pita.pl -- pita

This module performs reasoning over Logic Programs with Annotated Disjunctions and CP-Logic programs. It reads probabilistic program and computes the probability of queries.

See https://friguzzi.github.io/cplint/ for details.

Reexports cplint_util and bddem

author

- Fabrizio Riguzzi

copyright

- Fabrizio Riguzzi

license

- Artistic License 2.0 https://opensource.org/licenses/Artistic-2.0

 load(++File:atom) is det

Loads File.lpad if it exists, otherwise loads File.cpl if it exists.

 load_file(++FileWithExtension:atom) is det

Loads FileWithExtension.

 dt_solve(-Strategy:list, -Cost:float) is det

The predicate computes the best solution for the decision theory problem. It returns the best strategy in Strategy and it cost in Cost. Complete solution without pruning.

 prob_meta(:Query:conjunction_of_literals, -Probability:float) is nondet

To be used in place of prob/2 for meta calls (doesn't abolish tables)

 abd_prob(:Query:conjunction_of_literals, -Probability:float, -Delta:list) is nondet

The predicate computes the most probable abductive explanation of the ground query Query. It returns the explanation in Delta together with its Probability

 bdd_dot_file(:Query:atom, +FileName:string, -LV:list) is det

The predicate builds the BDD for Query and writes its dot representation to file FileName and a list in LV with the association of variables to rules. LV is a list of list, each sublist has three elements: the multivalued variable number, the rule number and the grounding substitution.

 bdd_dot_string(:Query:atom, -DotString:string, -LV:list) is det

The predicate builds the BDD for Query and returns its dot representation in DotString and a list in LV with the association of variables to rules. LV is a list of list, each sublist has three elements: the multivalued variable number, the rule number and the grounding substitution.

 abd_bdd_dot_string(:Query:atom, -DotString:string, -LV:list, -LAV:list) is det

The predicate builds the BDD for the abductive explanations for Query and returns its dot representation in DotString and lists LV and LAV, the association of variables to rules and to abductive variables to rules respectively. LV and LAV are lists of list, each sublist has three elements: the multivalued variable number, the rule number and the grounding substitution.

 abd_bdd_dot_string(:Query:atom, -DotString:string, -LV:list, -LAV:list, -Probability:float, -Delta:list) is det

The predicate builds the BDD for the abductive explanations for Query It returns the explanation in Delta together with its Probability. The predicate builds the BDD for Query and returns its dot representation in DotString and lists LV and LAV, the association of variables to rules and to abductive variables to rules respectively. LV and LAV are lists of list, each sublist has three elements: the multivalued variable number, the rule number and the grounding substitution.

 map(:Query:atom, -Probability:float, -Delta:list) is nondet

The predicate computes the explanation of the ground query Query with Maximum A Posteriori (MAP) probability. It returns the explanation in Delta together with its Probability

 map_bdd_dot_string(:Query:atom, -DotString:string, -LV:list, -LAV:list, -Probability:float, -Delta:list) is nondet

The predicate computes the explanation of the ground query Query with Maximum A Posteriori (MAP) probability. It returns the explanation in Delta together with its Probability The predicate builds the BDD for Query and returns its dot representation in DotString and lists LV and LAV, the association of variables to rules and of query variables to rules respectively. LV and LAV are lists of list, each sublist has three elements: the multivalued variable number, the rule number and the grounding substitution.

 prob(:Query:atom, -Probability:float) is nondet

The predicate computes the probability of Query If Query is not ground, it returns in backtracking all ground instantiations of Query together with their probabilities

 prob(:Query:conjunction_of_literals, :Evidence:conjunction_of_literals, -Probability:float) is nondet

Equivalent to prob/4 with an empty option list.

 prob_meta(:Query:conjunction_of_literals, :Evidence:conjunction_of_literals, -Probability:float) is nondet

To be used in place of prob/3 for meta calls (doesn't abolish tables)

 get_var_n(++M:atomic, ++Environment:int, ++Rule:int, ++Substitution:term, ++Probabilities:list, -Variable:int) is det

Returns the index Variable of the random variable associated to rule with index Rule, grounding substitution Substitution and head distribution Probabilities in environment Environment.

 get_dec_var_n(++M:atomic, ++Environment:int, ++Rule:int, ++Substitution:term, -Variable:int) is det

Returns the index Variable of the random variable associated to rule with index Rule in environment Environment.

