Krishnendu Chatterjee, Luca De Alfaro, Rupak Majumdar · 2006
Abstract. We present a compositional theory of system verica-tion, where specications assign real-numbered costs to systems. These costs can express a wide variety of quantitative system prop-erties, such as resource consumption, price, or a measure of how well a system satises its specication. The theory supports the composition of systems and specications, and the hiding of vari-ables. Boolean renement relations are replaced by real-numbered distances between descriptions of a system at different levels of detail. We show that the classical boolean rules for compositional reasoning have quantitative counterparts in our setting. While our general theory allows costs to be specied by arbi-trary cost functions, we also consider a class of linear cost func-tions, which give rise to an instance of our framework where all operations are computable in polynomial time. 1.
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Murali Sitaraman · 2007
A well-understood reason for component-based software engineering (CBSE) is improved productivity. CBSE is also important for another basic reason. It enables compositional or modular reasoning, and therefore, it facilitates production of high quality systems. In compositional reasoning, it is possible to reason about the behavior of the system using the behavioral specifications of reused components ignoring their internal details. Compositionality is essential for a reasoning process -- formal or informal -- to scale up.
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Mariëlle Stoelinga, R. Majumdar, Thomas A. Henzinger et al. · University of Twente Research Information · 2006
We present a compositional theory of system verification, where specifications assign real-numbered costs to systems. These costs can express a wide variety of quantitative system properties, such as resource consumption, price, or a measure of how well a system satisfies its specification. The theory supports the composition of systems and specifications, and the hiding of variables. Boolean refinement relations are replaced by real-numbered distances between descriptions of a system at different levels of detail. We show that the classical Boolean rules for compositional reasoning have quantitative counterparts in our setting. While our general theory allows costs to be specified by arbitrary cost functions, we also consider a class of linear cost functions, which give rise to an instance of our framework where all operations are computable in polynomial time
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Sergey Berezin, Sérgio Campos, Edmund M. Clarke · 1998
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Luca Aceto, Cristian Prisacariu, Luca Aceto et al. · 2012
We provide decomposition and quotienting results for “multi-modal/ epistemic logic ” with respect to a composition operator, traditionally used for epistemic models, due to van Eijck et al. (Journal of Ap-plied Non-Classical Logics 21(3–4):397–425, 2011), that involves sets of atomic propositions and valuation functions from Kripke models. While the composition operator was originally defined only for epis-temic S5n models, our results apply to the composition of any pair of Kripke models. In particular, our quotienting result extends a specific result in the above mentioned paper by van Eijck et al. for the com-position of epistemic models with disjoint sets of atomic propositions to compositions of any two Kripke models regardless of their sets of atomic propositions. We also explore the complexity of the formulas we construct in our decomposition result.
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Steven T. Piantadosi, Richard Ν. Aslin · PLoS ONE · 2016
Compositional "language of thought" models have recently been proposed to account for a wide range of children's conceptual and linguistic learning. The present work aims to evaluate one of the most basic assumptions of these models: children should have an ability to represent and compose functions. We show that 3.5-4.5 year olds are able to predictively compose two novel functions at significantly above chance levels, even without any explicit training or feedback on the composition itself. We take this as evidence that children at this age possess some capacity for compositionality, consistent with models that make this ability explicit, and providing an empirical challenge to those that do not.
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Crystal Chang Din, Johan Dovland, Olaf Owe · Lecture notes in computer science · 2012
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2009
1 Even “dialetheists ” almost invariably accept it, though they also accept its negation. But if you don’t accept it, I invite you to substitute another example that you do accept, perhaps For every sentence, if it is true then its double negation is true, and modify the following discussion accordingly. Hartry Field 1. Introduction. As Quine (1970, Ch. 1) and many others have pointed out, one of the main purposes of the notion of truth is to allow us to formulate generalizations that would otherwise be inexpressible. A simple example of such a generalization is (G) There is no sentence such that both it and its negation are true, whose purpose is to generalize over such sentences as
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Rupak Majumdar · 2008
UC Los Angeles Mari"elle StoelingaUniversity of Twente Abstract. We present a compositional theory of system verifica-tion, where specifications assign real-numbered costs to systems. These costs can express a wide variety of quantitative system prop-erties, such as resource consumption, price, or a measure of how well a system satisfies its specification. The theory supports thecomposition of systems and specifications, and the hiding of variables. Boolean refinement relations are replaced by real-numbereddistances between descriptions of a system at different levels of detail. We show that the classical boolean rules for compositionalreasoning have quantitative counterparts in our setting.
