Related papers: Ellipses and Lambda Definability
We give an account of the complex Arithmetic-Geometric Mean (AGM), as first studied by Gauss, together with details of its relationship with the theory of elliptic curves over $\C$, their period lattices and complex parametrisation. As an…
Most, if not all forms of ellipsis (e.g., so does Mary) are similar to reading comprehension questions (what does Mary do), in that in order to resolve them, we need to identify an appropriate text span in the preceding discourse. Following…
Domain-general model-based planners often derive their generality by constructing search heuristics through the relaxation or abstraction of symbolic world models. We illustrate how abstract interpretation can serve as a unifying framework…
Future predictions on sequence data (e.g., videos or audios) require the algorithms to capture non-Markovian and compositional properties of high-level semantics. Context-free grammars are natural choices to capture such properties, but…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…
We investigate the relationship between finite terms in lambda-letrec, the lambda calculus with letrec, and the infinite lambda terms they express. As there are easy examples of lambda-terms that, intuitively, are not unfoldings of terms in…
Calibration is a frequently invoked concept when useful label probability estimates are required on top of classification accuracy. A calibrated model is a function whose values correctly reflect underlying label probabilities. Calibration…
The formalizations of periods of time inside a linear model of Time are usually based on the notion of intervals, that may contain or may not their endpoints. This is not enought when the periods are written in terms of coarse granularities…
The task of natural language inference (NLI) asks whether a given premise (expressed in NL) entails a given NL hypothesis. NLI benchmarks contain human ratings of entailment, but the meaning relationships driving these ratings are not…
Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of {\em…
We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate…
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any…
Generalization is a central problem in Machine Learning. Indeed most prediction methods require careful calibration of hyperparameters usually carried out on a hold-out \textit{validation} dataset to achieve generalization. The main goal of…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…
Estimation and inference on causal parameters is typically reduced to a generalized method of moments problem, which involves auxiliary functions that correspond to solutions to a regression or classification problem. Recent line of work on…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
In this paper we consider the problem of configuring partial predicate abstraction that combines two techniques that have been effective in analyzing infinite-state systems: predicate abstraction and fixpoint approximations. A fundamental…
Substitution resolution supports the computational character of $\beta$-reduction, complementing its execution with a capture-avoiding exchange of terms for bound variables. Alas, the meta-level definition of substitution, masking a…
Dictionary definitions are historically the arbitrator of what words mean, but this primacy has come under threat by recent progress in NLP, including word embeddings and generative models like ChatGPT. We present an exploratory study of…