Related papers: Gradualist descriptionalist set theory
Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…
Temporal logics are a powerful tool to specify properties of computational systems. For concurrent programs, Higher Dimensional Automata (HDA) are a very expressive model of non-interleaving concurrency. HDA recognize languages of partially…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
We consider the algebra $\mathcal O(\mathsf M)$ of observables and the (formally) versal morphism $\eta: A \to \mathcal O(\mathsf M)$ defined by the noncommutative deformation functor $\mathsf{Def}_{\mathsf M}$ of a family $\mathsf M = \{…
We are motivated by the following question: which data languages admit an active learning algorithm? This question was left open in previous work by the authors, and is particularly challenging for languages recognised by nondeterministic…
Recent work proposed $\delta$-relevant inputs (or sets) as a probabilistic explanation for the predictions made by a classifier on a given input. $\delta$-relevant sets are significant because they serve to relate (model-agnostic) Anchors…
In this article we propose and validate an unsupervised probabilistic model, Gaussian Latent Dirichlet Allocation (GLDA), for the problem of discrete state discovery from repeated, multivariate psychophysiological samples collected from…
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
In order for machine learning to garner widespread public adoption, models must be able to provide interpretable and robust explanations for their decisions, as well as learn from human-provided explanations at train time. In this work, we…
We define a family of intuitionistic non-normal modal logics; they can bee seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only one between Necessity and Possibility. We then consider…
Recently the third named author defined a 2-parametric family of groups $G_n^k$ \cite{gnk}. Those groups may be regarded as a certain generalisation of braid groups. Study of the connection between the groups $G_n^k$ and dynamical systems…
In this paper, we propose a novel method for generating a synthetic dataset obeying Gaussian distribution. Compared to the commonly used benchmark datasets with unknown distribution, the synthetic dataset has an explicit distribution, i.e.,…
Recognizing implicit discourse relations is a challenging but important task in the field of Natural Language Processing. For such a complex text processing task, different from previous studies, we argue that it is necessary to repeatedly…
Extensive research has recently shown that recurrent neural language models are able to process a wide range of grammatical phenomena. How these models are able to perform these remarkable feats so well, however, is still an open question.…
Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that…
Answering compositional questions requiring multi-step reasoning is challenging. We introduce an end-to-end differentiable model for interpreting questions about a knowledge graph (KG), which is inspired by formal approaches to semantics.…
We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Gr\"adel and Tannen. Furthermore, we…
In this paper we develop a formal system called Natural Term Logic (NTL). NTL aims to represent key aspects of the logical and grammatical mechanisms of natural language as well as grammatical transformations which preserve core logical…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…