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< h2 class = "titleHead" > cplint Version beta2.0 Manual< / h2 >
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< div class = "author" > < span
class="cmr-12">Fabrizio Riguzzi< / span >
< br / > < span
class="cmr-12">fabrizio.riguzzi@unife.it< / span > < / div >
< br / >
< div class = "date" > < span
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class="cmr-12">June 19, 2008< / span > < / div >
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< / div >
< h3 class = "sectionHead" > < span class = "titlemark" > 1 < / span > < a
id="x1-10001">< / a > Introduction< / h3 >
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<!-- l. 30 --> < p class = "noindent" > < span
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class="cmtt-10">cplint < / span > is a suite of programs for reasoning with LPADs < span class = "cite" > [< a
href="#XVenVer03-TR">11< / a > ,  < a
href="#XVenVer04-ICLP04-IC">12< / a > ]< / span > and CP-logic
programs < span class = "cite" > [< a
href="#XVenDenBru-JELIA06">10< / a > ,  < a
href="#XCP-logic-unp">13< / a > ]< / span > .
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<!-- l. 32 --> < p class = "indent" > It consists of three Prolog modules for answering queries using goal-oriented
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procedures plus three Prolog modules for answering queries using the definition of the
semantics of LPADs and CP-logic.
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<!-- l. 36 --> < p class = "indent" > The modules for answering queries using using goal-oriented procedures are
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< span
class="cmtt-10">lpadsld.pl< / span > , < span
class="cmtt-10">lpad.pl < / span > and < span
class="cmtt-10">cpl.pl< / span > :
< ul class = "itemize1" >
< li class = "itemize" > < span
class="cmtt-10">lpadsld.pl< / span > : computes the probability of a query using the top-down
procedure described in in < span class = "cite" > [< a
href="#XRig-AIIA07-IC">7< / a > ]< / span > and < span class = "cite" > [< a
href="#XRig-RCRA07-IC">8< / a > ]< / span > . It is based on SLDNF resolution and
is an adaptation of the interpreter for ProbLog < span class = "cite" > [< a
href="#XDBLP:conf/ijcai/RaedtKT07">4< / a > ]< / span > .
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<!-- l. 42 --> < p class = "noindent" > It was proved correct < span class = "cite" > [< a
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href="#XRig-RCRA07-IC">8< / a > ]< / span > with respect to the semantics of LPADs for range
restricted acyclic programs < span class = "cite" > [< a
href="#XDBLP:journals/ngc/AptB91">1< / a > ]< / span > without function symbols.
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<!-- l. 44 --> < p class = "noindent" > It is also able to deal with extensions of LPADs and CP-logic: the clause
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bodies can contain < span
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class="cmtt-10">setof < / span > and < span
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class="cmtt-10">bagof< / span > , 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 < span
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class="cmtt-10">setof < / span > or < span
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class="cmtt-10">bagof < / span > operator.
These extended features have been introduced in order to represent
CLP(BN) < span class = "cite" > [< a
href="#XSanPagQaz03-UAI-IC">9< / a > ]< / span > programs and PRM models < span class = "cite" > [< a
href="#XGetoor+al:JMLR02">6< / a > ]< / span > : < span
class="cmtt-10">setof < / span > and < span
class="cmtt-10">bagof < / span > 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.
< / li >
< li class = "itemize" > < span
class="cmtt-10">lpad.pl< / span > : computes the probability of a query using a top-down procedure
based on SLG resolution < span class = "cite" > [< a
href="#XDBLP:journals/jacm/ChenW96">3< / a > ]< / span > . As a consequence, it works for any sound
LPADs, i.e., any LPAD such that each of its instances has a two valued
well founded model.
< / li >
< li class = "itemize" > < span
class="cmtt-10">cpl.pl< / span > : computes the probability of a query using a top-down procedure
based on SLG resolution and moreover checks that the CP-logic program
is valid, i.e., that it has at least an execution model.< / li > < / ul >
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<!-- l. 50 --> < p class = "indent" > The modules for answering queries using the definition of the semantics of LPADs
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and CP-logic are < span
class="cmtt-10">semlpadsld.pl< / span > , < span
class="cmtt-10">semlpad.pl < / span > and < span
class="cmtt-10">semcpl.pl< / span > :
< ul class = "itemize1" >
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< li class = "itemize" > < span
class="cmtt-10">semlpadsld.pl< / span > : given an LPAD < span
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class="cmmi-10">P< / span > , it generates all the instances of < span
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class="cmmi-10">P< / span > .
The probability of a query < span
class="cmmi-10">Q < / span > is computed by identifying all the instances
where < span
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class="cmmi-10">Q < / span > is derivable by SLDNF resolution.
< / li >
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< li class = "itemize" > < span
class="cmtt-10">semlpad.pl< / span > : given an LPAD < span
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class="cmmi-10">P< / span > , it generates all the instances of < span
class="cmmi-10">P< / span > . The
probability of a query < span
class="cmmi-10">Q < / span > is computed by identifying all the instances where
< span
class="cmmi-10">Q < / span > is derivable by SLG resolution.
