Elaboration in Dependent Type Theory

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean's elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved

Elimination of Spurious Ambiguity in Transition-Based Dependency Parsing

We present a novel technique to remove spurious ambiguity from transition systems for dependency parsing. Our technique chooses a canonical sequence of transition operations (computation) for a given dependency tree. Our technique can be applied to a large class of bottom-up transition systems, including for instance Nivre (2004) and Attardi (2006)

Capturing Ambiguity in Crowdsourcing Frame Disambiguation

FrameNet is a computational linguistics resource composed of semantic frames, high-level concepts that represent the meanings of words. In this paper, we present an approach to gather frame disambiguation annotations in sentences using a crowdsourcing approach with multiple workers per sentence to capture inter-annotator disagreement. We perform an experiment over a set of 433 sentences annotated with frames from the FrameNet corpus, and show that the aggregated crowd annotations achieve an F1 score greater than 0.67 as compared to expert linguists. We highlight cases where the crowd annotation was correct even though the expert is in disagreement, arguing for the need to have multiple annotators per sentence. Most importantly, we examine cases in which crowd workers could not agree, and demonstrate that these cases exhibit ambiguity, either in the sentence, frame, or the task itself, and argue that collapsing such cases to a single, discrete truth value (i.e. correct or incorrect) is inappropriate, creating arbitrary targets for machine learning.Comment: in publication at the sixth AAAI Conference on Human Computation and Crowdsourcing (HCOMP) 201

Constructional Tools as the Origin of Cognitive Capacities

It is argued that cognitive capacities can be understood as the outcome of the collective action of a set of agents created by tools that explore possible behaviours and train the agents to behave in such appropriate ways as may be discovered. The coherence of the whole system is assured by a combination of vetting the performance of new agents and dealing appropriately with any faults that the whole system may develop. This picture is shown to account for a range of cognitive capacities, including language