 get_abd_var_n(++M:atomic, ++Environment:int, ++Rule:int, ++Substitution:term, ++Probabilities:list, -Variable:int) is det

Returns the index Variable of the random variable associated to rule with index Rule, grounding substitution Substitution and head distribution Probabilities in environment Environment.

 msw(:Var:term, ?Value:term, ++Environment:int, --BDD:int) is det

Returns a BDD representing Var=Value. This is a predicate for programs in the PRISM syntax

 msw(:Var:term, ?Value:term, ++Environment:int, --BDD:int, ?DB:int) is det

Returns a BDD representing Var=Value when there is a depth bound on derivations. This is a predicate for programs in the PRISM syntax

 set_pita(:Parameter:atom, +Value:term) is det

The predicate sets the value of a parameter For a list of parameters see https://friguzzi.github.io/cplint/

 setting_pita(:Parameter:atom, ?Value:term) is det

The predicate returns the value of a parameter For a list of parameters see https://friguzzi.github.io/cplint/

Re-exported predicates

The following predicates are exported from this file while their implementation is defined in imported modules or non-module files loaded by this module.

 argbar(+Values:list, -Chart:dict) is det

Values is a list of pairs V-N where V is the value and N is the number of samples returning that value. The predicate returns a dict for rendering with c3 as a bar chart with a bar for each value V. The size of the bar is given by N.

 make_query_var(++Environment:int, +Variable:int, --BDD:int) is det

Makes Variable belonging to Environment a query random variable for MAP inference. Returns in BDD the diagram of the formula encoding the required constraints among the Boolean random variable that represent Variable.

 create_dot(++Env:int, ++BDD:int, ++File:string) is det

The predicate writes the BDD in dot format to to file FileName.

 ret_probc(++Environment:int, ++EBDD:couple, -Probability:float) is det

EBDD is a couple (Environment,BDD) Returns the Probability of BDD belonging to environment Environment Uses

 add_query_var(++Environment:int, ++ProbabilityDistribution:list, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new random variable to be queried in MAP inference with NumberOHeads values and probability distribution ProbabilityDistribution. The variable belongs to Environment.

 andc(++Environment:int, ++A:couple, ++B:couple, --AandB:couple) is semidet

A and B are couples (Environment, BDDA) and (Environment, BDDB) respectively Returns in AandB a couple (Environment, BDDAandB) where BDDAandB is pointer to a BDD belonging to environment Environment representing the conjunction of BDDs BDDA and BDDB. fails if BDDB represents the zero function

 std_dev(+Values:list, -Dev:float) is det

Computes the standard deviation of Values. Values can be

• a list of numbers
• a list of pairs number-weight, in which case each number is multiplied by the weight before being considered
• a list of pairs list-weight, in which case list is considered as a matrix of numbers. The matrix in each element of List must have the same dimension and are aggregated element- wise

 debug_cudd_var(++Environment:int, -Variable:out) is det

Prints the debug information which is the result of the call of Cudd_ReadDead, Cudd_CheckZeroRef, Cudd_CheckKeys and Cudd_DebugCheck(env->mgr));

 variance(+Values:list, -Average:float, -Variance:float) is det

Computes the variance the average of Values. Values can be

• a list of numbers
• a list of pairs number-weight, in which case each number is multiplied by the weight before being considered
• a list of pairs list-weight, in which case list is considered as a matrix of numbers. The matrix in each element of List must have the same dimension and are aggregated element- wise

 ret_prob(++Environment:int, ++BDD:int, -Probability:float) is det

Returns the Probability of BDD belonging to environment Environment.

 bin(+N:int, +Values:list, +Lower:number, +BinWidth:number, -Couples:list) is det

Given a list of numeric Values, a Lower value and BinWidth, returns in Couples a list of N pairs V-Freq where V is the midpoint of a bin and Freq is the number of values that are inside the bin interval [V-BinWidth/2,V+BinWidth/2) starting with the bin where V-BinWidth/2=Lower

 zero(++Environment:int, --Zero:int) is det

Returns in Zero a pointer to a BDD belonging to environment Environment representing the zero Boolean function.

 add_decision_var(++Environment:int, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new decision variable in Environment

 ret_strategy(++Environment:int, ++ADD:int, --Decision:list, --Cost:int) is det

Computes the optimal strategy given a pointer to the ADD belonging to environment Environment. Decision is a list of selected facts, Cost is the total cost.

 dirichlet_sample(++Alpha:list, --Value:list) is det

Returns a Value sampled from a Dirichlet distribution with parameters Alpha. Alpha and Value are lists of floating point numbers of the same length.

 density2d(+List:list, -Dens:list, +Options:list) is det

Returns a set of 3-dimensional points representing the plot of the density of a sets of 2-dimensional samples. The samples are in List as pairs [X,Y]-W where (X,Y) is a point and W its weigth.