< / li >
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< li class = "itemize" > < span
class="cmtt-10">semlcpl.pl< / span > : given an LPAD < span
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class="cmmi-10">P< / span > , it builds an execution model of < span
class="cmmi-10">P< / span > , i.e.,
a probabilistic process that satisfy the principles of universal causation,
sufficient causation, independent causation, no deus ex machina events
and temporal precedence. It uses the definition of the semantics given in
< span class = "cite" > [< a
href="#XCP-logic-unp">13< / a > ]< / span > .< / li > < / ul >
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<!-- l. 59 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 2 < / span > < a
id="x1-20002">< / a > Installation< / h3 >
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<!-- l. 60 --> < p class = "noindent" > < span
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class="cmtt-10">cplint < / span > is distributed in source code in the CVS version of Yap. It
includes Prolog and C files. Download it by following the instruction in < a
href="http://www.ncc.up.pt/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}vsc/Yap/downloads.html" >
http://www.ncc.up.pt/< span
class="cmsy-10">~< / span > vsc/Yap/downloads.html < / a > .
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<!-- l. 62 --> < p class = "indent" > < span
class="cmtt-10">cplint < / span > requires glu (a subpackage of vis) and glib-2.0. You can download glu
from < a
href="http://vlsi.colorado.edu/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}vis/getting_VIS_2.1.html" > http://vlsi.colorado.edu/< span
class="cmsy-10">~< / span > vis/getting_VIS_2.1.html < / a > You can download
glib-2.0 (version < span
class="cmsy-10">≥ < / span > 2< span
class="cmmi-10">.< / span > 0) from < a
href="http://www.gtk.org/" > http://www.gtk.org/ < / a > . This is a standard GNU package
so it is easy to install it using the package management software of your Linux or
Cygwin distribution.
<!-- l. 68 --> < p class = "indent" > Install glu:
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< ol class = "enumerate1" >
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< li class = "enumerate" > < a
id="x1-2002x1">< / a > downlad < span
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class="cmtt-10">glu-2.1.tar.gz< / span >
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< / li >
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< li class = "enumerate" > < a
id="x1-2004x2">< / a > decompress it
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< / li >
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< li class = "enumerate" > < a
id="x1-2006x3">< / a > < span
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class="cmtt-10">cd glu-2.1< / span >
< / li >
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< li class = "enumerate" > < a
id="x1-2008x4">< / a > < span
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class="cmtt-10">mkdir arch< / span >
< / li >
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< li class = "enumerate" > < a
id="x1-2010x5">< / a > < span
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class="cmtt-10">cd arch< / span >
< / li >
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< li class = "enumerate" > < a
id="x1-2012x6">< / a > < span
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class="cmtt-10">../configure< / span >
< / li >
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< li class = "enumerate" > < a
id="x1-2014x7">< / a > < span
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class="cmtt-10">make< / span >
< / li >
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< li class = "enumerate" > < a
id="x1-2016x8">< / a > < span
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class="cmtt-10">su< / span >
< / li >
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< li class = "enumerate" > < a
id="x1-2018x9">< / a > < span
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class="cmtt-10">make install< / span > < / li > < / ol >
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<!-- l. 80 --> < p class = "noindent" > This will install glu into < span
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class="cmtt-10">/usr/local< / span > , if you want to install to a different < span
class="cmtt-10">DIR < / span > use
< span
class="cmtt-10">../configure --prefix DIR< / span >
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<!-- l. 83 --> < p class = "indent" > Install Yap together with < span
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class="cmtt-10">cplint< / span > : when compiling Yap following the instuction of
the < span
class="cmtt-10">INSTALL < / span > file in the root of the Yap folder, use
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
configure  --enable-cplint
< / div >
< / td > < / tr > < / table >
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<!-- l. 87 --> < p class = "nopar" > Under Windows, you have to use Cygwin (glu does not compile under MinGW),
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so
< br class = "newline" / >
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
configure  --enable-cplint  --enable-cygwin
< / div >
< / td > < / tr > < / table >
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<!-- l. 91 --> < p class = "nopar" > If you installed glu in < span
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class="cmtt-10">DIR< / span > , use < span
class="cmtt-10">--enable-cplint=DIR< / span >
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<!-- l. 94 --> < p class = "indent" > After having performed < span
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class="cmtt-10">make install < / span > you can do < span
class="cmtt-10">make installcheck < / span > that will
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execute a suite of tests of the various programs. If no error is reported you have a
working installation of < span
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class="cmtt-10">cplint< / span > .
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<!-- l. 97 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 3 < / span > < a
id="x1-30003">< / a > Syntax< / h3 >
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<!-- l. 99 --> < p class = "noindent" > Disjunction in the head is represented with a semicolon and atoms in the head are
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separated from probabilities by a colon. For the rest, the usual syntax of Prolog is
used. For example, the CP-logic clause
< center class = "math-display" >
< img
src="manual0x.png" alt="h1 : p1 ∨ ...∨ hn : pn ← b1,...,bm,<2C> c1,...,<2C> cl " class="math-display" >< / center > is
represented by
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
h1:p1  ;  ...  ;  hn:pn  :-  b1,...,bm,\+  c1,....,\+  cl
< / div >
< / td > < / tr > < / table >
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<!-- l. 105 --> < p class = "nopar" > No parentheses are necessary. The < span
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class="cmtt-10">pi < / span > 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.
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<!-- l. 108 --> < p class = "indent" > If the clause has an empty body, it can be represented like this
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
h1:p1  ;  ...  ;hn:pn.
< / div >
< / td > < / tr > < / table >
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<!-- l. 111 --> < p class = "nopar" > If the clause has a single head with probability 1, the annotation can be omitted and
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the clause takes the form of a normal prolog clause, i.e.
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
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h1:-  b1,...,bm,\+  c1,...,\+  cl.
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< / div >
< / td > < / tr > < / table >
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<!-- l. 115 --> < p class = "nopar" > stands for
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
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h1:1  :-  b1,...,bm,\+  c1,...,\+  cl.
