The Bousi∼Prolog User Manual In A Nutshell (Version 1.04
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1. is syntactic sugar of Term1 Term2 gt 0 Also it is possible the following construction Terml Term2 Degree which succeeds if Term1 and Term2 are weak unifiable with approximation degree Degree otherwise fails When Degree is a variable it is bound to the unification degree of Term1 and Term2 These expressions may be introduced in a query as well as in the body of a clause Example 2 Assume that the BPL program of Example 1 is load The following is a simple session with the BPL system BPL gt sv adventures X interesting Y gt 0 5 With approximation degree 1 X _G1248 Y _G1248 Yes BPL gt sv adventures mystery With approximation degree 1 Yes Both goals succeed with approximation degree 1 because adventures X and interesting Y weak unify with unification degree 0 9 greater than 0 5 adventures and mystery trivially weak unify with unification degree 0 5 greater than 0 and the comparison operator is a crisp one BPL gt sv adventures X mystery Y D With approximation degree 1 X _G1714 Y _G1714 D 0 5 No answers This goal succeeds with approximation degree 1 because it is completely true that adventures X and mystery Y weak unify with unification degree 0 5 There are not more answers since only a weak unifier representative is returned Note that the last goal is equivalent to the following one BPL gt sv unify adventures X mystery Y D With approximation de2. 1 gt fail D is 1 DA D 1 where the predicate solve 2 is used internally by the BPL meta interpreter to solve BPL queries 5 3 Directives We can impose a limit to the expansion of the search space in a computation by what we called a lambda cut When the LambdaCut flag is set to a value different to zero the weak unification process fails if the computed approximation degree goes below the stored LambdaCut value Therefore the computation also fails and all possible branches starting from that choice point are discarded By default the LambdaCut value is zero that is no restriction to a computation is imposed However the LambdaCut flag can be set to a different value by means of a LambdaCut directive introduced inside of a BPL program or the 1c command of the BPL shell explained before On the other hand in a BPL program the user supplies an initial subset of similarity equations for defining a fuzzy relation and then the system au tomatically generates its reflexive symmetric transitive closure to obtain by default a similarity relation In order to resolve certain problems sometimes is preferable not to generate the similarity relation from the initial set of similar ity equations This effect can be achieved by means of the BPL directive transitivity no which inhibits the construction of the transitive closure during the translation phase If the BPL directive transitivity no is includ
3. Exp2 True if expression Expl evaluates to a number greater than or equal to Exp2 Exp1 lt Exp2 True if expression Exp evaluates to a number less than or equal to Exp2 Comparison operators Terms are ordered in the so called standard order This order is defined as follows 1 SOE Cob Variables are less than Numbers Numbers are less than Atoms Atoms are less than Strings Strings are less than Comound Terms Variables are sorted by address Atoms are compared alphabetically Strings are compared alphabetically Numbers are compared by value Compound terms are first checked on their arity then on their functor name alphabetically and finally recursively on their arguments leftmost argu ment first To compare the standard order between two terms the following operators are provided Term1 Term2 Succeeds if term Term1 is syntactically equivalent to term Term2 Termi Term2 Succeeds if term Term1 is not syntactically equivalent to term Term2 Term1 Term2 True if Term1 is structurally equal to Term2 Term1 Term2 True if Term1 is not structurally equal to Term2 Termi lt Term2 True if Term1 is greater than Term2 in the standard order of terms Termi gt Term2 True if Term1 is less than Term2 in the standard order of terms Termi gt Term2 True if Term1 is greater than or equal to Term2 in the standard order of terms Termi lt Term2 True if expression Term
