Applying automated deduction to natural language understanding

AbstractVery few natural language understanding applications employ methods from automated deduction. This is mainly because (i) a high level of interdisciplinary knowledge is required, (ii) there is a huge gap between formal semantic theory and practical implementation, and (iii) statistical rather than symbolic approaches dominate the current trends in natural language processing. Moreover, abduction rather than deduction is generally viewed as a promising way to apply reasoning in natural language understanding. We describe three applications where we show how first-order theorem proving and finite model construction can efficiently be employed in language understanding.The first is a text understanding system building semantic representations of texts, developed in the late 1990s. Theorem provers are here used to signal inconsistent interpretations and to check whether new contributions to the discourse are informative or not. This application shows that it is feasible to use general-purpose theorem provers for first-order logic, and that it pays off to use a battery of different inference engines as in practice they complement each other in terms of performance.The second application is a spoken-dialogue interface to a mobile robot and an automated home. We use the first-order theorem prover spass for checking inconsistencies and newness of information, but the inference tasks are complemented with the finite model builder mace used in parallel to the prover. The model builder is used to check for satisfiability of the input; in addition, the produced finite and minimal models are used to determine the actions that the robot or automated house has to execute. When the semantic representation of the dialogue as well as the number of objects in the context are kept fairly small, response times are acceptable to human users.The third demonstration of successful use of first-order inference engines comes from the task of recognising entailment between two (short) texts. We run a robust parser producing semantic representations for both texts, and use the theorem prover vampire to check whether one text entails the other. For many examples it is hard to compute the appropriate background knowledge in order to produce a proof, and the model builders mace and paradox are used to estimate the likelihood of an entailment

Connectionist Inference Models

The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule-based reasoning, and whether they involve distributed or localist representations. The benefits and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or when used for cognitive modeling

A Logic-based Approach for Recognizing Textual Entailment Supported by Ontological Background Knowledge

We present the architecture and the evaluation of a new system for recognizing textual entailment (RTE). In RTE we want to identify automatically the type of a logical relation between two input texts. In particular, we are interested in proving the existence of an entailment between them. We conceive our system as a modular environment allowing for a high-coverage syntactic and semantic text analysis combined with logical inference. For the syntactic and semantic analysis we combine a deep semantic analysis with a shallow one supported by statistical models in order to increase the quality and the accuracy of results. For RTE we use logical inference of first-order employing model-theoretic techniques and automated reasoning tools. The inference is supported with problem-relevant background knowledge extracted automatically and on demand from external sources like, e.g., WordNet, YAGO, and OpenCyc, or other, more experimental sources with, e.g., manually defined presupposition resolutions, or with axiomatized general and common sense knowledge. The results show that fine-grained and consistent knowledge coming from diverse sources is a necessary condition determining the correctness and traceability of results.Comment: 25 pages, 10 figure

Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file