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. -
Redistribution and use in source and binary forms, with or without modification, -are permitted provided that the following conditions are met: -
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS
AND CONTRIBUTORS ”AS IS” AND ANY EXPRESS OR IMPLIED
-WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
-WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
-INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
-
-(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
-GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
-INTERRUPTION) HOWEVER CAU-SED
AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
-LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
-ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
-ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-
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. -
-
-
- [1] K. R. Apt and M. Bezem. Acyclic programs. New Gener. Comput., - 9(3/4):335–364, 1991. -
-- [2] Elena Bellodi and Fabrizio Riguzzi. EM over binary decision diagrams - for probabilistic logic programs. In Proceedings of the 26th Italian - Conference on Computational Logic (CILC2011), Pescara, Italy, 31 August - 31-2 September, 2011, 2011. -
-- [3] Elena Bellodi and Fabrizio Riguzzi. EM over binary decision - diagrams for probabilistic logic programs. Technical Report CS-2011-01, - Dipartimento di Ingegneria, Universitą di Ferrara, Italy, 2011. -
-- [4] Elena Bellodi and Fabrizio Riguzzi. Learning the structure of - probabilistic logic programs. In Inductive Logic Programming, 21th - International Conference, ILP 2011, London, UK, 31 July-3 August, 2011, - 2011. -
-- [5] Elena Bellodi and Fabrizio Riguzzi. Expectation Maximization over - - binary decision diagrams for probabilistic logic programs. Intel. Data Anal., - 16(6), 2012. -
-- [6] H. Blockeel. Probabilistic logical models for mendel’s experiments: An - exercise. In Inductive Logic Programming (ILP 2004), Work in Progress - Track, 2004. -
-- [7] Stefano Bragaglia and Fabrizio Riguzzi. Approximate inference for logic - programs with annotated disjunctions. In Paolo Frasconi and Francesca - Lisi, editors, Inductive Logic Programming 20th International Conference, - ILP 2010, Florence, Italy, June 27-30, 2010. Revised Papers, volume 6489 - of LNCS, pages 30–37. Springer, 2011. -
-- [8] Weidong Chen and David Scott Warren. Tabled evaluation with - delaying for general logic programs. Journal of the ACM, 43(1):20–74, 1996. -
-- [9] L. De Raedt, A. Kimmig, and H. Toivonen. ProbLog: A probabilistic - Prolog and its application in link discovery. In International Joint - Conference on Artificial Intelligence, pages 2462–2467, 2007. -
-- [10] G. Elidan and N. Friedman. Learning hidden variable networks: The - information bottleneck approach. Journal of Machine Learning Research, - 6:81–127, 2005. -
-- [11] L. Getoor, N. Friedman, D. Koller, and A. Pfeffer. Learning - probabilistic relational models. In Saso Dzeroski and Nada Lavrac, editors, - Relational Data Mining. Springer-Verlag, Berlin, 2001. -
-- [12] L. Getoor, N. Friedman, D. Koller, and B. Taskar. Learning - probabilistic models of relational structure. Journal of Machine Learning - Research, 3:679–707, December 2002. - -
-- [13] David Poole. The independent choice logic for modelling multiple agents - under uncertainty. Artificial Intelligence, 94(1-2):7–56, 1997. -
-- [14] Fabrizio Riguzzi. A top down interpreter for LPAD and CP-logic. In - Congress of the Italian Association for Artificial Intelligence, volume 4733 - of LNAI, pages 109–120. Springer, 2007. -
-- [15] Fabrizio Riguzzi. A top down interpreter for LPAD and CP-logic. - In Proceedings of the 14th RCRA workshop Experimental Evaluation of - Algorithms for Solving Problems with Combinatorial Explosion, 2007. -
-- [16] Fabrizio Riguzzi. Extended semantics and inference for the Independent - Choice Logic. Logic Journal of the IGPL, 17(6):589–629, 2009. -
-- [17] Fabrizio Riguzzi. MCINTYRE: A Monte Carlo algorithm for - probabilistic logic programming. In Proceedings of the 26th Italian - Conference on Computational Logic (CILC2011), Pescara, Italy, 31 - August-2 September, 2011, 2011. -
-- [18] Fabrizio Riguzzi and Nicola Di Mauro. Applying the information - bottleneck to statistical relational learning. Machine Learning, 2011. To - appear. -
-
- [19] V. Santos Costa, D. Page, M. Qazi, and J. Cussens. CLP():
- Constraint logic programming for probabilistic knowledge. In Uncertainty
- in Artificial Intelligence. Morgan Kaufmann, 2003.