4. interactive Unix shell Default is bin sh The environment variable SHELL overrides this default Syntax She et shes oie eee 4 starts a new interactive shell process qt gt QUIT leaves the system 4 Edition and execution of a Program and a Query The BPL system does not provide an specific text editor This is not a real inconvenient in a unix based implementation If you wish to create a new BPL program or open an old one for edition you can use your favorite text editor In order to launch a BPL program you must follow these steps 1 Once a BPL program has been created use the 1d command for loading the program into the working space 2 Use the sv command to send a query to the BPL system 3 The BPL systems returns an answer or responds no answers if there is not any In the first case you can type the semi colon plus the new line keys lt new line gt if you want another solution or return if you are satisfied after which Bousi Prolog will say Yes If Bousi Prolog answers no answers this indicates it cannot find any more answers to the query 5 The Bousi Prolog programming language In this section we briefly summarize the features of Bousi Prolog We concentrate on the syntactical aspects The programming language we call Bousi Prolog is an extension of the stan dard Prolog language with a similarity relation defined on a syntactic domain Therefore the syntax is mainly the Prol
5. 1 is less than or equal to Term2 in the standard order of terms Syntactic unification Termi Term2 Unifies Term1 with Term2 True if the unification succeeds Term1 Term2 True if Termi does not unify with Term2 List manipulation Some standard predicates for list manipulation is_list Term True if Term is bound to the empty list or a term _ L where the second argument L is a list member Elem List Succeeds when Elem is one of the members of List append List1i List2 List True when List is the concatenation of List1 and List2 reverse List1 List2 Reverses the order of the elements in List1 and unifies the result with the elements of List2 last List Elem Succeeds if Elem unifies with the last element of List length List Int True if Int is the number of elements of List 10 Analysing and Constructing Terms Some predicates for cataloging terms var Term True if Term currently is a free variable integer Term True if Term is bound to an integer number Term True if Term is bound to an integer or floating point number atom Term True if Term is bound to an atom atomic Term True if Term is bound to an atom string integer or floating point number compound Term True if Term is bound to a compound term Some predicates for constructing terms functor Term Functor Arity True if Term is a term with functor Functor and arity Arity If
6. Term is a variable it is unified with a new term holding only variables arg Arg Term Value Term should be instantiated to a term Arg to an integer between 1 and the arity of Term Value is unified with the Arg th argument of Term Term List List is a list which head is the functor of Term and the remaining arguments are the arguments of the term Each of the arguments may be a variable but not both Edinburgh style I O The I O predicates refer to the current input stream and the current output stream Initially these streams are connected to the ter minal The current output stream is changed using tel1 1 The current input stream is changed using see 1 The streams current value can be obtained using telling 1 for output and seeing 1 for input streams The streams are connected to files or the terminal The reserved stream name user refers to the terminal The connection is made either by te11 1 or by see 1 which open a file for output or input respectively A simple working session is as follows see file_name open the file file_name which is made the current input stream predicates for reading the current input stream seen close the current input stream The I O predicates available on this implementation of Bousi Prolog are see File Open File for reading and makes it the current input stream tell File Open File for writing and makes it the current output stream seeing Stream Get
7. The Bousi Prolog User Manual In A Nutshell Version 1 04 Release April 2008 Pascual Julian Iranzo Clemente Rubio Manzano and Juan Gallardo Casero Department of Information Technologies and Systems University of Castilla La Mancha Pascual Julian uclm es Clemente Rubio Juan Gallardo alu uclm es 1 Introduction Bousi Prolog BPL for short is an extension of the Prolog language with an operational semantics based on the weak SLD resolution principle WSLD of 3 WSLD is an adaptation of the SLD resolution principle where classical uni fication has been replaced by an algorithm based on similarity relations defined on a syntactic domain The weak unification algorithm provides a weak most general unifier as well as a numerical value called the unification degree Hence Bousi Prolog computes answers as well as approximation degrees At this point it is worth to say that Bousi is the Spanish acronym for fuzzy unification by similarity The BPL system we are presenting is a prototype high level implementation written on top of SWI Prolog 5 The complete implementation consists of about 900 lines of Prolog code The parser and translator module translates compiles rules and facts of the source BPL code into an intermediate Prolog code repre sentation which is called TPL code Translated BPL code Then following standard techniques 4 a meta interpreter executes the TPL code according to the weak SLD resol
