Manual Logical Reasoning with Diagrams (Studies in Logic and Computation)

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Because symbolic reasoning encodes knowledge in symbols and strings of characters.


In supervised learning, those strings of characters are called labels, the categories by which we classify input data using a statistical model. That business logic is one form of symbolic reasoning. But you get my drift. It gets even weirder when you consider that the sensory data perceived by our minds, and to which signs refer, are themselves signs of the thing in itself, which we cannot know.

The finger is not the moon, but it is directionally useful. So, too, each sign is a finger pointing at sensations.

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Just how much reality do you think will fit into a ten-minute transmission? This page includes some recent, notable research that attempts to combine deep learning with symbolic learning to answer those questions.

Logical Reasoning Of Computer Science

We propose the Neuro-Symbolic Concept Learner NS-CL , a model that learns visual concepts, words, and semantic parsing of sentences without explicit supervision on any of them; instead, our model learns by simply looking at images and reading paired questions and answers.

Our model builds an object-based scene representation and translates sentences into executable, symbolic programs. To bridge the learning of two modules, we use a neuro-symbolic reasoning module that executes these programs on the latent scene representation. Analog to the human concept learning, given the parsed program, the perception module learns visual concepts based on the language description of the object being referred to. Meanwhile, the learned visual concepts facilitate learning new words and parsing new sentences. We use curriculum learning to guide searching over the large compositional space of images and language.

Extensive experiments demonstrate the accuracy and efficiency of our model on learning visual concepts, word representations, and semantic parsing of sentences. Further, our method allows easy generalization to new object attributes, compositions, language concepts, scenes and questions, and even new program domains. It also empowers applications including visual question answering and bidirectional image-text retrieval.

Deep reinforcement learning DRL brings the power of deep neural networks to bear on the generic task of trial-and-error learning, and its effectiveness has been convincingly demonstrated on tasks such as Atari video games and the game of Go. However, contemporary DRL systems inherit a number of shortcomings from the current generation of deep learning techniques. For example, they require very large datasets to work effectively, entailing that they are slow to learn even when such datasets are available.

Moreover, they lack the ability to reason on an abstract level, which makes it difficult to implement high-level cognitive functions such as transfer learning, analogical reasoning, and hypothesis-based reasoning. Finally, their operation is largely opaque to humans, rendering them unsuitable for domains in which verifiability is important.

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  7. In this paper, we propose an end-to-end reinforcement learning architecture comprising a neural back end and a symbolic front end with the potential to overcome each of these shortcomings. As proof-of-concept, we present a preliminary implementation of the architecture and apply it to several variants of a simple video game.

    We show that the resulting system — though just a prototype — learns effectively, and, by acquiring a set of symbolic rules that are easily comprehensible to humans, dramatically outperforms a conventional, fully neural DRL system on a stochastic variant of the game. Artificial Neural Networks are powerful function approximators capable of modelling solutions to a wide variety of problems, both supervised and unsupervised.

    As their size andexpressivity increases, so too does the variance of the model, yielding a nearly ubiquitous overfitting problem. Although mitigated by a variety of model regularisation methods, the common cure is to seek large amounts of training data—which is not necessarily easily obtained—that sufficiently approximates the data distribution of the domain we wish to test on.

    In contrast, logic programming methods such as Inductive Logic Programming offer an extremely data-efficient process by which models can be trained to reason on symbolic domains. However, these methods are unable to deal with the variety of domains neural networks can be applied to: they are not robust to noise in or mislabelling of inputs, and perhaps more importantly, cannot be applied to non-symbolic domains where the data is ambiguous, such as operating on raw pixels. In this paper, we propose a Differentiable Inductive Logic framework, which can not only solve tasks which traditional ILP systems are suited for, but shows a robustness to noise and error in the training data which ILP cannot cope with.

    Logical Reasoning with Diagrams & Sentences

    Furthermore, as it is trained by backpropagation against a likelihood objective, it can be hybridised by connecting it with neural networks over ambiguous data in order to be applied to domains which ILP cannot address, while providing data efficiency and generalisation beyond what neural networks on their own can achieve. The recent adaptation of deep neural network-based methods to reinforcement learning and planning domains has yielded remarkable progress on individual tasks.

    Nonetheless, progress on task-to-task transfer remains limited. In pursuit of efficient and robust generalization, we introduce the Schema Network, an object-oriented generative physics simulator capable of disentangling multiple causes of events and reasoning backward through causes to achieve goals. The richly structured architecture of the Schema Network can learn the dynamics of an environment directly from data. We compare Schema Networks with Asynchronous Advantage Actor-Critic and Progressive Networks on a suite of Breakout variations, reporting results on training efficiency and zero-shot generalization, consistently demonstrating faster, more robust learning and better transfer.

    The study of logic pdf

    We argue that generalizing from limited data and learning causal relationships are essential abilities on the path toward generally intelligent systems. The DSN model provides a simple, universal yet powerful structure, similar to DNN, to represent any knowledge of the world, which is transparent to humans. The conjecture behind the DSN model is that any type of real world objects sharing enough common features are mapped into human brains as a symbol.

    Those symbols are connected by links, representing the composition, correlation, causality, or other relationships between them, forming a deep, hierarchical symbolic network structure. Powered by such a structure, the DSN model is expected to learn like humans, because of its unique characteristics. First, it is universal, using the same structure to store any knowledge. Second, it can learn symbols from the world and construct the deep symbolic networks automatically, by utilizing the fact that real world objects have been naturally separated by singularities.

    Third, it is symbolic, with the capacity of performing causal deduction and generalization. Fourth, the symbols and the links between them are transparent to us, and thus we will know what it has learned or not - which is the key for the security of an AI system. Fifth, its transparency enables it to learn with relatively small data.

    Sixth, its knowledge can be accumulated. Last but not least, it is more friendly to unsupervised learning than DNN. The Venn diagram has become increasingly popular for representing data in a way that facilitates reasoning by propositional logic Figure 1A , inset; Venn, We used Venn diagrams to visually represent basic operations conjunction, disjunction, and negation when first teaching frequentist probability. For example, we asked students to make an inference using data from Liu et al. With the aid of Venn diagrams, it became easier to understand the mechanisms of common fallacy, such as affirming the consequent e.

    We believe that the combination of Venn diagrams and basic propositional logic—in particular, the notion that a conditional statement is logically equivalent to its contrapositive—lays a foundation for introducing more complex topics of tail probability and hypothesis testing Figure 1, C and D. Valid deductions can be performed based purely on the structure of propositions. If a certain observation e. Otherwise, it would be a fallacy of affirming the consequent. Finally, propositional logic can also be used to understand how one-sided versus two-sided hypothesis tests differ in their stringencies Figure 1D.

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    We hope Masel and colleagues will continue to study how to effectively support students in qualitative reasoning that promotes their statistical understanding. Perhaps they or others will measure how informal experiences such as ours could contribute to developing the quantitative biologists of the future. The authors thank D. Mowshowitz Columbia University for insight on teaching. National Center for Biotechnology Information , U. Author information Copyright and License information Disclaimer. Liu and R. This article is distributed by The American Society for Cell Biology under license from the author s.

    It is available to the public under an Attribution—Noncommercial—Share Alike 3. DEAR EDITOR : As the readers of CBE—Life Sciences Education know, modern biology has come a long way from its beginnings as a qualitative and descriptive science to its current status as a quantitative science, increasingly exploiting mathematical and computational tools to achieve mechanistic understanding of living systems Howard, ; Liu and Mao, Open in a separate window.

    Figure 1. Medline trend: automated yearly statistics of PubMed results for any query.