the topic is ai, the cited paper is selected uniformly from the papers about theory with probability 0.01 and from the papers about ai with probability 0.99.
PRMs take into account as well existence uncertainty, where the existence of instances is also probabilistic. For example, in the paper domain, the total number of citations may be unknown and a citation between any two paper may have a probability of existing. For example, a citation between two paper may be more probable if they are about the same topic:
This is an example where the probabilities in the head do not sum up to one so the null event is automatically added to the head. The first clause states that, if the topic of a paper X is theory and of paper Y is theory, there is a probability of 0.005 that there is a citation from X to Y. The other clauses consider the remaining cases for the topics.
In the directory where Yap keeps the library files (usually /usr/local/share/ Yap) you can find the directory cplint that contains the files:
The files *.uni that are present for some of the examples are used by the semantical modules. Some of the example files contain in an initial comment some queries together with their result.
cplint contains the following learning algorithms:
To execute the learning algorithms, prepare four files in the same folder:
where <stem> is your dataset name. Examples of these files can be found in the dataset pages.
In <stem>.kb the example interpretations have to be given as a list of Prolog facts initiated by begin(model(<name>)). and terminated by end(model(<name>)). as in
The interpretations may contain a fact of the form
assigning a probability (0.3 in this case) to the interpretations. If this is omitted, the probability of each interpretation is considered equal to 1∕n where n is the total number of interpretations. prob/1 can be used to set different multiplicity for the different interpretations.
In order for RIB to work, the input interpretations must share the Herbrand universe. If this is not the case, you have to translate the interpretations in this was, see for example the sp1 files in RIB’s folder, that are the results of the conversion of the first fold of the IMDB dataset.
<stem>.bg can contain Prolog clauses that can be used to derive additional conclusions from the atoms in the interpretations.
<stem>.l contains the declarations of the input and output predicates, of the unseen predicates and the commands for setting the algorithms’ parameters. Output predicates are declared as
and define the predicates whose atoms in the input interpretations are used as the goals for the prediction of which you want to optimize the parameters. Derivations for these goals are built by the systems.
Input predicates are those for the predictions of which you do not want to optimize the parameters. You can declare closed world input predicates with
For these predicates, the only true atoms are those in the interpretations, the clauses in the input program are not used to derive atoms not present in the interpretations.
Open world input predicates are declared with
In this case, if a subgoal for such a predicate is encountered when deriving the atoms for the output predicates, both the facts in the interpretations and the clauses of the input program are used.
For RIB, if there are unseen predicates, i.e., predicates that are present in the input program but not in the interpretations, you have to declare them with
For SLIPCASE, you have to specify the language bias by means of mode declarations in the style of Progol .
specifies the atoms that can appear in the head of clauses, while
specifies the atoms that can appear in the body of clauses. <recall> can be an integer or * (currently unused).
The arguments are of the form
for specifying an input variable of type <type>, or
for specifying an output variable of type <type>. or
for specifying a constant.
In order to set the algorithms’ parameters, you have to insert in <stem>.l commands of the form
The available parameters are:
To execute CEM, load em.pl with
and call:
To execute RIB, load rib.pl with
and call:
To execute EMBLEM, load slipcase.pl with
and call
To execute SLIPCASE, load slipcase.pl with
and call
cplint, as Yap, follows the Artistic License 2.0 that you can find in Yap CVS root dir. The copyright is by Fabrizio Riguzzi.
The modules in the approx subdirectory use SimplecuddLPADs, a modification of the Simplecudd library whose copyright is by Katholieke Universiteit Leuven and that follows the Artistic License 2.0.
Some modules use the library CUDD for manipulating BDDs that is included in glu. For the use of CUDD, the following license must be accepted:
Copyright (c) 1995-2004, Regents of the University of Colorado
All rights reserved.
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AND CONTRIBUTORS ”AS IS” AND ANY EXPRESS OR IMPLIED
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lpad.pl, semlpad.pl and cpl.pl are based on the SLG system by Weidong Chen and David Scott Warren , Copyright (C) 1993 Southern Methodist University, 1993 SUNY at Stony Brook, see the file COYPRIGHT_SLG for detailed information on this copyright.
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