8. and all possible branches starting from that choice point are dis carded The Lambdacut command can be used to show what is the current Lambdacut value or to set a new Lambdacut value Syntax TE fia Aiwa oe reads the current value of the lower bound for the approximation degree in a weak unification process lc lt Value gt sets the lower bound for the approximation degree in a weak unification process Value is a real between 0 and 1 hp gt HELP The Help command gives a summary of the BPL shell com mands or specific information on a BPL shell command Syntax Ap soi ae wet PAA gives a summary of BPL shell commands hp lt ShellCmnd gt gives information on a BPL shell command 1s gt LIST Executes the command ls B color on the operating sys tem That is this command shows a list of the files in the working directory ordered by columns ignoring backups and distinguishing plane files from directories executable files and so on by color Syntax LSC A658 ea telly aces lists the files in the working directory pwd gt PRINT WORKING DIRECTORY Print the full filename of the cur rent working directory Syntax Pud tate ee eas shows the filename of the working directory cd gt CHANGE DIR Changes the working directory Syntax cd lt Dir gt Changes the current directory to lt Dir gt where lt Dir gt is a pathname sh gt SHELL Starts an
9. ed at the beginning of a BPL program only the reflexive symmetric clo sure is computed By default the transitivity flag is set to yes 5 4 Built in predicates In this section we give a list of the built in predicates provided by Bousi Prolog As for the current implementation the core of the system is a meta interpreter built in predicates are sent directly to the Prolog interpreter Control and meta call predicates Control predicates are useful to manage repetition through backtracking We provide two simple predicates for control fail Always produces a fail repeat Always succeed providing an infinite number of choice points Meta call predicates are used to call terms constructed at run time The meta call mechanism offered by Bousi Prolog is call Goal Invokes Goal as a goal Arithmetic operators The basic operator for the evaluation of arithmetic expressions is Exp1 is Exp2 Forces the evaluation of Exp1 and Exp2 It will be successful if Exp1 and Exp2 unify after their evaluation The following arithmetic comparison operators are available Exp1 Exp2 Succeeds if expression Expl evaluates to a number equal to Exp2 Exp1 Exp2 Succeeds if expression Exp1 evaluates to a number different to Exp 2 Expl gt Exp2 True if expression Expl evaluates to a number greater than Exp 2 Exp1 lt Exp2 True if expression Exp evaluates to a number less than Exp2 Expl gt
10. g process what imposes some real limitations For instance we cannot use operators defined by the user that is the op _ _ _ directive In the future we want to add these missing features to our language OBSERVATION Bousi Prolog uses the standard cut predicate of the Pro log language in an indirect way embedded into more declarative predicates and operators such as not weak negation as failure crisp negation as failure and gt ifthen and if then else operators References 1 K R Apt From Logic Programming to Prolog Prentice Hall Englewood Cliffs NJ 1997 2 P Julian Iranzo C Rubio Manzano and J Gallardo Casero Bousi prolog a pro log extension language for flexible query answering page 14 2008 Submitted for publication 3 Maria I Sessa Approximate reasoning by similarity based sld resolution Theoret ical Computer Science 275 1 2 389 426 2002 4 L Sterling and E Shapiro The Art of Prolog Second Edition The MIT Press Cambridge MA 1994 5 J Wielemaker SWI Prolog 5 6 Reference Manual Technical report vesion 5 6 52 March 2008 University of Amsterdam 2008 12
11. gree 1 X _G2522 Y _G2522 D 0 5 Yes Finally observe that Bousi Prolog also provides the standard syntactic unifi cation operator The operator symbol is overloaded and it can be used in different contexts with different meanings i it behaves as an identity when it is used inside a similarity equation or inside the construction Term1l Term2 Degree ii it behaves as the syntactic unification operator when it is used dissociated of the weak unification operator 5 2 Distinct Classes of Negations Bousi Prolog provides an operator for crisp negation as failure and a pred icate not for weak negation as failure The implementation of these distinct classes of negation is as follows A goal A fails only if solve A DA succeeds with approximation degree DA 1 Otherwise A is true with approximation degree 1 That is operates as the classical negation as failure Crisp negation as failure solve A D solve A DA gt DA 1 gt fail D 1 D 1 A goal not A fails only if solve A DA succeeds with approximation de gree DA 1 When solve A DA succeeds but the approximation degree DA is lesser than 1 not A also succeeds with approximation degree D 1 DA If it is the case that solve A DA fails not A succeeds with approxi mation degree D 1 Weak negation as failure solve not A D solve A DA gt DA