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< / div >
< / td > < / tr > < / table >
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<!-- l. 119 --> < p class = "nopar" >
<!-- l. 121 --> < p class = "indent" > The coin example of < span class = "cite" > [< a
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href="#XVenVer04-ICLP04-IC">12< / a > ]< / span > is represented as (see file < span
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class="cmtt-10">coin.cpl< / span > )
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
heads(Coin):1/2  ;  tails(Coin):1/2:-
  < br / >           toss(Coin),\+biased(Coin).
  < br / >
  < br / > heads(Coin):0.6  ;  tails(Coin):0.4:-
  < br / >           toss(Coin),biased(Coin).
  < br / >
  < br / > fair(Coin):0.9  ;  biased(Coin):0.1.
  < br / >
  < br / > toss(coin).
< / div >
< / td > < / tr > < / table >
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<!-- l. 132 --> < p class = "nopar" > The first clause states that if we toss a coin that is not biased it has equal
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probability of landing heads and tails. The second states that if the coin is biased it
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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.
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<!-- l. 137 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 4 < / span > < a
id="x1-40004">< / a > Commands< / h3 >
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<!-- l. 138 --> < p class = "noindent" > All six modules accept the same commands for reading in files and answering queries.
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The LPAD or CP-logic program must be stored in a text file with extension < span
class="cmtt-10">.cpl< / span > .
Suppose you have stored the example above in file < span
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class="cmtt-10">coin.cpl< / span > . In order to answer
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queries from this program, you have to run Yap, load one of the modules (such as for
example < span
class="cmtt-10">lpad.pl< / span > ) by issuing the command
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
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use_module(library(lpad)).
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< / div >
< / td > < / tr > < / table >
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<!-- l. 144 --> < p class = "nopar" > at the command prompt. Then you must parse the source file < span
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class="cmtt-10">coin.cpl < / span > with the
command
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
p(coin).
< / div >
< / td > < / tr > < / table >
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<!-- l. 149 --> < p class = "nopar" > if < span
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class="cmtt-10">coin.cpl < / span > is in the current directory, or
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
p(’ path_to_coin/coin’ ).
< / div >
< / td > < / tr > < / table >
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<!-- l. 153 --> < p class = "nopar" > if < span
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class="cmtt-10">coin.cpl < / span > is in a different directory. At this point you can pose query to the
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program by using the predicate < span
class="cmtt-10">s/2 < / span > (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
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< span
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class="cmtt-10">head(coin),biased(coin) < / span > can be asked with the query
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
s([head(coin),biased(coin)],P).
< / div >
< / td > < / tr > < / table >
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<!-- l. 158 --> < p class = "nopar" > For computing the probability of a conjunction given another conjunction you can
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use the predicate < span
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class="cmtt-10">sc/3 < / span > (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 < span
class="cmtt-10">heads(coin) < / span > given the evidence < span
class="cmtt-10">biased(coin) < / span > can be asked with the
query
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
sc([heads(coin)],[biased(coin)],P).
< / div >
< / td > < / tr > < / table >
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<!-- l. 163 --> < p class = "nopar" > After having parsed a program, in order to read in a new program you must restart
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Yap when using < span
class="cmtt-10">semlpadsld.pl < / span > and < span
class="cmtt-10">semlpad.pl< / span > . With the other modules, you can
directly parse a new program.
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<!-- l. 167 --> < p class = "indent" > When using < span
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class="cmtt-10">lpad.pl< / span > , 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.
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<!-- l. 169 --> < p class = "indent" > When using < span
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class="cmtt-10">semcpl.pl< / span > , you can print the execution process by using the
command < span
class="cmtt-10">print. < / span > after < span
class="cmtt-10">p(file). < / span > Moreover, you can build an execution
process given a context by issuing the command < span
class="cmtt-10">parse(file)< / span > . and then
< span
class="cmtt-10">build(context). < / span > where < span
class="cmtt-10">context < / span > is a list of atoms that are true in the context.
< span
class="cmtt-10">semcpl.pl < / span > can print “ Invalid program” in the case in which no execution process
exists.
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<!-- l. 174 --> < p class = "indent" > When using < span
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class="cmtt-10">cpl.pl < / span > you can print a partial execution model including all the
clauses involved in the query issued with < span
class="cmtt-10">print. cpl.pl < / span > can print the messages
“ Uunsound program” , “ It requires the choice of a head atom from a non ground
head” and “ Invalid program” .
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<!-- l. 177 --> < p class = "indent" > The modules make use of a number of parameters in order to control their
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behavior. They that can be set with the command
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
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set(parameter,value).
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< / div >
< / td > < / tr > < / table >
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<!-- l. 180 --> < p class = "nopar" > from the Yap prompt after having loaded the module. The current value can be read
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with
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
setting(parameter,Value).
