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]: We envision a machine learning service provider facing a continuous stream of problems with the same input domain, but with output domains that may differ. Clients present the provider with problems implicitly, by labeling a few example inputs, and then ask the provider to train models which reasonably extend their labelings to novel inputs. The provider wants to avoid constraining its users to a set of common labels, so it does not assume any particular correspondence between labels for a new task and labels for previously encountered tasks. To perform well in this setting, the provider needs a representation of the input domain which, in expectation, permits effective models for new problems to be learned efficiently from a small number of examples. While this bears a resemblance to settings considered in previous work on multitask and lifelong learning, our non-assumption of inter-task label correspondence leads to a novel algorithm: Lifelong Learner of Discriminative Representations (LLDR), which explicitly minimizes a proxy for the intra-task small-sample generalization error. We examine the relative benefits of our approach on a diverse set of real-world datasets in three significant scenarios: representation learning, multitask learning and lifelong learning.
[A]: Lifelong Learning of Discriminative Representations


[Q]: The belief bias effect is a phenomenon which occurs when we think that we judge an argument based on our reasoning, but are actually influenced by our beliefs and prior knowledge. Evans, Barston and Pollard carried out a psychological syllogistic reasoning task to prove this effect. Participants were asked whether they would accept or reject a given syllogism. We discuss one specific case which is commonly assumed to be believable but which is actually not logically valid. By introducing abnormalities, abduction and background knowledge, we adequately model this case under the weak completion semantics. Our formalization reveals new questions about possible extensions in abductive reasoning. For instance, observations and their explanations might include some relevant prior abductive contextual information concerning some side-effect or leading to a contestable or refutable side-effect. A weaker notion indicates the support of some relevant consequences by a prior abductive context. Yet another definition describes jointly supported relevant consequences, which captures the idea of two observations containing mutually supportive side-effects. Though motivated with and exemplified by the running psychology application, the various new general abductive context definitions are introduced here and given a declarative semantics for the first time, and have a much wider scope of application. Inspection points, a concept introduced by Pereira and Pinto, allows us to express these definitions syntactically and intertwine them into an operational semantics.
[A]: Contextual Abductive Reasoning with Side-Effects


[Q]: The historic background of algorithmic processing with regard to etymology and methodology is translated into terms of mathematical logic and Computer Science. A formal logic structure is introduced by exemplary questions posed to Fiqh-chapters to define a logic query language. As a foundation, a generic algorithm for deciding Fiqhrulings is designed to enable and further leverage rule of law (vs. rule by law) with full transparency and complete algorithmic coverage of Islamic law eventually providing legal security, legal equality, and full legal accountability. This is implemented by disentangling and reinstating classic Fiqh-methodology (usul al-Fiqh) with the expressive power of subsets of First Order Logic (FOL) sustainably substituting ad hoc reasoning with falsifiable rational argumentation. The results are discussed in formal terms of completeness, decidability and complexity of formal Fiqh-systems. An Entscheidungsproblem for formal Fiqh-Systems is formulated and validated.
[A]:
The Algorithm of Islamic Jurisprudence (Fiqh) with Validation of an Entscheidungsproblem