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DLT USER MANUAL

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TableOfContents

Overview

DLT is a front-end for disjunctive datalog, extending the DLV system with Template predicates, Frame Logic and higher order predicate names. Template predicates can be seen as a way to define intensional predicates by means of a subprogram, where the subprogram is generic and reusable as many times is necessary. Frame Logic extends classical logic and enables frame-based or object-oriented syntax. Higher order predicates allow to treat predicate names as variables (although this semantics has quite nothing to deal with second order logics). The language implemented by the DLT system is named DLP^T.BR

More information (including an online version of this manual and an online tutorial) and the executable program for Linux platform are available at the DLT homepage (http://dlt.gibbi.com).[[BR]]

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Chapter 1. Getting Started

We can invoke the DLT system directly from the command-line, after the prompt of the system, as well the DLV system. Note that DLT relies on an external solver ES, which takes an input generated by DLT. Models generated by ES are then parsed back to the DLT syntax. ES can be chosen from a variety of solvers (see the Compatibility Table below)

If you do not specify any options or files, DLT will just print some informational output:

 > ./dlt  BR {{{ DLW. Disjunctive Logic Framework for the Web [Build DEV/May 3 2006 gcc 3.3.5 (Debian 1:3.3.5-13)]

usage: ./dlt {FRONTEND} {OPTIONS} [-higherorder] [-solver=<path>] [-preparsing] [-postparsing] [-filter=<predicate>] [-pfilter=<predicate>] [-silent] [-solverparams={options_solver}] [filename [filename [...]]]

Specify -help for more detailed usage information.

• }}}

BR The first line shows, first of all, the name of the executable program (DLW), then it gives information about the version of the executable program, the date when the binary was built and the identifier of the compiler. The last three lines give a brief explanation on how to use dlt, the last line informing the user of the -help option for futher instructions.BR Anchor(HELP)The -help or -h optionBRBR

 > ./dlt -help     or     > ./dlt -h BRBR gives the following output: BR {{{ DLW. Disjunctive Logic Framework for the Web [Build DEV/May 5 2006 gcc 3.3.5 (Debian 1:3.3.5-13)]

usage: ./dlt {FRONTEND} {OPTIONS} [-higherorder] [-solver=<path>] [-preparsing] [-postparsing] [-filter=<predicate>] [-pfilter=<predicate>] [-silent] [-solverparams={options_solver}] [filename [filename [...]]]

DLW Specific options:

-higherorder Enables higher order predicate names -solver=[path_name] The path of the solver executable file

• For example: -solver=/dlv/dl

-preparsing Print out re-written code and exit -postparsing Maps higher-order atoms into first-order atom -filter=name1,..,nameN Output only instances of the specified predicates -pfilter=name1,..,nameN Output only positive of the instances

• specified predicates

-solverparams={options} The specific solver options

• For example: -solverparams={-v -nofacts}

}}}

Anchor(SIL) If you do not want to see this status line, use the -silent option, which suppresses various informational output and blank lines.

•  > ./dlt -silent

{{{ usage: ./dlt {FRONTEND} {OPTIONS} [-higherorder] [-solver=<path>] [-preparsing] [-postparsing] [-filter=<predicate>] [-pfilter=<predicate>] [-silent] [-solverparams={options_solver}] [filename [filename [...]]]

Specify -help for more detailed usage information.

}}}

Section 1.1. DLW Specific options

The following table shows the specific options of DLW.BRBR note: The –filter e –pfilter options are inherited by DLV, but they must to be considered as specific options of DLT. Indeed, DLT can change the predicate names before passing them to DLV ( DLT set them up again it in the post-parsing phase ). Thus, it’s necessary that DLT performs filtering operations directly, before printing the results.

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Chapter 2. DLP^T Language

DLT's native language is [http://www.dbai.tuwien.ac.at/proj/dlv/ DLV] extended with Template predicates and other constructs. We remember that DLV's native language is Disjunctive Datalog extended with constraints, true negation, aggregates and queries.

How to write a DLP^T program

For a correct writing and usage of the DLP^T language here are a few general conditions that must be satisfied.

