Related papers: Lambda Calculus with Explicit Read-back
This paper considers quasi-reductivity - essentially, the property that an evaluation cannot get "stuck" due to a missing case in pattern matching - in the context of term rewriting with logical constraints.
Terms in the lambda-calculus can be represented as planar trees decorated with symbols for abstraction and application, and having variables as leaves. In this paper, we concentrate on the branches of such trees, rather than on the trees…
We extend the diagrammatic calculus of syllogisms introduced in our previous paper to the general case of n-term syllogisms, showing that the valid ones are exactly those whose conclusion follows by calculation. Moreover, by pointing out…
Rule-induction models have demonstrated great power in the inductive setting of knowledge graph completion. In this setting, the models are tested on a knowledge graph entirely composed of unseen entities. These models learn relation…
We introduce the Rebound library that supports well-scoped term representations in Haskell and automates the definition of substitution, alpha-equivalence, and other operations that work with binding structures. The key idea of our design…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Unsupervised word embeddings have become a popular approach of word representation in NLP tasks. However there are limitations to the semantics represented by unsupervised embeddings, and inadequate fine-tuning of embeddings can lead to…
This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two…
Ensuring that online discussions are civil and productive is a major challenge for social media platforms. Such platforms usually rely both on users and on automated detection tools to flag inappropriate arguments of other users, which…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
We study strictly positive logics in the language $\mathscr{L}^+$, which constructs formulas from $\top$, propositional variables, conjunction, and diamond modalities. We begin with the base system $\bf K^+$, the strictly positive fragment…
We demonstrate that a wide array of machine learning algorithms are specific instances of one single paradigm: reciprocal learning. These instances range from active learning over multi-armed bandits to self-training. We show that all these…
For the lambda-calculus with letrec we develop an optimisation, which is based on the contraction of a certain class of 'future' (also: virtual) redexes. In the implementation of functional programming languages it is common practice to…
We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…
A major challenge of semantic parsing is the vocabulary mismatch problem between natural language and target ontology. In this paper, we propose a sentence rewriting based semantic parsing method, which can effectively resolve the mismatch…
A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by…
We propose a new regression algorithm that learns from a set of input-output pairs. Our algorithm is designed for populations where the relation between the input variables and the output variable exhibits a heterogeneous behavior across…
This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed…
While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…