A non monotonic declarative approach for analyzing
discrete genetic regulation networks
(Integrative Post-Genomics , Lyon, 26-11-10)
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,
lab. TIMC-IMAG, Grenoble
25 novembre 2010
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
Declarative approach
A typical declarative approach for analyzing a Thomas network :
First step : Integrate as many constraints as possible
representing the structure and the dynamics of the network
(even hypothesis).
Second step : Automatic consistency testing of the set of
constraints. In case of inconsistency, automatic relaxation of a
minimal number of constraints.
Third step : Automatic prediction of all properties belonging to
a predened language.
Forth step : Removing (resp. adding) well-chosen constraints
(after examination of the preceding results and/or new
experiments)for a further analysis by returning to step 3 (resp.
2).
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
ASP (Answer Set Programming) for non monotonic
reasoning
The semantics of a set of ASP rules is based on a non
monotonic logic accepting stable models, particularly suited
to deal with the incomplete information problem.
A ASP rule has the following form :
a : −b1 , ..., b , not b +1 , ..., not b .
where a and b are atomic formulas. It means that a is inferred
if each of b1 , ..., b , can be proved and each of
b +1 , ..., not b is proved to be false or cannot be proved. If
any of b (with m + 1 ≤ i ≤ n) can be proved then a is not
m
m
n
i
m
m
n
i
inferred.
Stable models (answer sets) are minimal, i.e. no atomic
formula can be removed (as it is for the unique minimal model
of a set of Horn clauses, on which Prolog is based).
Then more properties can be deduced than in classical logic.
See Step 3 of the analysis method.
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
Advantages of ASP. Belief revision.
From :
ies (X ) : −bird (X ).
bird (tweety ).
one can prove ies (tweety ).
The problem is with penguins.
To take them into account in classical (monotonic) logic, one
has to modify the 1st axiom by introducing ¬penguin(x ) as a
premise and to qualify all birds (are they or not penguins ?).
With ASP, one avoids these manual revisions by using
defaults : unless the contrary is proved, a bird is not a
penguin. From :
ies (X ) : −bird (X ), not penguin(X ).
bird (tweety ).
one can prove ies (tweety ).
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
Advantages of ASP. Belief revision(cont.)
If later on, by addition of new knowledge (belief revision, e.g.
result of experiment), penguin(tweety ) can been proved then
ies (tweety ) is no more provable (non monotony).
Typically, in our case, an hypothesis A (like for example an
additivity constraint between interactions) could be
represented by a normal default :
A : − not − A .
meaning that A is true unless −A can be proved. −A is the
exact negation of A, i.e. verifying the integrity rule
: − − A ,A .
i
i
i
i
Then a para-logic approach for constraint relaxation can be
avoided. See Step 2 of the analysis method.
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
Advantage of ASP. Integrity constraints
By using integrity constraints like :
: − b1 , ..., b , not b
m
m
+1 , ..., not
b .
n
one can reject all models such that this premise is true.
It is a way for imposing universal CTL formulas (A-formulas)
describing dynamic behaviors. See Step 1 of the analysis
method
Example : all paths of length 3 beginning with state (0, 1)
must contain a state (X, Y) such that Y = 0 :
existpath(X 1, Y 1, X 2, Y 2, X 3, Y 3) : −
succ (X 1, Y 1, X 2, Y 2), succ (X 2, Y 2, X 3, Y 3).
We exclude models with a path such that all their states
following (0, 1) have Y dierent from 0 :
: −existpath(0, 1, X 2, Y 2, X 3, Y 3), Y 2! = 0, Y 3! = 0.
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
Advantages of ASP. Expression power and eciency.
Previously, for the sake of eciency, we used ordinary logic
programming (PROLOG) combined with a translation of some basic
(not all) constraints (like successor, observability and additivity
constraints) into CNF (clauses) to be submitted to SAT solvers.
ASP provides also a high-level language to express programs.
And potentially all needed constraints can be expressed at that
level.
Eciency of the ASP implementation that we use ( grounder
Gringo and solver Clasp, T. Schaub et al., Postdam U.) is
comparable to SAT ones.
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete
Perspectives
Mathematical modeling.
Introduction the notions of time (delay) and of spatiality.
Composition of models and of their properties. Design of
sophisticated property languages to suggest real experiments.
Computer implementation.
Coupling ASP with other solvers specic to global, continuous
or stochastic constraints.
Biological applications (carbon starvation response in E. coli ,
Drosophila Gap-gene system, mammalian iron regulation
system).
Fabien Corblin, Eric Fanchon, Nicolas Mobilia, Laurent Trilling,Alab.
nonTIMC-IMAG,
monotonic declarative
Grenoble approach for analyzing discrete