Options is a list of options, the following are recognised by density2d/3:

xmin(+XMin:float)

the minimum value of the X domain, default value the minimum in List

xmax(-XMax:float)

the maximum value of the X domain, default value the maximum in List

ymin(-YMin:float)

the minimum value of the Y domain, default value the minimum in List

ymax(-YMax:float)

the maximum value of the Y domain, default value the maximum in List

nbins(+NBins:int)

the number of bins for dividing the X and Y domains, default value 40

 densities(+PriorList:list, +PostList:list, -Chart:dict, +Options:list) is det

Draws a line chart of the density of two sets of samples, usually prior and post observations. The samples from the prior are in PriorList while the samples from the posterior are in PostList. PriorList and PostList must be lists of pairs of the form [V]-W or V-W where V is a sampled value and W is its weight, or lists of values V. Options is a list of options, the following are recognised by histogram/3:

nbins(+NBins:int)

the number of bins for dividing the domain, default value 40 */

 init(--Environment:int) is det

Initializes a data structure for storing a single BDD. Returns an integer Environment that is a pointer to a data structure for storing a single BDD to be used for inference only (no learning).

 rand_seed(+Seed:int) is det

The pseudo-random number generator is initialized using the argument passed as Seed. It calls the C function srand.

 or_listc(++ListOfBDDs:list, ++Environment, --BDD:int) is det

Returns in BDD a couple (Env,B) with B a pointer to a BDD belonging to environment Environment representing the disjunction of all the BDDs in ListOfBDDs (a list of couples (Env,BDD))

 bar1(+Probability:float, -Chart:dict) is det

The predicate returns a dict for rendering with c3 as a bar chart with a bar for the probability

 orc(++A:couple, ++B:couple, --AorB:couple) is det

A and B are couples (Environment, BDDA) and (Environment, BDDB) respectively Returns in AorB a couple (Environment, BDDAorB) where BDDAorB is pointer to a BDD belonging to environment Environment representing the disjunction of BDDs BDDA and BDDB.

 zeroc(++Environment:int, --Zero:couple) is det

Returns in Zero a couple (Environment,BDD) where BDD is pointer to a BDD belonging to environment Environment representing the zero Boolean function

 ret_abd_prob(++Environment:int, ++BDD:int, -Probability:float, -Explanation:list) is det

Returns the abductive Explanation of BDD and its Probability. BDD belongs to environment Environment.

 std_dev(+Values:list, -Average:float, -Dev:float) is det

Computes the standard deviation and the average of Values. Values can be

• a list of numbers
• a list of pairs number-weight, in which case each number is multiplied by the weight before being considered
• a list of pairs list-weight, in which case list is considered as a matrix of numbers. The matrix in each element of List must have the same dimension and are aggregated element- wise

 to_atom(+In:pair, -Out:pair) is det

Given In=A0-N, to_atom/2 returns Out=A-N where A is an atom representing A0

 variance(+Values:list, -Variance:float) is det

Computes the variance of Values. Values can be

• a list of numbers
• a list of pairs number-weight, in which case each number is multiplied by the weight before being considered
• a list of pairs list-weight, in which case list is considered as a matrix of numbers. The matrix in each element of List must have the same dimension and are aggregated element- wise

 and(++Environment:int, ++A:int, ++B:int, --AandB:int) is det

Returns in AandB a pointer to a BDD belonging to environment Environment representing the conjunction of BDDs A and B.

 value_pair(+Pair:pair, -Value:term) is det

Given a pair Key-Vaule, returns its second element Value

 initial_values(++Environment:int, ++Alpha:float) is det

Sets the type of parameter initialization for EM on Environment: if Alpha is 0.0, it uses a truncated Dirichlet process if Alpha is a float > 0.0, it uses a symmetric Dirichlet distribution with that value as parameter

 equality(++Environment:int, ++Variable:int, ++Value:int, --BDD:int) is det

Returns in BDD the BDD belonging to environment Environment that represents the equation Variable=Value.

 em(++Context:int, ++RuleInfo:list, ++ListOfBDDs:list, ++EA:float, ++ER:float, ++Iterations:int, -LL:float, -Parameters:list, -ExampleProbabilities:list) is det

NumberOfHeads is a list of terms, one for each rule. Each term is either an integer, indicating the number of head atoms in the rule, or a list [N] where N is the number of head atoms. In the first case, the parameters of the rule are tunable, in the latter they are fixed.

