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.

[EX Q]: We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions (e.g., pi) and iterated connectives ∨ or ∧ ranging over intervals parameterized by arithmetic variables (e.g., ∧n i=1 pi, where n is a parameter). The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called bound-linear, for which this problem becomes decidable. This result is obtained by reduction to a particular class of schemata called regular, for which we provide a sound and complete terminating proof procedure. This schemata calculus (called stab) allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. We also show that the satisfiability problem becomes again undecidable for slight extensions of this class, thus demonstrating that bound-linear schemata represent a good compromise between expressivity and decidability.
[EX A]: Decidability and Undecidability Results for Propositional Schemata

[EX Q]: Marginal MAP inference involves making MAP predictions in systems defined<lb>with latent variables or missing information. It is significantly more difficult than<lb>pure marginalization and MAP tasks, for which a large class of efficient and con-<lb>vergent variational algorithms, such as dual decomposition, exist. In this work, we<lb>generalize dual decomposition to a generic power sum inference task, which in-<lb>cludes marginal MAP, along with pure marginalization and MAP, as special cases.<lb>Our method is based on a block coordinate descent algorithm on a new convex<lb>decomposition bound, that is guaranteed to converge monotonically, and can be<lb>parallelized efficiently. We demonstrate our approach on marginal MAP queries<lb>defined on real-world problems from the UAI approximate inference challenge,<lb>showing that our framework is faster and more reliable than previous methods.
[EX A]: Decomposition Bounds for Marginal MAP

[EX Q]: The goal of open information extraction (OIE) is to extract surface relations and their arguments from naturallanguage text in an unsupervised, domainindependent manner. In this paper, we explore how overly-specific extractions can be reduced in OIE systems without producing uninformative or inaccurate results. We propose MinIE, an OIE system that produces minimized, annotated extractions. At its heart, MinIE rewrites OIE extractions by (1) identifying and removing parts that are considered overly specific; (2) representing information about polarity, modality, attribution, and quantities with suitable annotations instead of in the actual extraction. We conducted an experimental study with several real-world datasets and found that MinIE achieves competitive or higher precision and recall than most prior systems, while at the same time producing much shorter extractions.
[EX A]:
MinIE: Minimizing Facts in Open Information Extraction