Section 2.1. Writing Template Definition

A template definition D consists of a template header and an associated DLP^T subprogram closed into curly braces. We consider a generic definition of template:

All the following conditions must be respected:

• In the body of a template definition at least a rule must have an atom in its head with the same name of the template in which it is defined;

• The formal parameters (p₁(a₁),..., p_n(a_n)) cannot appear in a head;

• All the formal parameters should appear in some rules;
• In the program cannot exist two or more template definitions having the same name;
• The formal parameters cannot be preceded from the true negation symbol and the negation as failure simbol in the template header in which they are uses;
• The global predicates defined using the GLOBAL directive cannot appear in the head of a rule defined in the body of the template;
• Definitions of template cannot appear in the body of a template;

Example 2-1. Correct Template Definitions

Example 2-2 Wrong Template Definitions

t₁ is a wrong template definition because the formal parameter pcannot appear in the head of a rule.

t₂ is a wrong template definition because the formal parameter p is preceded from the true negation symbol, while the formal parameter c is preceded from the negation as failure symbol.

Anchor(ES23) Example 2-3. The following is a template definition:

This template introduces a generic template program, defining the predicate max, intended to compute the maximum value over the domain of a generic unary predicate p. In this example we have that

is the template header, and

is a DLP^T subprogram. max is the template name; p is a predicate name, called formal predicate. The arity of formal predicate p is 1 and the output arity of template definition is 1.

Section 2.2. Writing Template Atoms

We consider a generic definition of template:

All the following conditions must be respected:

• For every template atom, defined in some rule of the general program, there must exist a definition having the same name of template_name;

• The number of actual predicates (p₁(X₁),..., p_n(X_n)) must be equal to the number of formal predicates of the correspondent definition;

• The arity of the output terms must be equal to the output arity of the correspondent definition;
• The number of asterisks of every actual parameter must be equal to the arity of the correspondent formal parameter;
• The actual parameters cannot appear negated in the atom template that uses them(note that true negation is allowed instead).

Example 2-4 Correct Template Atoms

Example 2-5 Wrong Template Atoms

We consider the template definition of the Example 2-3(definition of template max). The following are wrong template atoms:

a₁ is a wrong template atom because the arity of the output terms is not equal to the output arity of the correspondent definition.

a₂ is a wrong template atom because the actual parameter person is preceded by negation as failure.

a₃ is a wrong template atom because the number of actual predicates is not equal to the number of formal predicates of the correspondent definition.

Note: The DLP^T subprogram may contain disjunctive rules, constraints, weak constraints, aggregates, built-in predicates, negative literals, true negation, template atoms (or invocations), and it do not contains template definitions.

Section 2.3. Negative Rules with Template Atoms and True Negation

Template atoms can be used also as negated and negative atoms in the generic rules of the program. Then we can use a template atom after the negation as failure symbol (not) as it happens for the usual atoms.

Example 2-6. The following is an example of negated and negative template atom, respectively.

Negation for template atoms is treated as well negation for DLV atom. For more information about negation as failure and true negation we send back at the DLV user manual available at the DLV homepage (http://www.dbai.tuwien.ac.at/proj/dlv/).

Section 2.4. Template Definition with Global Predicates

Template programming can become a very useful feature in applications where it is necessary to compact repetitive pieces of code. We consider a planning program for the Space Shuttle Reaction Control System. Here is a sketch from the program:

the above template is employed to remove a set of repeated rules, which are changed this way

Section 2.5. Group-by

A template definition may be instantiated as many times as necessary, trough template atoms. The template atom or invocation consists of a template name, a list of atom and a list of variables and/or constants (literal constants and numerical constants).

Example 2-7. The followings are template atoms:

max is the template name; weight and student are predicate names, called actual predicates; variables and constants are called standard terms (Sex is a standard term); the dollar $ symbol is called projection term and the symbol * is called parameter term. M and Age are a list of usual terms (i.e. either variables or constants), and are called output lists.