Performs EM learning. Takes as input the Context, information on the rules, a list of BDDs each representing one example, the minimum absolute difference EA and relative difference ER between the log likelihood of examples in two different iterations and the maximum number of iterations Iterations. RuleInfo is a list of elements, one for each rule, with are either

• an integer, indicating the number of heads, in which case the parameters of the corresponding rule should be randomized,
• a list of floats, in which case the parameters should be set to those indicated in the list and not changed during learning (fixed parameters)
• [a list of floats], in which case the initial values of the parameters should be set to those indicated in the list and changed during learning (initial values of the parameters) Returns the final log likelihood of examples LL, the list of new Parameters and a list with the final probabilities of each example. Parameters is a list whose elements are of the form [N,P] where N is the rule number and P is a list of probabilities, one for each head atom of rule N, in reverse order.

 density2d(+List:list, -Dens:list) is det

Equivalent to density2d/3 with an empty option list.

 add_sum(++Environment:int, ++ADD1:int, ++ADD2:int, --ADDOut:int) is det

Computes the sum of the two ADDs ADD1 ADD2 belonging to environment Environment. The result in saved in ADDOut.

 densities(+PriorList:list, +PostList:list, -Chart:dict) is det

Equivalent to densities/4 with an empty option list.

 uniform_sample(--Value:float) is det

Returns a Value sampled from a uniform distribution in [0,1]

 end_em(++Context:int) is det

Terminates the context data structure for performing parameter learning. Context is a pointer to a context data structure for performing the EM algorithm. Context must have been returned by a call to init_em/1. It frees the memory occupied by Context.

 end(++Environment:int) is det

Terminates the environment data structure for storing a single BDD. Environment is a pointer to a data structure returned by a call to init/1.

 bar(+Successes:int, +Failures:int, -Chart:dict) is det

The predicate returns a dict for rendering with c3 as a bar chart with a bar for the number of successes and a bar for the number of failures

 or_list(++ListOfBDDs:list, ++Environment, --BDD:int) is det

Returns in BDD a pointer to a BDD belonging to environment Environment representing the disjunction of all the BDDs in ListOfBDDs

 bdd_notc(++Environment:int, ++EBDD:couple, --NotEBDD:couple) is det

EBDD is a couple (Environment,A) Returns in NotEBDD a couple (Environment,NotA) where NotA is pointer to a BDD belonging to environment Environment representing the negation of BDD A

 add_abd_var(++Environment:int, ++ProbabilityDistribution:list, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new abducible random variable in Environment with NumberOHeads values and probability distribution ProbabilityDistribution.

 onec(++Environment:int, --One:couple) is det

Returns in One a couple (Environment,BDD) where BDD is pointer to a BDD belonging to environment Environment representing the one Boolean function

 agg_val(+Couple:atom, +PartialSum:number, -Sum:number) is det

Aggregate values by summation. The first argument is a couple _-N with N the new value to sum to PartialSum

 average(+Values:list, -Average:float) is det

Computes the average of Values. Values can be

• a list of numbers
• a list of pairs number-weight, in which case each number is multiplied by the weight before being summed
• a list of lists, in which case lists are considered as matrices of numbers and averaged element-wise
• a list of pairs list-weight, in which case the list is considered as a matrix of numbers. The matrix in each element of List must have the same dimension and are aggregated element- wise

 end_ex(++Environment:int) is det

Terminates the evnironment data structure for storing a BDD. Environment is a pointer to a data structure returned by init_ex/2. It frees the memory occupied by the BDD.

 or(++Environment:int, ++A:int, ++B:int, --AorB:int) is det

Returns in AorB a pointer to a BDD belonging to environment Environment representing the disjunction of BDDs A and B.

 key_pair(+Pair:pair, -Key:term) is det

Given a pair Key-Vaule, returns its first element Key

 discrete_sample(++Theta:list, --Value:int) is det

Returns a Value sampled from a discrete distribution with parameters Theta. Theta is a list of floating point numbers in [0,1] that sum to 1. Value is in 0..(length(Theta)-1)

 add_prod(++Environment:int, ++ADDIn:int, ++Utility:float, --ADDOut:int) is det

Multiplies the ADD belonging to environment Environment with the value Utility and stores the result in ADDOut.

 init_em(--Context:int) is det

Initializes a data structure for performing parameter learning. It returns an integer in Context that is a pointer to a context data structure for performing the EM algorithm.

 density(+List:list, -Chart:dict, +Options:list) is det

Draws a line chart of the density of a sets of samples. The samples are in List as pairs [V]-W or V-W where V is a value and W its weigth.