< / div >
< / td > < / tr > < / table >
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<!-- l. 185 --> < p class = "nopar" > from the Yap prompt. The available parameters are:
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< ul class = "itemize1" >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">epsilon_parsing< / span > < / span > < / span > (valid for all six modules): if (1 - the sum of the
probabilities of all the head atoms) is smaller than < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">epsilon_parsing< / span > < / span > < / span > then
< span
class="cmtt-10">cplint < / span > adds the null events to the head. Default value 0.00001
< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">save_dot< / span > < / span > < / span > (valid for all goal-oriented modules): if < span
class="cmtt-10">true < / span > a graph representing the
BDD is saved in the file < span
class="cmtt-10">cpl.dot < / span > in the current directory in dot format. The
variables names are of the form < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">Xn_m< / span > < / span > < / span > where < span
class="cmtt-10">n < / span > is the number of the multivalued
variable and < span
class="cmtt-10">m < / span > is the number of the binary variable. The correspondence
between variables and clauses can be evinced from the message printed on the
screen, such as
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
Variables:  [(2,[X=2,X1=1]),(2,[X=1,X1=0]),(1,[])]
< / div >
< / td > < / tr > < / table >
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<!-- l. 199 --> < p class = "nopar" > where the first element of each couple is the clause number of the input file
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(starting from 1). In the example above variable < span
class="cmtt-10">X0 < / span > corresponds to clause < span
class="cmtt-10">2< / span >
with the substitutions < span
class="cmtt-10">X=2,X1=1< / span > , variable < span
class="cmtt-10">X1 < / span > corresponds to clause < span
class="cmtt-10">2 < / span > with the
substitutions < span
class="cmtt-10">X=1,X1=0 < / span > and variable < span
class="cmtt-10">X2 < / span > corresponds to clause < span
class="cmtt-10">1 < / span > with the empty
substitution. You can view the graph with < span
class="cmtt-10">graphviz < / span > (< a
href="www.graphviz.org" > www.graphviz.org < / a > )
using the command
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
dotty  cpl.dot  &
< / div >
< / td > < / tr > < / table >
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<!-- l. 208 --> < p class = "nopar" >
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< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">ground_body< / span > < / span > < / span > (valid for < span
class="cmtt-10">lpadsld.pl < / span > and all semantic modules): determines how
non ground clauses are treated: if < span
class="cmtt-10">true< / span > , ground clauses are obtained from a non
ground clause by replacing each variable with a constant, if < span
class="cmtt-10">false< / span > , ground
clauses are obtained by replacing only variables in the head with a
constant. In the case where the body contains variables not in the
head, setting it to false means that the body represents an existential
event.< / li > < / ul >
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<!-- l. 212 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 5 < / span > < a
id="x1-50005">< / a > Semantic Modules< / h3 >
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<!-- l. 213 --> < p class = "noindent" > The three semantic modules need to produce a grounding of the program in order to
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compute the semantics. They require an extra file with extension < span
class="cmtt-10">.uni < / span > (for universe)
in the same directory where the < span
class="cmtt-10">.cpl < / span > file is.
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<!-- l. 216 --> < p class = "indent" > There are two ways to specify how to ground a program. The first consists in
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providing the list of constants to which each variable can be instantiated. For
example, in our case the current directory will contain a file < span
class="cmtt-10">coin.uni < / span > that is a
Prolog file containing facts of the form
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
universe(var_list,const_list).
< / div >
< / td > < / tr > < / table >
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<!-- l. 219 --> < p class = "nopar" > where < span class = "obeylines-h" > < span class = "verb" > < span
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class="cmtt-10">var_list< / span > < / span > < / span > is a list of variables names (each must be included in single quotes)
and < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">const_list< / span > < / span > < / span > is a list of constants. The semantic modules generate the grounding
by instantiating in all possible ways the variables of < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">var_list< / span > < / span > < / span > with the constants of
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">const_list< / span > < / span > < / span > . Note that the variables are identified by name, so a variable with
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the same name in two different clauses will be instantiated with the same
constants.
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<!-- l. 222 --> < p class = "indent" > The other way to specify how to ground a program consists in using mode and
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type information. For each predicate, the file < span
class="cmtt-10">.uni < / span > must contain a fact of the
form
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
mode(predicate(t1,...,tn)).
< / div >
< / td > < / tr > < / table >
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<!-- l. 225 --> < p class = "nopar" > that specifies the number and types of each argument of the predicate. Then, the list
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of constants that are in the domain of each type < span
class="cmtt-10">ti < / span > must be specified with a fact of
the form
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
type(ti,list_of_constants).
< / div >
< / td > < / tr > < / table >
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<!-- l. 230 --> < p class = "nopar" > The file < span
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class="cmtt-10">.uni < / span > can contain both universe and mode declaration, the ones to be used
depend on the value of the parameter < span
class="cmtt-10">grounding< / span > : with value < span
class="cmtt-10">variables< / span > , the
universe declarations are used, with value < span
class="cmtt-10">modes < / span > the mode declarations are
used.
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<!-- l. 233 --> < p class = "indent" > With < span
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class="cmtt-10">semcpl.pl < / span > only mode declarations can be used.
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<!-- l. 237 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 6 < / span > < a
id="x1-60006">< / a > Extensions< / h3 >
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<!-- l. 238 --> < p class = "noindent" > In this section we will present the extensions to the syntax of LPADs and CP-logic
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programs that < span
class="cmtt-10">cplint < / span > can handle.
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<!-- l. 240 --> < p class = "indent" > The first is the use of some standard Prolog predicates. The bodies can contain
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the built-in predicates:
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
is/2
  < br / > > /2
  < br / > < /2
  < br / > > =/2
  < br / > =< /2
  < br / > =:=/2
  < br / > =\=/2
  < br / > true/0
  < br / > false/0
  < br / > =/2
  < br / > ==/2
  < br / > \=/2
  < br / > \==/2
  < br / > length/2
< / div >
< / td > < / tr > < / table >
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<!-- l. 257 --> < p class = "nopar" > The bodies can also contain the following library predicates:
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
member/2
  < br / > max_list/2
  < br / > min_list/2
  < br / > nth0/3
  < br / > nth/3
< / div >
< / td > < / tr > < / table >
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<!-- l. 266 --> < p class = "nopar" > plus the predicate
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
average/2
< / div >
< / td > < / tr > < / table >
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<!-- l. 270 --> < p class = "nopar" > that, given a list of numbers, computes its arithmetic mean.