-
- [20] J. Vennekens, M. Denecker, and M. Bruynooghe. Representing causal - information about a probabilistic process. In Proceedings of the 10th - European Conference on Logics in Artificial Intelligence, LNAI. Springer, - September 2006. - -
-- [21] J. Vennekens, Marc Denecker, and Maurice Bruynooghe. CP-logic: - A language of causal probabilistic events and its relation to logic - programming. Theory Pract. Log. Program., 9(3):245–308, 2009. -
-- [22] J. Vennekens and S. Verbaeten. Logic programs with annotated - disjunctions. Technical Report CW386, K. U. Leuven, 2003. -
-- [23] J. Vennekens, S. Verbaeten, and M. Bruynooghe. Logic programs - with annotated disjunctions. In International Conference on Logic - Programming, volume 3131 of LNCS, pages 195–209. Springer, 2004. -
-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.dcc.fc.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. +
Redistribution and use in source and binary forms, with or without modification, +are permitted provided that the following conditions are met: +
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS
AND CONTRIBUTORS ”AS IS” AND ANY EXPRESS OR IMPLIED
+WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
+GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAU-SED
AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
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. +
+
+
+ [1] K. R. Apt and M. Bezem. Acyclic programs. New Gener. Comput., + 9(3/4):335–364, 1991. +
++ [2] Elena Bellodi and Fabrizio Riguzzi. EM over binary decision diagrams + for probabilistic logic programs. In Proceedings of the 26th Italian + Conference on Computational Logic (CILC2011), Pescara, Italy, 31 August + 31-2 September, 2011, 2011. +
++ [3] Elena Bellodi and Fabrizio Riguzzi. EM over binary decision + diagrams for probabilistic logic programs. Technical Report CS-2011-01, + Dipartimento di Ingegneria, Universitą di Ferrara, Italy, 2011. +
++ [4] Elena Bellodi and Fabrizio Riguzzi. Learning the structure of + probabilistic logic programs. In Inductive Logic Programming, 21th + International Conference, ILP 2011, London, UK, 31 July-3 August, 2011, + 2011. +
++ [5] Elena Bellodi and Fabrizio Riguzzi. Expectation Maximization over + + binary decision diagrams for probabilistic logic programs. Intel. Data Anal., + 16(6), 2012. +
++ [6] H. Blockeel. Probabilistic logical models for mendel’s experiments: An + exercise. In Inductive Logic Programming (ILP 2004), Work in Progress + Track, 2004. +
++ [7] Stefano Bragaglia and Fabrizio Riguzzi. Approximate inference for logic + programs with annotated disjunctions. In Paolo Frasconi and Francesca + Lisi, editors, Inductive Logic Programming 20th International Conference, + ILP 2010, Florence, Italy, June 27-30, 2010. Revised Papers, volume 6489 + of LNCS, pages 30–37. Springer, 2011. +
++ [8] Weidong Chen and David Scott Warren. Tabled evaluation with + delaying for general logic programs. Journal of the ACM, 43(1):20–74, 1996. +
++ [9] L. De Raedt, A. Kimmig, and H. Toivonen. ProbLog: A probabilistic + Prolog and its application in link discovery. In International Joint + Conference on Artificial Intelligence, pages 2462–2467, 2007. +
++ [10] G. Elidan and N. Friedman. Learning hidden variable networks: The + information bottleneck approach. Journal of Machine Learning Research, + 6:81–127, 2005. +
++ [11] L. Getoor, N. Friedman, D. Koller, and A. Pfeffer. Learning + probabilistic relational models. In Saso Dzeroski and Nada Lavrac, editors, + Relational Data Mining. Springer-Verlag, Berlin, 2001. +
++ [12] L. Getoor, N. Friedman, D. Koller, and B. Taskar. Learning + probabilistic models of relational structure. Journal of Machine Learning + Research, 3:679–707, December 2002. + +
++ [13] David Poole. The independent choice logic for modelling multiple agents + under uncertainty. Artificial Intelligence, 94(1-2):7–56, 1997. +
++ [14] Fabrizio Riguzzi. A top down interpreter for LPAD and CP-logic. In + Congress of the Italian Association for Artificial Intelligence, volume 4733 + of LNAI, pages 109–120. Springer, 2007. +
++ [15] Fabrizio Riguzzi. A top down interpreter for LPAD and CP-logic. + In Proceedings of the 14th RCRA workshop Experimental Evaluation of + Algorithms for Solving Problems with Combinatorial Explosion, 2007. +
++ [16] Fabrizio Riguzzi. Extended semantics and inference for the Independent + Choice Logic. Logic Journal of the IGPL, 17(6):589–629, 2009. +
++ [17] Fabrizio Riguzzi. MCINTYRE: A Monte Carlo algorithm for + probabilistic logic programming. In Proceedings of the 26th Italian + Conference on Computational Logic (CILC2011), Pescara, Italy, 31 + August-2 September, 2011, 2011. +
++ [18] Fabrizio Riguzzi and Nicola Di Mauro. Applying the information + bottleneck to statistical relational learning. Machine Learning, 2011. To + appear. +
+
+ [19] V. Santos Costa, D. Page, M. Qazi, and J. Cussens. CLP():
+ Constraint logic programming for probabilistic knowledge. In Uncertainty
+ in Artificial Intelligence. Morgan Kaufmann, 2003.
+
+ [20] J. Vennekens, M. Denecker, and M. Bruynooghe. Representing causal + information about a probabilistic process. In Proceedings of the 10th + European Conference on Logics in Artificial Intelligence, LNAI. Springer, + September 2006. + +
++ [21] J. Vennekens, Marc Denecker, and Maurice Bruynooghe. CP-logic: + A language of causal probabilistic events and its relation to logic + programming. Theory Pract. Log. Program., 9(3):245–308, 2009. +
++ [22] J. Vennekens and S. Verbaeten. Logic programs with annotated + disjunctions. Technical Report CW386, K. U. Leuven, 2003. +
++ [23] J. Vennekens, S. Verbaeten, and M. Bruynooghe. Logic programs + with annotated disjunctions. In International Conference on Logic + Programming, volume 3131 of LNCS, pages 195–209. Springer, 2004. +
+