12. island adventures the_call_of_the_wild mystery murders_in_the_rue_morgue horror dracula science_fiction the_city_and_the_stars science_fiction the_martian_chronicles RULES good X interesting X SIMILARITY EQUATIONS adventures mystery 0 5 adventures science_fiction 0 8 adventures interesting 0 9 mystery horror 0 9 mystery science_fiction 0 5 science_fiction horror 0 5 When this program is loaded an internal procedure constructs a similarity relation i e a reflexive symmetric transitive fuzzy binary relation on the syn tactic domain of the program alphabet Therefore all kind of books considered as interesting are retrieved by the query BPL gt sv good X 5 1 The weak unification operator Bousi Prolog implements a weak unification operator denoted by which is the fuzzy counterpart of the syntactical unification operator of stan dard Prolog It can be used in the source language to construct expressions like Termi Term2 Degree which is interpreted as follows The ex pression is true if Term1 and Term2 are unifiable by similarity with approx imation degree AD equal to Degree In general we can construct expressions Terml Term2 lt op gt Degree where lt op gt is a comparison arithmetic op erator that is an operator in the set gt lt gt lt Observe that the expression Term1 Term2
13. ment is running you can type in the following commands ld gt LOAD The Load command can be used to show what program has been loaded when used without an argument In this case it shows the name of the loaded program or the notice No program loaded Also when used with a single argument it can be used to load a file containing the source program Syntax io Oe ae ao shows if there is a current loaded program ld lt FileName gt reads the file FileName containing the source pro gram translates it into a TPL file and consults the TPL file lt FileName gt is a BPL file name without extension lt gt LIST The List command shows the rules in the current loaded program Note that similarity equations are not shown Syntax Lts ua displays the current loaded program sv gt SOLVE The Solve command sends a possibly conjunctive query to be solved by the Evaluator It requires a single argument that must be an atom or a conjunction of atoms Conjunctive queries must be enclosed by curved parenthesis signs Syntax sv lt Atom gt sv lt Atom_1 gt lt Atom_2 gt lt Atom_N gt lc gt LAMBDACUT We can impose a limit to the expansion of the search space in a computation by what we called a lambdacut When Lambda cut is set the weak unification process fails if the computed approximation degree goes below the stored lambdacut value Therefore the computation also fails
14. of the command bousi Universidad de 10 ID Castilla La Mancha 10 O UCS ITI I IR 0 IL 0 GI Version 1 04 February 2008 Welcome to Bousi Prolog This software is for research and educational purposes only and it is distributed with NO WARRANTY Please report bugs and send your suggestions to Pascual Julian uclm es ld gt load reads a file containing the source program for loading lt gt list displays the current loaded program sv gt solve solves a possibly conjunctive query lc gt lambdacut reads or sets the lower bound for the approximation degree in a weak unification process hp gt help shows this help info ls gt list lists the files in the working directory pwd gt print working directory shows information of the working directory cd gt change Dir changes the working directory sh gt shell starts a new interactive shell process qt gt quit leaves the system 255 Write hp Topic to obtain more help on that Topic ast Fig 1 Welcome screen and shell commands of the Bousi Prolog system 3 The BPL Environment In this section we give a brief tutorial on how to use the BPL environment wich is the interface between the user and this high level implementation The BPL environment implements a command shell Figure 1 shows the welcome screen and a summary of the shell commands To start the BPL envi ronment execute the command bousi Once the BPL environ
15. og syntax but enriched with a built in symbol used for describing similarity relations actually fuzzy binary relations which are automatically converted into similarity relations by means of simi larity equations of the form lt alphabet symbol gt lt alphabet symbol gt lt similarity degree gt meaning that two constants n ary function symbols or n ary predicate symbols are similar with a certain degree A BPL program is a sequence of Prolog facts and rules plus a sequence of similarity equations A rule is a conditional formula of the form A L L eee Lin where the A is an atomic formula i e a relational symbol applied to a tuple of rst order terms and the L are literals e i either atomic formulas or negation of atomic formulas The atomic formula A is called the head of the rule and the conjunction of literals Li L2 Ln is called the body In general the body may be an aggregation of literals connected by conjunctions disjunctions and if then else gt operators A fact is a rule without a body Bousi Prolog uses the similarity based SLD principle 3 also called weak SLD resolution as operational semantics This operational mechanism is well suited for flexible query answering Example 1 This BPL program fragment specify features and preferences on books stored in a data base The preferences are specified by means of similarity equations FACTS adventures treasure_