<!-- l. 273 --> < p class = "indent" > When using < span
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class="cmtt-10">lpadsld.pl< / span > , the bodies can contain the predicates < span
class="cmtt-10">setof/3 < / span > and
< span
class="cmtt-10">bagof/3 < / span > with the same meaning as in Prolog. Existential quantifiers are allowed in
both, so for example the query
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
setof(Z,  (term(X,Y))^foo(X,Y,Z),  L).
< / div >
< / td > < / tr > < / table >
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<!-- l. 276 --> < p class = "nopar" > returns all the instantiations of < span
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class="cmtt-10">Z < / span > such that there exists an instantiation of < span
class="cmtt-10">X < / span > and < span
class="cmtt-10">Y< / span >
for which < span
class="cmtt-10">foo(X,Y,Z) < / span > is true.
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<!-- l. 279 --> < p class = "indent" > An example of the use of < span
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class="cmtt-10">setof < / span > and < span
class="cmtt-10">bagof < / span > is in the file < span
class="cmtt-10">female.cpl< / span > :
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
male(C):M/P  ;  female(C):F/P:-
  < br / >         person(C),
  < br / >         setof(Male,known_male(Male),LM),
  < br / >         length(LM,M),
  < br / >         setof(Female,known_female(Female),LF),
  < br / >         length(LF,F),
  < br / >         P  is  F+M.
  < br / >
  < br / > person(f).
  < br / >
  < br / > known_female(a).
  < br / >
  < br / > known_female(b).
  < br / >
  < br / > known_female(c).
  < br / >
  < br / > known_male(d).
  < br / >
  < br / > known_male(e).
< / div >
< / td > < / tr > < / table >
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<!-- l. 300 --> < p class = "nopar" > The disjunctive rule expresses the probability of a person of unknown sex of being
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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 < span
class="cmtt-10">P < / span > is 0).
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<!-- l. 304 --> < p class = "indent" > Another use of < span
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class="cmtt-10">setof < / span > and < span
class="cmtt-10">bagof < / span > is to have an attribute depend on an
aggregate function of another attribute, similarly to what is done in PRM and
CLP(BN).
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<!-- l. 306 --> < p class = "indent" > So, in the classical school example (available in < span
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class="cmtt-10">student.cpl< / span > ) you can find the
following clauses:
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
student_rank(S,h):0.6  ;  student_rank(S,l):0.4:-
  < br / >         bagof(G,R^(registr_stu(R,S),registr_gr(R,G)),L),
  < br / >         average(L,Av),Av> 1.5.
  < br / >
  < br / > student_rank(S,h):0.4  ;  student_rank(S,l):0.6:-
  < br / >         bagof(G,R^(registr_stu(R,S),registr_gr(R,G)),L),
  < br / >         average(L,Av),Av  =<   1.5.
< / div >
< / td > < / tr > < / table >
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<!-- l. 316 --> < p class = "nopar" > where < span class = "obeylines-h" > < span class = "verb" > < span
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class="cmtt-10">registr_stu(R,S)< / span > < / span > < / span > expresses that registration < span
class="cmtt-10">R < / span > refers to student < span
class="cmtt-10">S < / span > and
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">registr_gr(R,G)< / span > < / span > < / span > expresses that registration < span
class="cmtt-10">R < / span > reports grade < span
class="cmtt-10">G < / span > which is a natural
number. The two clauses express a dependency of the rank of the student from the
average of her grades.
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<!-- l. 319 --> < p class = "indent" > Another extension can be used with < span
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class="cmtt-10">lpadsld.pl < / span > 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
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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
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">paper_ref_simple.cpl< / span > < / span > < / span > ):
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
uniform(cites_cited(C,P),P,L):-
  < br / >         bagof(Pap,paper_topic(Pap,theory),L).
  < br / >
  < br / > uniform(cites_citing(C,P),P,L):-
  < br / >         bagof(Pap,paper_topic(Pap,ai),L).
< / div >
< / td > < / tr > < / table >
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<!-- l. 326 --> < p class = "nopar" > The first clauses states that the paper < span
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class="cmtt-10">P < / span > cited in a citation < span
class="cmtt-10">C < / span > 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.
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<!-- l. 331 --> < p class = "indent" > These clauses make use of the predicate
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< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
uniform(Atom,Variable,List)
< / div >
< / td > < / tr > < / table >
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<!-- l. 334 --> < p class = "nopar" > in the head, where < span
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class="cmtt-10">Atom < / span > must contain < span
class="cmtt-10">Variable< / span > . The meaning is the following:
the set of all the atoms obtained by instantiating < span
class="cmtt-10">Variable < / span > of < span
class="cmtt-10">Atom < / span > with a
term taken from < span
class="cmtt-10">List < / span > is generated and the head is obtained by having a
disjunct for each instantiation with probability 1< span
class="cmmi-10">∕ N < / span > where < span
class="cmmi-10">N < / span > is the length of
< span
class="cmtt-10">List< / span > .
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<!-- l. 338 --> < p class = "indent" > A more elaborate example is present in file < span class = "obeylines-h" > < span class = "verb" > < span
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class="cmtt-10">paper_ref.cpl< / span > < / span > < / span > :
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
uniform(cites_citing(C,P),P,L):-
  < br / >         setof(Pap,paper(Pap),L).
  < br / >
  < br / > cites_cited_group(C,theory):0.9  ;  cites_cited_group(C,ai):0.1:-
  < br / >         cites_citing(C,P),paper_topic(P,theory).
