Table Of ContentComputers in Language Research
Trends in Linguistics
Studies and Monographs 5
Editor
Werner Winter
Mouton Publishers
The Hague • Paris • New York
Computers
in Language Research
Formal Methods
edited by
Walter A. Sedelow, Jr.
Sally Yeates Sedelow
Mouton Publishers
The Hague • Paris • New York
Sally Yeates Sedelow, Ph. D.
Professor of Computer Science and of Linguistics
The University of Kansas, Lawrence
Walter A. Sedelow, Jr., Ph. D.
Professor of Computer Science and of Sociology,
and in the Program for the History & Philosophy of Science,
The University of Kansas, Lawrence
ISBN 90 279 7846 8
© Copyright 1979 by Mouton Publishers, The Hague. All rights reserved, including those
of translation into foreign languages. No part of this book may be reproduced in any
form - by photoprint, microfilm, or any other means - nor transmitted nor translated
into a machine language without written permission from the publisher. Typesetting:
Walter de Gruyter & Co. Berlin. - Printing: Karl Gerike, Berlin. - Binding: Liideritz &
Bauer Buchgewerbe GmbH, Berlin.
Printed in Germany
Contents
Language and people, modelling and science 1
Walter A. Sedelow, Jr. and Sally Yeates Sedelow
Graph theory, logic and formal languages in relation to language re-
search 7
S. E. Goodman and S. T. Hedetniemi
A descriptive introduction to graph theory and some of its applications
1. Fundamentals 19
1.1 Graphs, points and lines 19
1.2 Degrees 21
1.3 Regular graphs 22
1.4 Subgraphs 25
1.5 Isomorphism 26
1.6 Walks and connectedness 27
2. Trees 30
2.1 Introduction 30
2.2 Properties of trees 32
2.3 Spanning trees 34
2.4 Trees as an aid in searching and enumeration 36
2.5 The concept of a good computational algorithm 41
3. Representations of graphs 42
3.1 Introduction 42
3.2 The adjacency matrix 43
3.3 The incidence matrix 43
3.4 Adjacency vectors 44
3.5 Intersection graphs 46
3.6 Adjacency lists 47
3.7 Binary trees 49
VI Contents
3.8 Graph isomorphism 50
4. Traversais in graphs 51
4.1 Introduction 51
4.2 Eulerian walks 51
4.3 Hamiltonian traversais 54
4.4 Shortest path problems 57
4.5 Network flows 59
5. Orderings and matchings 63
5.1 Relations and orders 63
5.2 Critical path scheduling 64
5.3 Matchings and coverings 70
6. An overview of graph theory 73
6.1 Topological 74
6.1.1 Connectivity 74
6.1.2 Planarity 75
6.1.3 Colorings 77
6.1.4 Coverings 77
6.1.5 Intersection graphs 78
6.2 Combinatorial 80
6.2.1 Algebraic 80
6.2.2 Enumeration 81
6.2.3 Generalized Ramsey theory 82
6.2.4 Extremal problems 83
6.3 Computing 84
6.3.1 Isomorphism 84
6.3.2 Matchings and traversais 85
6.3.3 Connectivity 85
6.3.4 Shortest paths 85
6.3.5 Spanning trees 86
6.3.6 Cycles 86
6.3.7 Cliques and maximal independent sets 86
6.3.8 Chromatic number 86
6.3.9 Planarity 87
6.3.10 Line graphs 87
6.3.11 Ordering the points of a graph 87
6.3.12 Partitioning the points of a graph 87
6.4 Generalizations 88
6.4.1 Matroids 88
6.4.2 Hypergraphs 89
6.4.3 Integer linear planning (ILP) 89
References 90
Contents VII
David B. Benson
Formal languages vis-à-vis 'natural' languages
0. Introduction 97
1. Formal language theory 99
1.1 Introduction 99
1.2 Definition and classification of formal languages via grammars 100
1.3 The equivalence of generating and recognizing devices 103
1.4 Classification theory and decidability 106
1.5 Syntactic structure 107
1.6 Tree automata 114
1.7 Parsing theory 128
2. 'Natural' language practice 138
2.1 The syntax-directed model 138
2.2 The pattern-match model 144
2.3 Semantics and sentence generation 148
2.4 Conclusion 150
Note 151
References 151
H. C. Bohnert and P. O. Backer
Automatic English-to-logic translation in a simplified model. A study in
the logic of grammar
Preface 165
1. The logic of grammar: Motives and Methods 165
2. The grammar of logic: Predicating, compounding, generalizing . . 171
2.1 Elementary predication 171
2.2 Compounding 172
2.3 Generalizing 172
2.4 Problems for the logical analyst 174
3. The grammar of English I and II 175
3.1 Predication 175
3.2 Notation 178
3.3 Demand 178
3.4 Compounding: The grouping problem 179
3.4.1 Compounding terms 182
3.4.2 Compounding fragments 184
3.4.3 Informal explanation of the foregoing rules 186
3.5 General sentences 189
3.5.1 Determiners 189
3.5.2 "Is": Predication and identity 196
3.5.3 Whentheactive-passivetransformationinvolvesgeneralterms 199
VIII Contents
3.5.4 Relative pronouns and dependent clauses 200
3.5.5 Prepositional phrases 200
3.5.6 Translational principle for relative pronouns 201
4. Conclusions 204
Notes 208
References 209
Appendix A: English II syntax rules collected for reference 213
Appendix B: Sample translations English II to English I 215
Appendix C: Sample dictionary cards 223
Language and people, modelling and science
Brain size; coordination of eye/hand (cum opposable thumb)/brain; the inven-
tion and use of tools; language — each of these has had its proponents in the
great international 'accounting' contest. The accounting in question is that
needed for the human species' remarkable relationship to the other species
and to global ecology. No doubt each of those properties of humankind is an
important entry in the account. It might even seem evident that each is criti-
cal, and, further, that it is the interaction among them that has — for better
or for worse, for richer or for poorer — given us the Human System for
relating to environment.
