Three Modern Roles for Logic in AI

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.Comment: To be published in PODS 202

Efficient Computation of Shap Explanation Scores for Neural Network Classifiers via Knowledge Compilation

The use of Shap scores has become widespread in Explainable AI. However, their computation is in general intractable, in particular when done with a black-box classifier, such as neural network. Recent research has unveiled classes of open-box Boolean Circuit classifiers for which Shap can be computed efficiently. We show how to transform binary neural networks into those circuits for efficient Shap computation. We use logic-based knowledge compilation techniques. The performance gain is huge, as we show in the light of our experiments.Comment: Conference submission. It replaces the previously uploaded paper "Opening Up the Neural Network Classifier for Shap Score Computation", by the same authors. This version considerably revised the previous on

Incremental syntactic generation of natural language with tree adjoining grammars

This document combines the basic ideas of my master´s thesis - which has been developped within the WIP project - with new results from my work as a member of WIP, as far as they concern the integration and further development of the implemented system. ISGT (in German \u27Inkrementeller Syntaktischer Generierer natürlicher Sprache mit TAGs´) is a syntactic component for a text generation system and is based on Tree Adjoining Grammars. It is lexically guided and consists of two levels of syntactic processing: A component that computes the hierarchical structure of the sentence under construction (hierarchical level) and a component that computes the word position and utters the sentence (positional level). The central aim of this work has been to design a syntactic generator that computes sentences in an incremental fashion. The realization of the incremental syntactic generator has been supported by a distributed parallel model that is used to speed up the computation of single parts of the sentence

Complement clauses and complementation systems: a cross-linguistic study of grammatical organization

The dissertation provides a cross-linguistic investigation into the grammatical structure of complement clauses and the organization of complementation systems. Based on a balanced sample of 100 widely dispersed languages, the major goals of the present work are to set the two landmark typological reference articles on complementation (Noonan 1985|2007, Dixon 2006) onto a broad empirical basis and to explore hitherto understudied phenomena in the constitution of complementation systems. In particular, the traditional focus on object complement clauses is shifted to complements in ‘subject’ function, and the dissertation is the first to analyse systematically the cross-linguistic productivity, morphosyntactic coding, syntagmatic arrangement and diachronic rise of complements in S- and A-function, as compared to their corresponding object clauses. On a methodological plane, it combines a multivariate approach to clause-linkage with recent statistical techniques of data mining (e.g. HCFA, cluster analyses, NeighborNet, MDS) in order to measure (dis)similarities in the cross-linguistic organization of complementation constructions. This comprises, for example, a precise gauging of the degree to which the internal structure of complements is ‘desententialized’ (Lehmann 1988) and made NP-like, of the ways in which this correlates with the possible external functions and positions of the complement in the main clause, and of the ways in which these distributional patterns in complementation systems reflect the historical origins and lexical diffusion of the relevant constructions. Above all, the dissertation problematizes the conceptual and terminological foundations for the typological study of complementation, which, despite decades of intensive research, remain challenging to establish in a cross-linguistically satisfactory way

Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Meaning versus Grammar

This volume investigates the complicated relationship between grammar, computation, and meaning in natural languages. It details conditions under which meaning-driven processing of natural language is feasible, discusses an operational and accessible implementation of the grammatical cycle for Dutch, and offers analyses of a number of further conjectures about constituency and entailment in natural language

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

Classification-based phrase structure grammar: an extended revised version of HPSG

This thesis is concerned with a presentation of Classification -based Phrase Structure Grammar (or cPSG), a grammatical theory that has grown out of extensive revisions of, and extensions to, HPSG. The fundamental difference between this theory and HPSG concerns the central role that classification plays in the grammar: the grammar classifies strings, according to their feature structure descriptions, as being of various types. Apart from the role of classification, the theory bears a close resemblance to HPSG, though it is by no means a direct translation, including numerous revisions and extensions. A central goal in the development of the theory has been its computational implementation, which is included in the thesis.The presentation may be divided into four parts. In the first, chapters 1 and 2, we present the grammatical formalism within which the theory is stated. This consists of a development of the notion of a classificatory system (chapter 1), and the incorporation of hierarchality into that notion (chapter 2).The second part concerns syntactic issues. Chapter 3 revises the HPSG treatment of specifiers, complements and adjuncts, incorporating ideas that specifiers and complements should be distinguished and presenting a treatment of adjuncts whereby the head is selected for by the adjunct. Chapter 4 presents several options for an account of unbounded dependencies. The accounts are based loosely on that of GPSG, and a reconstruction of GPSG's Foot Feature Principle is presented which does not involve a notion of default. Chapter 5 discusses coordination, employing an extension of Rounds- Kasper logic to allow a treatment of cross -categorial coordination.In the third part, chapters 6, 7 and 8, we turn to semantic issues. We begin (Chapter 6) with a discussion of Situation Theory, the background semantic theory, attempting to establish a precise and coherent version of the theory within which to work. Chapter 7 presents the bulk of the treatment of semantics, and can be seen as an extensive revision of the HPSG treatment of semantics. The aim is to provide a semantic treatment which is faithful to the version of Situation Theory presented in Chapter 6. Chapter 8 deals with quantification, discussing the nature of quantification in Situation Theory before presenting a treatment of quantification in CPSG. Some residual questions about the semantics of coordinated noun phrases are also addressed in this chapter.The final part, Chapter 9, concerns the actual computational implementation of the theory. A parsing algorithm based on hierarchical classification is presented, along with four strategies that might be adopted given that algorithm. Also discussed are some implementation details. A concluding chapter summarises the arguments of the thesis and outlines some avenues for future research

Proceedings of the Third Symposium on Programming Languages and Software Tools : Kääriku, Estonia, August 23-24 1993

http://www.ester.ee/record=b1064507*es