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.

[Q]: In this paper we study lifted inference for the Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in firstorder logic (FOL); it has applications in Statistical Relational Learning (SRL) and Probabilistic Databases (PDB). We present several results. First, we describe a lifted inference algorithm that generalizes prior approaches in SRL and PDB. Second, we provide a novel dichotomy result for a non-trivial fragment of FO CNF sentences, showing that for each sentence the WFOMC problem is either in PTIME or #P-hard in the size of the input domain; we prove that, in the first case our algorithm solves the WFOMC problem in PTIME, and in the second case it fails. Third, we present several properties of the algorithm. Finally, we discuss limitations of lifted inference for symmetric probabilistic databases (where the weights of ground literals depend only on the relation name, and not on the constants of the domain), and prove the impossibility of a dichotomy result for the complexity of probabilistic inference for the entire language FOL.
[A]: Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting


[Q]: In this paper, we introduce a notion of backdoors to Reiter’s propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor evaluation (parameterised by the size of the given backdoor), for various kinds of target classes (cnf, horn, krom, monotone, positive-unit). We show that backdoor detection is fixed-parameter tractable for the considered target classes, and backdoor evaluation is either fixed-parameter tractable, in para-∆P2 , or in para-NP, depending on the target class.
[A]: Strong Backdoors for Default Logic


[Q]: The problem of business-IT alignment is of widespread economic concern. As one way of addressing the problem, this paper describes an online system that functions as a kind of Wiki -one that supports the collaborative writing and running of business and scientific applications, as rules in open vocabulary, executable English, using a browser. Since the rules are in English, they are indexed by Google and other search engines. This is useful when looking for rules for a task that one has in mind. The design of the system integrates the semantics of data, with a semantics of an inference method, and also with the meanings of English sentences. As such, the system has functionality that may be useful for the Rules, Logic, Proof and Trust requirements of the Semantic Web. The system accepts rules, and small numbers of facts, typed or copy-pasted directly into a browser. One can then run the rules, again using a browser. For larger amounts of data, the system uses information in the rules to automatically generate and run SQL over networked databases. From a few highly declarative rules, the system typically generates SQL that would be too complicated to write reliably by hand. However, the system can explain its results in step-by-step hypertexted English, at the business or scientific level As befits a Wiki, shared use of the system is free. Introduction The well known "layer cake" diagram (Berners-Lee 2004) outlines a high level agenda for work on the Semantic Web. Figure 1. The Semantic Web Layer Cake
[A]:
A Wiki for Business Rules in Open Vocabulary, Executable English