16. s the current input stream telling Stream Gets the current output stream seen Closes the current input stream The new input stream becomes user 11 told Closes the current output stream The new output stream becomes user read Term Reads the next term from the current input stream and unifies it with Term When reaching end of file Term is unified with the atom end_of_file write Term Writes Term to the current output stream get Char Reads the current input stream and unifies the next non blank character with Char Char is unified with 1 at end of file get0 Char Reads the current input stream and unifies Code with the char acter code of the next character Code is unified with 1 at end of file put Char Writes Char to the current output stream nl Writes a new line character to the current output stream Runtime Statistics statistics Key Value Unifies system statistics determined by Key with Value Some possible keys are e cputime cpu time since Prolog was started in seconds e inferences Total number of predicate calls since Prolog was started See the SWI Prolog documentation for more details 5 5 Some limitations Although Bousi Prolog implements the main features of a standard Prolog other features such as working with modules are not covered Also because the parser phase is delegated to standard Prolog predicates we lost the control of the whole parsin
17. ution principle More information about the structure and main features of the BPL system can be found in 2 Since the BPL system is a prototype implementation some bugs may arise during its execution Please send your comments to Pascual Julian uclm es In the following we assume some familiarity with the field of logic program ming 1 So some basic concepts such as term atomic formula clause substi tution etc are not introduced 2 Requirements and Instalation Procedure Bousi Prolog version 1 04 release April 2008 is available in two distribution formats the executable distribution and the complete source code distribution The current version of the low level implementation of Bousi Prolog runs on Unix based platforms and has been tested under Linux Red Hat Fedora and Debian Ubuntu distributions If you want to install the BPL system on your computer starting from the complete source code distribution you need SWI Prolog Also for compiling the source code in order to generate an executable state file you may need the following packages installed on your computer Red Hat Fedora distributions gmp devel ncurses devel readline devel Debian Ubuntu distributions libgmp3 dev libncurses5 dev libncursesw5 dev libreadline5 dev On the other hand if you want to install and run the executable distribution you do not need SWI Prolog and in order to run the executable state file you only may need the follo
18. wing packages installed on your computer Red Hat Fedora distributions gmp ncurses readline Debian Ubuntu distributions libgmp3c2 libncurses5 libncursesw5 libread lined The following installation procedure is only for the executable distribu tion Go into the directory where you want to download the executable distribu tion and download it Decompress the file bousi installer tgz by the command tar xzf bousi installer tgz Then a subdirectory called bousi installer is created containing the files of the executable distribution Go into the bousi installer directory launching the installation process by the command installer sh Then follow the installation instructions If you are an ordinary user and you choose the default installation option the executable file bousi and the shared library closure so are installed into the directory HOME bousi prolog If you are root the default directory where those files are installed is usr local bousi prolog Once the installation is ended you can start the BPL system via the com mand bousi WARNING If you try to launch the BPL system by double clicking the ex ecutable file bousi from a file browser window it might happen that the BPL system is not open but it remains resident in memory consuming a great amount of CPU resources Always it is preferable to launch the BPL system from a unix shell terminal by means
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