In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

We develop a new semantics for defeasible infer­ ence based on extended probability measures al­ lowed to take infinitesimal values, on the inter­ pretation of defaults as generalized conditional probability constraints and on a preferred-model implementation of entropy-maximization.
Defaults and lnfinitesimals Defeasible Inference by Nonarchimedean Entropy Maximization

The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural networks describing the associative dependency of variables. These networks have a proba­ bility distribution, which is a special case of the distribution generated by proba­ bilistic inference networks. Hence both types of networks can be combined al­ lowing to integrate probabilistic rules as well as unspecified associations in a sound way. The resulting network may have a number of interesting features including cycles of probabilistic rules, hidden 'un­ observable' variables, and uncertain and contradictory evidence.
Integrating Probabilistic Rules into Neural Networks: A Stochastic EM Learning Algorithm

Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for soft-constraint optimization problems in which the soft constraints are mostly satisfied. Unsatisfiable-core approaches to solving soft constraint problems in SAT (e.g. MAXSAT) force all soft constraints to be hard initially. When solving fails they return an unsatisfiable core, as a set of soft constraints that cannot hold simultaneously. These are reverted to soft and solving continues. Since lazy clause generation solvers can also return unsatisfiable cores we can adapt this approach to constraint programming. We adapt the original MAXSAT unsatisfiable core solving approach to be usable for constraint programming and define a number of extensions. Experimental results show that our methods are beneficial on a broad class of CP-optimization benchmarks involving soft constraints, cardinality or preferences.

Unsatisfiable Cores and Lower Bounding for Constraint Programming