Options is a list of options, the following are recognised by density/3:

min(+Min:float)

the minimum value of domain, default value the minimum in List

max(+Max:float)

the maximum value of domain, default value the maximum in List

nbins(+NBins:int)

the number of bins for dividing the domain, default value 40

 gauss_sample(++Mean:float, ++Variance:float, --Value:float) is det

Returns a Value sampled from a Gaussian distribution with parameters Mean and Variance

 histogram(+List:list, -Chart:dict, +Options:list) is det

Draws a histogram of the samples in List. List must be a list of pairs of the form [V]-W or V-W where V is a sampled value and W is its weight, or a list of values.

Options is a list of options, the following are recognised by histogram/3:

min(+Min:float)

the minimum value of domain, default value the minimum in List

max(+Max:float)

the maximum value of domain, default value the maximum in List

nbins(+NBins:int)

the number of bins for dividing the domain, default value 40

 create_dot_string(++Env:int, ++BDD:int, -Dot:string) is det

The predicate returns the BDD in dot format.

 bar(+Probability:float, -Chart:dict) is det

The predicate returns a dict for rendering with c3 as a bar chart with a bar for the probability and a bar for one minus the probability.

 andcnf(++Environment:int, ++A:couple, ++B:couple, --AandB:couple) is semidet

A and B are couples (Environment, BDDA) and (Environment, BDDB) respectively Returns in AandB a couple (Environment, BDDAandB) where BDDAandB is pointer to a BDD belonging to environment Environment representing the conjunction of BDDs BDDA and BDDB.

 equalityc(++Environment:int, ++Variable:int, ++Value:int, --EBDD:couple) is det

Returns in EBDD a couple (Environment,BDD) where BDD belongs to environment Environment and represents the equation Variable=Value.

 add_var(++Environment:int, ++ProbabilityDistribution:list, ++Rule:int, -Variable:int) is det

Returns in Variable the index of a new random variable in Environment with NumberOHeads values and probability distribution ProbabilityDistribution.

 ret_map_prob(++Environment:int, ++BDD:int, -Probability:float, -MAPState:list) is det

Returns the MAP state MPAState of BDD and its Probability. BDD belongs to environment Environment.

 swi_builtin(+Goal:atom) is det

Succeeds if Goal is an atom whose predicate is defined in Prolog (either builtin or defined in a standard library).

 probability_dd(++Environment:int, ++BDD:int, --ADD:int) is det

Converts the BDD belonging to environment Environment into an ADD.

 beta(+Alphas:list, -Beta:float) is det

Computes the value of the multivariate beta function for vector Alphas https://en.wikipedia.org/wiki/Beta_function#Multivariate_beta_function Alphas is a list of floats

 bdd_not(++Environment:int, ++A:int, --NotA:int) is det

Returns in NotA a pointer to a BDD belonging to environment Environment representing the negation of BDD A.

 one(++Environment:int, --One:int) is det

Returns in One a pointer to a BDD belonging to environment Environment representing the one Boolean function.

 to_pair(+Pair:pair, -FlattenedPair:pair) is det

Given a pair E-W, returns a pair Ep-W where Ep=EE if E=[EE], otherwise Ep=E

 symmetric_dirichlet_sample(++Alpha:float, ++K:int, --Value:list) is det

Returns a Value sampled from a symmetric Dirichlet distribution with parameter Alpha. K is the number of dimensions of the result.

 init_ex(++Context:int, --Environment:int) is det

Initializes an enviroment data structure for storing a BDD. Context is an integer that is a pointer to a context data structure created using init_em/1. Returns an integer Environment that is a pointer to a data structure for storing a single BDD to be used for the EM algorithm.

 density(+List:list, -Chart:dict) is det

Equivalent to density/3 with an empty option list.

 gamma_sample(++Shape:float, ++Scale:float, --Value:float) is det

Returns a Value sampled from a gamma distribution with parameters Shape and Scale

 histogram(+List:list, -Chart:dict) is det

Equivalent to histogram/3 with an empty option list.