We note that the template definitions may be unified with a template atom in many ways. The above example contains a plain invocation ( max{weight(*)}(M) ), and a compound invocation ( max{ student($,Sex,*) }(Age) ). Intuitively, projection terms ($ symbols) are intended in order to indicate attributes of an actual predicate which have to be ignored. A standard term (a constant or a variable) within an actual atom indicates a group-by attribute, whereas parameter terms (* symbols) indicate attributes to be considered as parameter.

For example, the template atom max{student($,Sex,*)}(Age) allows to employ the definition of the template predicate max on a ternary predicate student, discarding the first attribute of student, and grouping by values of the second attribute. The intuitive meaning of this invocation is to define a predicate computing the student with maximum value of the Age attribute (the third attribute of the student predicate), grouped by the Sex attribute (the second one), ignoring the first attribute. The computed values of Age are returned through the output list.

Example 2-8. We consider the following EDB:

it represents a set of persons of which it is known name, sex and age. We consider the template definition of max given in [#ES23 Example 2-3]. The following:

is a template atom that compute the oldest person with grouping on the sex attribute, that is the person of age greater than female sex and that one of male sex. Launching dlt from command line, as it follows:

•  >  ./dlt -silent -solverparams={-nofacts} programFileName 

we obtain the model

{{{ {older_sex(paddy,f,27),older_sex(gibbi,m,29)} }}}

Therefore paddy is the greatest person of female sex, while gibbi is the greateest person of male sex.

Example 2-9. We consider another example and the following template:

It allows to sum all the values of the second attribute of the argument emp in an iterative manner. The first attribute must be an ID which identifies unambiguously the instance. The template first orders the instances of emp by their ID (first rule), then using the next rules it defines the successor of each instance. It introduces a new atom, succ(I,II), thus finding the first and the last of the list (first(X),first(X)). The predicate partialSum scans the entire ordered list and addes the sum of the preceding values to the following value. The sum predicate receives the value associated with the last instance of emp. This is possible due to the predicate last.

Now we consider the following EDB:

it represents a set of persons of which it is known ID, name and salary. We use the template sum and we consider the following:

result(DIP,S):- sum{impiegato(*,$,DIP,*)}(S).

this is a template atom which calculates the sum of the values of the 4th attribute of employee (salary) also taking into consideration the first (ID), ommiting the second(name) and grouping the result by the third attribute(department).

Launching dlt from command line, as it follows:

> ./ dlt name_file -silent -filter=result 

we obtain the model

{{{{result(direction,153), result(production,114), result(administration,125), result(distribution,45)} }}}

The result is obtained in a simple manner. First, the template is executed as if the DIP parameter, which is later used to group the results, is only used for the selection. Therefore the instances of employee are ordered by their ID. Then the DIP and salary of each are selected. A table with a row for each employee and two columns, the first for departiment and the second for salary is obtained. The table is then analysed dividing the rows in groups defined by their DIP values. After this, the sum is separately calculated for each group. The output (filtering only the result predicate) contains the sum of the salaries for each departiment.

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Chapter 3. Safety

Safety of variables in template atom follows the usual criterion. We suppose to have in the body of a generic rule a negated invocation; then must be valid the following condition must be valid:

Example 3-1. Unsafe Rules and Constraints

u₁ is unsafe because the variable Y that appear in the head of the rule does not appear in at least a positive atom of the body of the same rule.

u₂ is unsafe because the variable X in the output list of the given invocation does not appear in at least a positive atom of the body of the same rule.

Example 3-2. Safe Rules and Constraints

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Chapter 4. Knowledge Representation by DLP^T

In this section we show by example the main advantages of template programming. Example put in evidence the easiness of providing a succinct and elegant way for quickly introducing new constructs using the DLP^T language.

Section 4.1. Aggregates

Aggregate predicates allow to represent properties over sets of elements: the next example shows how to fast prototype aggregate semantics without taking into account of the efficiency of a built-in implementation.Here we take advantage of the template predicate max, defined in Example 2.1. The next template predicate defines a general program to count distinct values of a predicate p, given an order relation succ defined on the domain of p.

