Related papers: Gradualist descriptionalist set theory
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…
In this paper we generalise and unify the results and methods used by Benson, Liardet, Evetts, and Evetts & Levine, to show that rational sets in a virtually abelian group G have rational (relative) growth series with respect to any…
A central challenge in program induction has long been the trade-off between symbolic and neural approaches. Symbolic methods offer compositional generalisation and data efficiency, yet their scalability is constrained by formalisms such as…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
We present three ordinal notation systems representing ordinals below $\varepsilon_0$ in type theory, using recent type-theoretical innovations such as mutual inductive-inductive definitions and higher inductive types. We show how ordinal…
Descriptive set theory was originally developed on Polish spaces. It was later extended to $\omega$-continuous domains [Selivanov 2004] and recently to quasi-Polish spaces [de Brecht 2013]. All these spaces are countably-based. Extending…
Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance. We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the…
Text classification is fundamental in natural language processing (NLP), and Graph Neural Networks (GNN) are recently applied in this task. However, the existing graph-based works can neither capture the contextual word relationships within…
Explanation constitutes an archetypal feature of human rationality, underpinning learning and generalisation, and representing one of the media supporting scientific discovery and communication. Due to the importance of explanations in…
Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…
While information from the field of linguistic typology has the potential to improve performance on NLP tasks, reliable typological data is a prerequisite. Existing typological databases, including WALS and Grambank, suffer from…
Evans and Gazdar introduced DATR as a simple, non-monotonic language for representing natural language lexicons. Although a number of implementations of DATR exist, the full language has until now lacked an explicit, declarative semantics.…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
The bialgebraic abstract GSOS framework by Turi and Plotkin provides an elegant categorical approach to modelling the operational and denotational semantics of programming and process languages. In abstract GSOS, bisimilarity is always a…
Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be…
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…
Natural Language Processing prides itself to be an empirically-minded, if not outright empiricist field, and yet lately it seems to get itself into essentialist debates on issues of meaning and measurement ("Do Large Language Models…
Let $k$ be a field, $\tilde{G}$ a connected reductive $k$-group, and $\Gamma$ a finite group. In a previous work, the authors defined what it means for a connected reductive $k$-group $G$ to be "parascopic" for $(\tilde{G},\Gamma)$.…
I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…