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Ismael Figueroa, Tom Schrijvers, Nicolas Tabareau et al. · Lirias (KU Leuven) · 2014
Oliveira and colleagues recently developed a powerful model to reason about mixin-based composition of effectful components and their interference, exploiting a wide variety of techniques such as equational reasoning, parametricity, and algebraic laws about monadic effects. This work addresses the issue of reasoning about interference with effectful aspects in the presence of unrestricted quantification through pointcuts. While global reasoning isrequired, we show that it is possible to reason in a compositional manner, which is key for the scalability of the approach in the face of large and evolving systems. We establish a general equivalence theorem that is based on a few conditions that can be established, reused, and adapted separately as the system evolves. Interestingly, one of these conditions, local harmlessness, can be proven by a translation to the mixin setting, making it possible to directly exploit previously established results about certain kinds of harmless extensions.
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Yifeng Chen, J. W. Sanders · Lecture notes in computer science · 2006
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Yifeng Chen, J. W. Sanders · 2006
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Nina Amla, E. Allen Emerson, Kedar S. Namjoshi et al. · 2003
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Hartry Field · The Monist · 2006
Journal Article Compositional Principles vs. Schematic Reasoning Get access Hartry Field Hartry Field New York University Search for other works by this author on: Oxford Academic PubMed Google Scholar The Monist, Volume 89, Issue 1, 1 January 2006, Pages 9–27, https://doi.org/10.5840/monist200689131 Published: 15 November 2014
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Hannah Mertens, Tim Quatmann, Joost-Pieter Katoen · ArXiv.org · 2025
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions over a finite set of parameters. We lift an existing framework for PA to the pPA setting, incorporating asymmetric, circular, and interleaving proof rules. Our approach enables the verification of a broad spectrum of multi-objective queries for pPA, encompassing probabilistic properties and (parametric) expected total rewards. Additionally, we introduce a rule for reasoning about monotonicity in composed pPAs.
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Julien Colin, Sebastian Musslick, Thomas Serre et al. · 2022
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Bob Coecke, Ross Duncan, Aleks Kissinger et al. · Fundamental theories of physics · 2015
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Aissa, Wafa, Ferecatu, Marin, Crucianu, Michel · arXiv (Cornell University) · 2023
Visual Question Answering (VQA) is a complex task requiring large datasets and expensive training. Neural Module Networks (NMN) first translate the question to a reasoning path, then follow that path to analyze the image and provide an answer. We propose an NMN method that relies on predefined cross-modal embeddings to ``warm start'' learning on the GQA dataset, then focus on Curriculum Learning (CL) as a way to improve training and make a better use of the data. Several difficulty criteria are employed for defining CL methods. We show that by an appropriate selection of the CL method the cost of training and the amount of training data can be greatly reduced, with a limited impact on the final VQA accuracy. Furthermore, we introduce intermediate losses during training and find that this allows to simplify the CL strategy.
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Alexandru Oarga, Yilun Du · ArXiv.org · 2025
Generalization is a key challenge in machine learning, specifically in reasoning tasks, where models are expected to solve problems more complex than those encountered during training. Existing approaches typically train reasoning models in an end-to-end fashion, directly mapping input instances to solutions. While this allows models to learn useful heuristics from data, it often results in limited generalization beyond the training distribution. In this work, we propose a novel approach to reasoning generalization by learning energy landscapes over the solution spaces of smaller, more tractable subproblems. At test time, we construct a global energy landscape for a given problem by combining the energy functions of multiple subproblems. This compositional approach enables the incorporation of additional constraints during inference, allowing the construction of energy landscapes for problems of increasing difficulty. To improve the sample quality from this newly constructed energy landscape, we introduce Parallel Energy Minimization (PEM). We evaluate our approach on a wide set of reasoning problems. Our method outperforms existing state-of-the-art methods, demonstrating its ability to generalize to larger and more complex problems. Project website can be found at: https://alexoarga.github.io/compositional_reasoning/
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Mertens, Hannah, Quatmann, Tim, Katoen, Joost-Pieter · RWTH Publications (RWTH Aachen) · 2024
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