The above template definition is conceived in order to count, in a iterative-like way, values of the p predicate through the partialCount predicate. A ground atom partialCount(i,a) means that at the stage i, the constant a has been counted up. The predicate count takes the value which has been counted at the highest (i.e. the last) stage value. It is worth noting how max is employed over the binary predicate partialCount, instead of an unary one. Indeed, the $ and * symbols are employed to project out the first argument of partialCount. The last rule is equivalent to the piece of code:

Template definitions can be employed to introduce and reuse constructs defining the most common search spaces. This improves declarativity of ASP programs to a larger extent. The next two examples show how to define a predicate subset and a predicate permutation, ranging, respectively, over subsets and permutations of the domain of a given predicate p.

The explanation of the subset template predicate is quite straightforward. As for the permutation definition, a ground atom permutation(x,i) tells that the element x (taken from the domain of p), is in position i within the currently guessed permutation. The rest of the template subprogram forces permutations properties to be met.

Next we show how count and subset can be exploited to succinctly encode the k-clique problem, i.e., given a graph G (represented by predicates node and edge), find if there exists a complete subgraph containing at least k nodes (we consider here the 5-clique problem):

The first rule of this example guesses a clique from a subset of nodes. The first constraint forces a candidate clique to be at least of nodes, while the last forces a candidate clique to be strongly connected. The permutation template can be employed, for instance, to encode the Hamiltonian Path problem: given a graph G, find a path visiting each node of G exactly once:

Sets: Extending Datalog with Set programming is another matter of interest for the ASP field. It is fairly quick to introduce set primitives using DLP^T; a set S is modeled through the domain of a given unary predicate s. Intuitive constructs like intersection, union, or symmetricdifference, may be modeled as follows.

Dates: managing time and date data types is another important issue in engineering applications of DLP. The following template shows how to compare dates represented through a ternary relation day, month, year.

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Anchor(HIGH)

Chapter 5. Higher order predicates

With the use of higher order predicates it is possibile to consider the names of the predicates as variables. The user inserts atoms as if they where of first order, but if the option -higherorder is used it is possible to execute higher order queries. Moreover they are fundamental for the [#HIG1 Frame Logic] and for the use of predicates that may appear with [#HIG2 different arities].

Example 5-1. We consider the following EDB:

it represents a set of persons; the names of the predicates define the relations between the persons. The use higher order allows the user to use the names of the predicates as though they where attributes of other predicates. The following rule simply rewrites the facts, but also allows the user to understand how to perform higher order queries.

Launching dlt from command line with option -higherorder, as it follows:

 >  ./dlt name_file -higherorder -solverparams={-nofact}

we obtain the model

{relationship(gisella,sister,maria), 
relationship(gisella,friend,rosina), 
relationship(gisella,aunt,sara), 
relationship(maria,mother,giovanni), 
relationship(gino,husband,carmela)}

Please note that now the predicate names appear also as attributes of the relations (see for instance relationship(gisella,sister,maria)).

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Chapter 6. Frame Logic

F -logic is really useful, since it allows to model reality in a very simple way. Furthermore, with frames the code is compact and the meaning of the program is more clear than a great set of isolated rules. Indeed, everything that can be expressed with the frames can be without them , but they make the programs more simple and intuitive. Frame Logic uses frames to represent objects. In general a frame is an object which has a name (subject) and a list of attributes, which may be empty:

Example 6-1.

The attributes may have 1 value, as in the previous example, multiple values, or they may be boolean.

Example 6-2.

children is a multivalued attribute. Its value for mary is a list including the objects alice and nancy. The second fact informs that mary has an additional child, jack. It is worth noting that for multivalued attributes the notation:

is used. This notation is also used for additional attributes. While single variable attributes use the:

notation. Please note that in general curly brackets are not used when only one element is specified. The last clause is a boolean attribute which indicates that married is true for the object mary.

While some attributes may be described as facts, other may be defined using inference rules. In the previous example john is married to mary and mary has three children. It can be assumed that john is the father of alice, nancy, and jack. Therefore the following fact:

may be automatically derived if we add the following rule:

In addition it is possible to specify the class an object belongs to using the following rules:

Once the class of the object is identified, a specific list of attributes can be assigned at the same time:

Anchor(ES63) Example 6-3. We consider an other definition frame:

The frame describes the relationships existing between some member of the Britannic royal family. carlo is a man and he’s married with camilla. He has two children: william and harry, and their mother was diana. carlo ‘s mother is elisabeth and his father is philip. camilla is a woman and she has a daughter, laura, and a son, tom. laura is betroth with harryT , and tom ’s girlfriend is sara.

