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We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.

Combinatorics · Mathematics 2020-08-13 Shaul Zemel

Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…

Computation and Language · Computer Science 2023-10-24 Stefan F. Schouten , Peter Bloem , Ilia Markov , Piek Vossen

Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between…

Artificial Intelligence · Computer Science 2024-08-21 Assaf Libman , Nir Oren , Bruno Yun

Artificial Intelligence (AI) systems, trained in controlled environments, often struggle in real-world complexities. We propose a general framework for estimating domain complexity across diverse environments, like open-world learning and…

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…

Software Engineering · Computer Science 2007-05-23 Ian Hayes , Robert Colvin , David Hemer , Paul Strooper , Ray Nickson

Enabling open-domain dialogue systems to ask clarifying questions when appropriate is an important direction for improving the quality of the system response. Namely, for cases when a user request is not specific enough for a conversation…

Computation and Language · Computer Science 2021-09-14 Mohammad Aliannejadi , Julia Kiseleva , Aleksandr Chuklin , Jeffrey Dalton , Mikhail Burtsev

The semantic Web service discovery has been given massive attention within the last few years. With the increasing number of Web services available on the web, looking for a particular service has become very difficult, especially with the…

Information Retrieval · Computer Science 2014-09-11 Ibrahim El Bitar , Fatima-Zahra Belouadha , Ounsa Roudies

Mathematical symbols and descriptions appear in various forms across document section boundaries without explicit markup. In this paper, we present a new large-scale dataset that emphasizes extracting symbols and descriptions in scientific…

Computation and Language · Computer Science 2022-04-27 Viet Dac Lai , Amir Pouran Ben Veyseh , Franck Dernoncourt , Thien Huu Nguyen

Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…

Artificial Intelligence · Computer Science 2021-08-31 Tim French , Tom Smoker

Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…

Logic in Computer Science · Computer Science 2026-04-20 Murdoch J. Gabbay

The contribution of this paper is to provide a semantic model (using soft constraints) of the words used by web-users to describe objects in a language game; a game in which one user describes a selected object of those composing the scene,…

Computation and Language · Computer Science 2010-05-31 Sergio Guadarrama , David P. Pancho

This work is the first to propose the concept of a semantic numeration system (SNS) as a certain class of context-based numeration methods. The development of the SNS concept required the introduction of fundamentally new concepts such as a…

Artificial Intelligence · Computer Science 2021-06-08 Alexander Chunikhin

Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…

Artificial Intelligence · Computer Science 2023-04-18 Giovanni Casini , Thomas Meyer , Ivan Varzinczak

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…

Logic in Computer Science · Computer Science 2007-12-11 Klaus Aehlig , Arnold Beckmann

Nowadays, the need for system interoperability in or across enterprises has become more and more ubiquitous. Lots of research works have been carried out in the information exchange, transformation, discovery and reuse. One of the main…

Software Engineering · Computer Science 2014-11-17 Y. Liao , M. Lezoche , H. Panetto , N. Boudjlida , Eduardo Rocha Loures

Much real-world data come with explicitly defined domain orders; e.g., lexicographic order for strings, numeric for integers, and chronological for time. Our goal is to discover implicit domain orders that we do not already know; for…

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the…

Artificial Intelligence · Computer Science 2011-10-13 T. Di Noia , E. Di Sciascio , F. M. Donini

Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…

Logic in Computer Science · Computer Science 2024-02-02 Eduard Kamburjan , Dilian Gurov

Large Language Models (LLMs) have demonstrated strong generalization across a wide range of tasks. Reasoning with LLMs is central to solving multi-step problems and complex decision-making. To support efficient reasoning, recent studies…

Computation and Language · Computer Science 2025-09-03 Jindong Li , Yali Fu , Li Fan , Jiahong Liu , Yao Shu , Chengwei Qin , Menglin Yang , Irwin King , Rex Ying

Semantic role labeling (SRL) -- identifying the semantic relationships between a predicate and other constituents in the same sentence -- is a well-studied task in natural language understanding (NLU). However, many of these relationships…

Computation and Language · Computer Science 2021-07-20 William Gantt