Related papers: What do ultraproducts remember about the original …
We present a method for learning large-scale, broad-coverage construction grammars from corpora of language use. Starting from utterances annotated with constituency structure and semantic frames, the method facilitates the learning of…
We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.
We develop an approach to estimate the probability that a program sampled from a large language model is correct. Given a natural language description of a programming problem, our method samples both candidate programs as well as candidate…
A product line approach can save valuable resources by reusing artifacts. Especially for software artifacts, the reuse of existing components is highly desirable. In recent literature, the creation of software product lines is mainly…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
We prove a criterion that allows to construct units in product systems of correspondences with prescribed infinitesimal characterizations. This criterion summarizes proofs of known results and new applications. It also frees the hypothesis…
We focus on the production of efficient descriptions of objects, actions and events. We define a type of efficiency, textual economy, that exploits the hearer's recognition of inferential links to material elsewhere within a sentence.…
We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
While methods of code abstraction and reuse are widespread and well researched, methods of proof abstraction and reuse are still emerging. We consider the use of dependent types for this purpose, introducing a completely mechanical approach…
We study methods for learning sentence embeddings with syntactic structure. We focus on methods of learning syntactic sentence-embeddings by using a multilingual parallel-corpus augmented by Universal Parts-of-Speech tags. We evaluate the…
Abstract Machine understanding of questions is tightly related to recognition of articulation in the context of the computational capabilities of an underlying processing algorithm. In this paper a mathematical model to capture and…
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a…
Our main result is the equivalence of two notions of reducibility between structures. One is a syntactical notion which is an effective version of interpretability as in model theory, and the other one is a computational notion which is a…
We introduce a neural semantic parser that converts natural language utterances to intermediate representations in the form of predicate-argument structures, which are induced with a transition system and subsequently mapped to target…
Seq2seq learning has produced promising results on summarization. However, in many cases, system summaries still struggle to keep the meaning of the original intact. They may miss out important words or relations that play critical roles in…
We propose stratified institutions (a decade old generalised version of the theory of institutions of Goguen and Burstall) as a fully abstract model theoretic approach to modal logic. This allows for a uniform treatment of model theoretic…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…