Related papers: Sense, reference, and computation
Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Incomputability results in Formal Logic and the Theory of Computation (i.e., incompleteness and undecidability) have deep implications for the foundations of mathematics and computer science. Likewise, Social Choice Theory, a branch of…
The subtle human values we acquire through life experiences govern our thoughts and gets reflected in our speech. It plays an integral part in capturing the essence of our individuality and making it imperative to identify such values in…
Commonsense reasoning is an appealing topic in natural language processing (NLP) as it plays a fundamental role in supporting the human-like actions of NLP systems. With large-scale language models as the backbone, unsupervised pre-training…
Contextualized representations trained over large raw text data have given remarkable improvements for NLP tasks including question answering and reading comprehension. There have been works showing that syntactic, semantic and word sense…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
Few-shot relation extraction (FSRE) is of great importance in long-tail distribution problem, especially in special domain with low-resource data. Most existing FSRE algorithms fail to accurately classify the relations merely based on the…
The treatment of equality as a type in type theory gives rise to an interesting type-theoretic structure known as `identity type'. The idea is that, given terms $a,b$ of a type $A$, one may form the type $Id_{A}(a,b)$, whose elements are…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
The article considers the quantitative assessment approach to the innovativeness of different objects. The proposed assessment model is based on the object data retrieval from various databases including the Internet. We present an object…
Coreference resolution is typically evaluated using aggregate statistical metrics such as CoNLL-F1, which measure structural overlap between predicted and gold clusters. While widely used, these metrics offer limited diagnostic insights,…
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
This article studies the problem of assessing relevance to each of the rules of a reference resolution system. The reference solver described here stems from a formal model of reference and is integrated in a reference processing workbench.…
We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
We study the equivalence relation on states of labelled transition systems of satisfying the same formulas in Computation Tree Logic without the next state modality (CTL-X). This relation is obtained by De Nicola & Vaandrager by translating…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…