Launching dlt from command line:

 >  ./dlt name_file

we obtain the model

{married(carlo,camilla), children(carlo,harry), children(carlo,william), children(camilla,tom), children(camilla,laura), engaged(tom,sara), engaged(laura,harryT), man(carlo), man(tom), man(harry), man(william), woman(camilla), woman(laura), woman(elisabeth), father(carlo,philip), father(camilla,bruce), mother(carlo,elisabeth), mother(harry,diana), mother(william,diana)}

The higher order atoms are fundamental for the frames. Indeed, the output consists of predicates whose names were attributes in the frames. For example look at the first part of the definition of the frame:

carlo is a man, and he is married to camilla; 'married' is an attribute of the object carlo, but in the output it's presented as the name of a predicate:

Anchor(PREP) Obviously, beside those defined by facts, it's possible to establish other logical relations exploiting inference rules. In this case, though, it is necessary to know how the frames were written, since the user must write the rules using the atoms in the same format. It is possible to know how a frame is rewritten, using the option -preparsing. Executing the previous example using -preparsing the program is rewritten and returned in output. The inference rules must be written based on the atoms given in output.

Launching a program with -preparsing option:

 >  ./dlt nome_file -preparsing

{{{DLW. Disjunctive Logic Framework for the Web [Build DEV/May 3 2006 gcc 3.3.5 (Debian 1:3.3.5-13)]

% LEGENDA OF TEMPLATE INVOCATIONS % END OF LEGENDA married(carlo,camilla). children(camilla,tom). fidanz(tom,sara). man(tom). children(camilla,laura). fidanz(laura,harry). woman(laura). father(camilla,bruce). woman(camilla). children(carlo,william). mother(william,diana). man(william). children(carlo,harry). mother(harry,diana). man(harry). mother(carlo,elisabetta). woman(elisabetta). father(carlo,philip). man(carlo). }}}

At this point it's simple to determine which atoms must be used for the query. If we wish to know the grandchildren of the Queen Elisabeth, the following rule would suffices:

X (elisabetta, in this case) is the grandmother of Y(william and harry, in this case) if there exists a Z(carlo, in this case) which is the child of X and the father of Y.

With the addition of this rule we obtain:

 >  ./dlt  nome_file -solverparams={-filter=grandmother}

{{{{grandmother(elisabetta,harry), grandmother(elisabetta,william)} }}}

As expected Elisabeth is the grandmother of harry and william, the children of carl.

Example 6-4. Let's show another example:

Anchor(HIG2) The frame says that Gianni is a student and has a pc named mistery. The pc is a notebook which uses debian as operating system. In addition information on the OS is given: kind and kernel. Launching this program without the option higherorder results with an error:

 >  ./dlt nome_file

os, first used with arity 2, now seen with arity 1.

The cause of the error is clear once we look at the opuput with the option -higherorder

 >  ./dlt -higherorder nome_file

{pc(gianni,mistero), os(mistero,debian), kind(debian,gnu), kernel(debian,linux), os(debian), notebook(mistero), student(gianni)}

The atoms os(mistero,debian) e os(debian) appears in the output. The same predicate is present with different arity. In the case of first order atoms this is not permitted. It is only possible using higher order atoms.

Section 6.1. Frame Space directive

The Frame Space is a new directive introduced in DLT:

@name.

• From the point after the directive each frame is interpreted as belonging to the frame space 'name'. A frame

  X[f->Y] is rewritten as f(X,Y,name).

@.

• Cancels out the default Frame Space. Goes back to the normal

  rewriting X[f->Y] = f(X,Y).