In this present series within a series, Computers in language research, we
examine, inter alia, one of the most remarkable achievements of that Human
System: through symbols modelling its own behavior and, notably, recently
available techniques for modelling its own symbol behavior (e. g., modelling
symbolic models). It is at least arguable that this human activity of symboliz-
ing symbolism is the most quintessential^ human — the distinctively, perhaps
uniquely, human — of all behaviors, as it is also, at least potentially, much
the most powerful. The mathematical logician's pen is mightier than the
sword; in fact, it is now essential even to the production of those most con-
temporary swords of war: atomic energy devices, biochemical agents, and their
weaponly peers. Similarly, new food plant strains, new ecological comprehen-
sion, new curative therapies, new symbolic forms increasingly depend on a
preliminary symbolic mediating — and to a degree undreamt of even so
recently as at the onset of modern physics a century ago. The experimental
fraction of science, though ever more socially significant through the impact
of critical experiments, is continually shrinking; the symbol-manipulative
fraction, continually growing. Skills in the generation of formalisms come to
occupy an ever more modal situs in scientific careers, and identity crises
emerge, unclearly, as to the professional personae appropriate to the chemist,
the geneticist, or even the geologist or botanist. All such scientific professional
2 Language and people, modelling and science
roles are by way of being partially transformed in generic, but profound,
respects into those of linguists of a sort, and part of the time many of the
best scientists are effectively specialized metalinguists. Scientific method,
epistemology and metaphysics, paradigmatics, and even the traditional theory
component of the sciences are in process of becoming 'linguistic' specializa-
tions: dialects within scientific linguae francae. These are providing us with a
formalist science of science, with ways of modelling those dialects we call
the sciences.
Through their respective processes of professional socialization or encultura-
tion, each science approximates a replication of itself in each successor aca-
demic generation. The replication is only proximal for, as we well know with
all languages and dialects, change pervades. And nowhere in language is change
so pervasive and so rapid as in the science languages, except in those formal
and quasi-formal languages developed and developing in conjunction with
computer science and computer technics. Those languages which are most
'natural' - least self-conscious, least deliberately artifactual, least constructed —
change most slowly. They are least well understood, partly because not cut
to a pattern, partly because not used to achieve limited and well-specified
objectives. Those languages which are most fully designed also are most logic-
ally coherent and hence most formally tractable. As it happens, the segment
of reality which they address and symbolize, the computing machines - or,
as we would prefer, the logic machine, the 'logic-er' rather than the com-
puter — is also, as physical artifacts go, highly unstable, and very rapidly
changing and developing in certain structural properties. Thus these languages
which can be changed easily and systematically, do change easily and
systematically partly because that is what is happening to the specific realities
they are meant to give us control over.
It is, then, not surprising that as the sciences become increasingly (physical)
computer-dependent and (physical) computer-implicated — not to mention
abstract machine-implicated, abstract computer-implicated — their linguistic
aspect evolves more rapidly. The language of science and the individual dialects
of the individual sciences stand precisely between traditional, mundane natural
language and the contemporary (quasi-) formal languages which are the arti-
factual by-products of computing machines and abstract concepts of such
machines. The science languages, then, being a mix of the substantially un-
planned evolution of everyday language and the substantially planned special-
ized symbolizations of the computerniks and their ilk, is it any surprise that
their change rate is intermediate as between 'natural' languages and that of
more formal languages?
Dichotomizing is one of the most profound, significant, consequential
properties of Occidental cultures. It is a generic feature of most of our