  < br / >
  < br / > cites_cited_group(C,theory):0.01;cites_cited_group(C,ai):0.99:-
  < br / >         cites_citing(C,P),paper_topic(P,ai).
  < br / >
  < br / > uniform(cites_cited(C,P),P,L):-
  < br / >         cites_cited_group(C,T),bagof(Pap,paper_topic(Pap,T),L).
< / div >
< / td > < / tr > < / table >
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<!-- l. 351 --> < p class = "nopar" > where the cited paper depends on the topic of the citing paper. In particular, if the
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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.
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<!-- l. 354 --> < p class = "indent" > PRMs take into account as well existence uncertainty, where the existence of
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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:
< table
class="verbatim">< tr class = "verbatim" > < td
class="verbatim">< div class = "verbatim" >
cites(X,Y):0.005  :-
  < br / >         paper_topic(X,theory),paper_topic(Y,theory).
  < br / >
  < br / > cites(X,Y):0.001  :-
  < br / >         paper_topic(X,theory),paper_topic(Y,ai).
  < br / >
  < br / > cites(X,Y):0.003  :-
  < br / >         paper_topic(X,ai),paper_topic(Y,theory).
  < br / >
  < br / > cites(X,Y):0.008  :-
  < br / >         paper_topic(X,ai),paper_topic(Y,ai).
< / div >
< / td > < / tr > < / table >
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<!-- l. 367 --> < p class = "nopar" > This is an example where the probabilities in the head do not sum up to one so the
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null event is automatically added to the head. The first clause states that, if the topic
of a paper < span
class="cmtt-10">X < / span > is theory and of paper < span
class="cmtt-10">Y < / span > is theory, there is a probability of 0.005 that
there is a citation from < span
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class="cmtt-10">X < / span > to < span
class="cmtt-10">Y< / span > . The other clauses consider the remaining cases for the
topics.
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<!-- l. 372 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 7 < / span > < a
id="x1-70007">< / a > Additional Files< / h3 >
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<!-- l. 373 --> < p class = "noindent" > In the directory where Yap keeps the library files (usually < span
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class="cmtt-10">/usr/local/share/ Yap< / span > )
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you can find the directory < span
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class="cmtt-10">cplint < / span > that contains the files:
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< ul class = "itemize1" >
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< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">testlpadsld_gbtrue.pl,< / span > < span
class="cmtt-10">  testlpadsld_gbfalse.pl,< / span > < span
class="cmtt-10">  testlpad.pl,< / span > < / span > < / span >
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">testcpl.pl,< / span > < span
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class="cmtt-10">  testsemlpadsld.pl,< / span > < span
class="cmtt-10">  testsemlpad.pl< / span > < span
class="cmtt-10">  testsemcpl.pl< / span > < / span > < / span > :
Prolog programs for testing the modules. They are executed when issuing
the command < span
class="cmtt-10">make installcheck < / span > during the installation. To execute
them afterwords, load the file and issue the command < span
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class="cmtt-10">t.< / span >
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< / li >
< li class = "itemize" > Subdirectory < span
class="cmtt-10">examples< / span > :
< ul class = "itemize2" >
< li class = "itemize" > < span
class="cmtt-10">alarm.cpl< / span > : representation of the Bayesian network in Figure 2 of
< span class = "cite" > [< a
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href="#XVenVer04-ICLP04-IC">12< / a > ]< / span > .
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< / li >
< li class = "itemize" > < span
class="cmtt-10">coin.cpl< / span > : coin example from < span class = "cite" > [< a
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href="#XVenVer04-ICLP04-IC">12< / a > ]< / span > .
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< / li >
< li class = "itemize" > < span
class="cmtt-10">coin2.cpl< / span > : coin example with two coins.
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< / li >
< li class = "itemize" > < span
class="cmtt-10">dice.cpl< / span > : dice example from < span class = "cite" > [< a
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href="#XVenVer04-ICLP04-IC">12< / a > ]< / span > .
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< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
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class="cmtt-10">twosideddice.cpl,< / span > < span
class="cmtt-10">  threesideddice.cpl< / span > < / span > < / span > game with idealized dice
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with two or three sides. Used in the experiments in < span class = "cite" > [< a
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href="#XRig-RCRA07-IC">8< / a > ]< / span > .
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< / li >
< li class = "itemize" > < span
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class="cmtt-10">ex.cpl< / span > : first example in < span class = "cite" > [< a
href="#XRig-RCRA07-IC">8< / a > ]< / span > .
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< / li >
< li class = "itemize" > < span
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class="cmtt-10">exapprox.cpl< / span > : example showing the problems of approximate
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inference (see < span class = "cite" > [< a
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href="#XRig-RCRA07-IC">8< / a > ]< / span > ).
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< / li >
< li class = "itemize" > < span
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class="cmtt-10">exrange.cpl< / span > : example showing the problems with non range
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restricted programs (see < span class = "cite" > [< a
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href="#XRig-RCRA07-IC">8< / a > ]< / span > ).
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< / li >
< li class = "itemize" > < span
class="cmtt-10">female.cpl< / span > : example showing the dependence of probabilities in the
head from variables in the body (from < span class = "cite" > [< a
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href="#XVenVer04-ICLP04-IC">12< / a > ]< / span > ).
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< / li >
< li class = "itemize" > < span
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class="cmtt-10">mendel.cpl, mendels.cpl< / span > : programs describing the Mendelian
rules of inheritance, taken from < span class = "cite" > [< a
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href="#XBlo04-ILP04WIP-IC">2< / a > ]< / span > .
< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
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class="cmtt-10">paper_ref.cpl,< / span > < span
class="cmtt-10">  paper_ref_simple.cpl< / span > < / span > < / span > : paper citations examples,
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showing reference uncertainty, inspired by < span class = "cite" > [< a
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href="#XGetoor+al:JMLR02">6< / a > ]< / span > .
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< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">paper_ref_not.cpl< / span > < / span > < / span > : paper citations example showing that negation
can be used also for predicates defined by clauses with < span
class="cmtt-10">uniform < / span > in
the head.
< / li >
< li class = "itemize" > < span
class="cmtt-10">school.cpl< / span > : example inspired by the example < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">school_32.yap< / span > < / span > < / span > from
the source distribution of Yap in the < span
class="cmtt-10">CLPBN < / span > directory.
< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">school_simple.cpl< / span > < / span > < / span > : simplified version of < span
class="cmtt-10">school.cpl< / span > .
< / li >
< li class = "itemize" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-10">student.cpl< / span > < / span > < / span > : student example from Figure 1.3 of < span class = "cite" > [< a
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href="#XGetFri01-BC">5< / a > ]< / span > .
< / li >
< li class = "itemize" > < span
class="cmtt-10">win.cpl, light.cpl, trigger.cpl, throws.cpl, hiv.cpl,< / span >
< br class = "newline" / > < span
class="cmtt-10">invalid.cpl< / span > : programs taken from < span class = "cite" > [< a
href="#XCP-logic-unp">13< / a > ]< / span > . < span
class="cmtt-10">invalid.cpl < / span > is an example
of a program that is invalid but sound.< / li > < / ul >
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<!-- l. 398 --> < p class = "noindent" > The files < span
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class="cmtt-10">*.uni < / span > 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.
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< / li >
< li class = "itemize" > Subdirectory < span
class="cmtt-10">doc< / span > : contains this manual in latex, html and pdf.< / li > < / ul >
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<!-- l. 401 --> < p class = "noindent" >
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< h3 class = "sectionHead" > < span class = "titlemark" > 8 < / span > < a
id="x1-80008">< / a > License< / h3 >
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<!-- l. 406 --> < p class = "noindent" > < span
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class="cmtt-10">cplint< / span > , as Yap, follows the Artistic License 2.0 that you can find in Yap CVS root
dir. The copyright is by Fabrizio Riguzzi.
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<!-- l. 411 --> < p class = "indent" > The program uses the library < a
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href="http://vlsi.colorado.edu/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}fabio/" > CUDD < / a > for manipulating BDDs that is included in
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glu. For the use of CUDD, the following license must be accepted:
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<!-- l. 416 --> < p class = "indent" > Copyright (c) 1995-2004, Regents of the University of Colorado
<!-- l. 418 --> < p class = "indent" > All rights reserved.
<!-- l. 420 --> < p class = "indent" > Redistribution and use in source and binary forms, with or without modification,
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are permitted provided that the following conditions are met:
< ul class = "itemize1" >
< li class = "itemize" > Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
< / li >
< li class = "itemize" > Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
< / li >
< li class = "itemize" > Neither the name of the University of Colorado nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.< / li > < / ul >
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<!-- l. 437 --> < p class = "noindent" > THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS
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< br class = "newline" / > 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
< br class = "newline" / > 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.
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<!-- l. 451 --> < p class = "indent" > < span
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class="cmtt-10">lpad.pl< / span > , < span
class="cmtt-10">semlpad.pl < / span > and < span
class="cmtt-10">cpl.pl < / span > are based on the SLG system by < a
href="http://engr.smu.edu/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}wchen/" > Weidong
Chen < / a > and < a
href="http://www.cs.sunysb.edu/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}warren/" > David Scott Warren < / a > , Copyright (C) 1993 Southern Methodist University,
1993 SUNY at Stony Brook, see the file COYPRIGHT_SLG for detailed information
on this copyright.
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<!-- l. 1 --> < p class = "noindent" >
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< h3 class = "likesectionHead" > < a
id="x1-90008">< / a > References< / h3 >
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<!-- l. 1 --> < p class = "noindent" >
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< div class = "thebibliography" >
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< p class = "bibitem" > < span class = "biblabel" >
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[1]< span class = "bibsp" >       < / span > < / span > < a
id="XDBLP:journals/ngc/AptB91">< / a > K.  R. Apt and M.  Bezem. Acyclic programs. < span
class="cmti-10">New Generation< / span >
< span
class="cmti-10">Comput.< / span > , 9(3/4):335– 364, 1991.