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Chapter 7. System Architecture

A DLP^T program P, is sent to a DLP^T pre-parser, which performs syntactic checks (included nonrecursivity checks), and builds an internal representation of the DLP^T program. The DLP^T Inflater produces an equivalent SOLVER program P'; P' is piped towards the SOLVER system. The models M(P') of P', computed by SOLVER, are then converted in a readable format through the Post-parser module; the Post-parser filters out from M(P') informations about internally generated predicates and rules.

Figure 1.

attachment:flow.gif

Section 7.1 DLT Work-Flow

We show here the work-flow of DLT, exploiting [#ES63 example 6-3]. We launch the program with -preparsing option and divert the output in the file (tmp):BR Anchor(HIG1)  >  ./dlt -silent -higherorder -preparser nome_file >tmp

The file tmp will appear as following:

% LEGENDA OF TEMPLATE INVOCATIONS
% END OF LEGENDA
a_2(married,carlo,camilla).
a_2(children,camilla,tom).
a_2(engaged,tom,sara).
a_1(man,tom).
a_2(children,camilla,laura).
a_2(engaged,laura,harryT).
a_1(woman,laura).
a_2(father,camilla,bruce).
a_1(woman,camilla).
a_2(children,carlo,william).
a_2(mother,william,diana).
a_1(man,william).
a_2(children,carlo,harry).
a_2(mother,harry,diana).
a_1(man,harry).
a_2(mother,carlo,elisabeth).
a_1(woman,elisabeth).
a_2(father,carlo,philip).
a_1(man,philip).
a_1(man,carlo).

Passing the content of tmp to the solver (i.e., DLV in this case) and diverting the output in another file (tmp2):

 >  ./dl -silent tmp > tmp2

the file tmp2 will look as following:

{a_2(married,carlo,camilla), a_2(children,carlo,william), a_2(children,carlo,harry), a_2(children,camilla,tom), a_2(children,camilla,laura), a_2(engaged,tom,sara), a_2(engaged,laura,harryT), a_2(father,carlo,philip), a_2(father,camilla,bruce), a_2(mother,carlo,elisabeth), a_2(mother,william,diana), a_2(mother,harry,diana), a_1(man,carlo), a_1(man,tom), a_1(man,william), a_1(man,harry), a_1(man,philip), a_1(woman,camilla), a_1(woman,laura), a_1(woman,elisabeth)}

Anchor(POST) Finally, we send the content of tmp2 to DLT postparser module as following:

 >  ./dlt -postparsing <tmp2 

and we obtain the following:

{married(carlo,camilla), children(carlo,william), children(carlo,harry), children(camilla,tom), children(camilla,laura), engaged(tom,sara), engaged(laura,harryT), father(carlo,philip), father(camilla,bruce), mother(carlo,elisabeth), mother(william,diana), mother(harry,diana), man(carlo), man(tom), man(william), man(harry), man(philip), woman(camilla), woman(laura), woman(elisabeth)}

the same output that we would have obtained launching the command:

 >  ./dlt family

Indeed, performing the whole process launching directly DLT as above, the only model is:

{married(carlo,camilla), children(carlo,william), children(carlo,harry), children(camilla,tom), children(camilla,laura), engaged(tom,sara), engaged(laura,harryT), man(carlo), man(tom), man(william), man(harry), man(philip), woman(camilla),woman(laura), woman(elisabeth), father(carlo,philip), father(camilla,bruce), mother(carlo,elisabeth), mother(william,diana), mother(harry,diana)}

exactly the same of what obtained performing explicitly all the operations constituting the flow.

Section 7.2. Compatibility with other solvers

Anchor(SOLV) DLT can virtually support any solver. At the moment, we can state the compatibility with the syntax of some of them. The following table shows the instructions of the solvers which dlt natively recognizes.

Note: All the SOLVER options must be passed using the option -solverparams={}.

Section 7.3. Notes on using DLV-HEX with DLT

DLV-HEX has higher order reasoning built-in, so it is not necessary to invoke DLT with the option -higherorder switched on. Also, DLV-HEX supports natively DLT. DLT can be used with DLV-HEX with different command line combinations such as

   dlt -silent -preparsing program.dlt | dlvhex --silent -- | dlt -postparsing

or

   dlvhex --dlt program.dlt

makes dlvhex to invoke dlt as a preparser