< / p >
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< p class = "bibitem" > < span class = "biblabel" >
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[2]< span class = "bibsp" >       < / span > < / span > < a
id="XBlo04-ILP04WIP-IC">< / a > H.  Blockeel. Probabilistic logical models for mendel’ s experiments: An
exercise. In < span
class="cmti-10">Inductive Logic Programming (ILP 2004), Work in Progress< / span >
< span
class="cmti-10">Track< / span > , 2004.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[3]< span class = "bibsp" >       < / span > < / span > < a
2007-11-15 12:35:29 +00:00
id="XDBLP:journals/jacm/ChenW96">< / a > Weidong Chen and David  Scott Warren. Tabled evaluation with
delaying for general logic programs. < span
class="cmti-10">J. ACM< / span > , 43(1):20– 74, 1996.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[4]< span class = "bibsp" >       < / span > < / span > < a
2007-11-08 12:47:24 +00:00
id="XDBLP:conf/ijcai/RaedtKT07">< / a > L.  De  Raedt, A.  Kimmig, and H.  Toivonen. Problog: A probabilistic
prolog and its application in link discovery. In < span
class="cmti-10">Proceedings of the 20th< / span >
< span
class="cmti-10">International Joint Conference on Artificial Intelligence< / span > , pages 2462– 2467,
2007.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[5]< span class = "bibsp" >       < / span > < / span > < a
2007-11-08 12:47:24 +00:00
id="XGetFri01-BC">< / a > L.  Getoor, N.  Friedman, D.  Koller, and A.  Pfeffer. Learning
probabilistic relational models. In Saso Dzeroski and Nada Lavrac, editors,
< span
class="cmti-10">Relational Data Mining< / span > . Springer-Verlag, Berlin, 2001.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[6]< span class = "bibsp" >       < / span > < / span > < a
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id="XGetoor+al:JMLR02">< / a > L.  Getoor, N.  Friedman, D.  Koller, and B.  Taskar. Learning
probabilistic models of relational structure. < span
class="cmti-10">Journal of Machine Learning< / span >
< span
class="cmti-10">Research< / span > , 3:679– 707, December 2002.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[7]< span class = "bibsp" >       < / span > < / span > < a
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id="XRig-AIIA07-IC">< / a > Fabrizio Riguzzi. A top down interpreter for lpad and cp-logic. In
< span
class="cmti-10">10th Congress of the Italian Association for Artificial Intelligence< / span > . Springer,
2007.
< a
href="http://www.ing.unife.it/docenti/FabrizioRiguzzi/Papers/Rig-AIIA07.pdf" > http://www.ing.unife.it/docenti/FabrizioRiguzzi/Papers/Rig-AIIA07.pdf
< / a > .
2007-11-15 12:35:29 +00:00
2007-11-08 12:47:24 +00:00
< / p >
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< p class = "bibitem" > < span class = "biblabel" >
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[8]< span class = "bibsp" >       < / span > < / span > < a
2007-11-08 12:47:24 +00:00
id="XRig-RCRA07-IC">< / a > Fabrizio Riguzzi. A top down interpreter for lpad and
cp-logic. In < span
class="cmti-10">The 14th RCRA workshop Experimental Evaluation of< / span >
< span
class="cmti-10">Algorithms for Solving Problems with Combinatorial Explosion< / span > , 2007. < a
href="http://pst.istc.cnr.it/RCRA07/articoli/P19-riguzzi-RCRA07.pdf" >
http://pst.istc.cnr.it/RCRA07/articoli/P19-riguzzi-RCRA07.pdf < / a > .
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[9]< span class = "bibsp" >       < / span > < / span > < a
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id="XSanPagQaz03-UAI-IC">< / a > V.  Santos  Costa, D.  Page, M.  Qazi, and J.  Cussens. CLP(BN):
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Constraint logic programming for probabilistic knowledge. In < span
class="cmti-10">Uncertainty< / span >
< span
class="cmti-10">in Artificial Intelligence (UAI 2003)< / span > , 2003.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[10]< span class = "bibsp" >       < / span > < / span > < a
2007-11-08 12:47:24 +00:00
id="XVenDenBru-JELIA06">< / a > J.  Vennekens, M.  Denecker, and M.  Bruynooghe. Representing causal
information about a probabilistic process. In < span
class="cmti-10">10th European Conference on< / span >
< span
class="cmti-10">Logics in Artificial Intelligence, JELIA 2006< / span > , LNAI. Springer, September
2006.
< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
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[11]< span class = "bibsp" >       < / span > < / span > < a
2007-11-08 12:47:24 +00:00
id="XVenVer03-TR">< / a > J.  Vennekens and S.  Verbaeten. Logic programs with annotated
disjunctions. Technical Report CW386, K. U. Leuven, 2003. < a
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href="http://www.cs.kuleuven.ac.be/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}joost/techrep.ps" >
http://www.cs.kuleuven.ac.be/< span
class="cmsy-10">~< / span > joost/techrep.ps < / a > .
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< / p >
2008-06-19 21:28:33 +00:00
< p class = "bibitem" > < span class = "biblabel" >
2007-11-15 12:35:29 +00:00
[12]< span class = "bibsp" >       < / span > < / span > < a
id="XVenVer04-ICLP04-IC">< / a > J.  Vennekens, S.  Verbaeten, and M.  Bruynooghe. Logic programs with
annotated disjunctions. In < span
class="cmti-10">The 20th International Conference on Logic< / span >
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< span
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class="cmti-10">Programming (ICLP 2004)< / span > , 2004. < a
href="http://www.cs.kuleuven.ac.be/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}joost/" > http://www.cs.kuleuven.ac.be/< span
class="cmsy-10">~< / span > joost/
< / a > .
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< / p >
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< p class = "bibitem" > < span class = "biblabel" >
2007-11-15 12:35:29 +00:00
[13]< span class = "bibsp" >       < / span > < / span > < a
2007-11-08 12:47:24 +00:00
id="XCP-logic-unp">< / a > Joost Vennekens, Marc Denecker, and Maurice Bruynooge. Extending
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the role of causality in
probabilistic modeling. < a
href="http://www.cs.kuleuven.ac.be/\protect \unhbox \voidb@x \penalty \@M \relax \unhbox \voidb@x \special {t4ht@+& {35}x00A0{59}}x{}joost/cplogic.pdf" > http://www.cs.kuleuven.ac.be/< span
class="cmsy-10">~< / span > joost/cplogic.pdf
< / a > , 2006.
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< / p >
< / div >
< / body > < / html >
