Strong Generative Capacity

by Miller, Philip

• ISBN13: 9781575862149
• ISBN10: 157586214X
• Format: Paperback
• Copyright: 2000-03-01
• Publisher: Stanford Univ Center for the Study

Summary

The concept of "strong generative capacity" (SGe of a linguistic formalism was introduced by Chomsky in the early sixties in order to characterize descriptive capacity. However, the original definition proposed by Chomsky turned out to be unusable, especially when one wished to compare the SGC of different types of formalisms. This book provides for the first time a rigorous and useful characterization of SGC, defining it as the model theoretic semantics of linguistic formalism. The book begins by reviewing classical definitions of weak and strong generative capacity. An in-depth discussion of how abstract interpretation domains are defined in theory-neutral set-theoretical terms is presented. The book also explains how interpretation domains are defined for labeled constituency, dependency, endocentricity, and linking, and applied to the analysis of a range of linguistic formalisms, among which are context-free grammars, dependency grammars, X-bar grammars, tree-adjoining grammars, transformational grammars and categorial grammars.

Table of Contents

Preface	ix
Classical Definitions of Weak and Strong Generative Capacity	1	(6)
Constituency, Dependency, Labeling and Ordering	7	(24)
Equivalence in SGC in Terms of Isomorphisms	7	(1)
Relevant Functions and Relations	8	(1)
Interpretation Domains: the Case of Constituent Structure	9	(2)
Interpretation Functions	11	(1)
Advantages of the Approach	12	(3)
Explicitness	13	(1)
Alternate Definitions	13	(2)
General Applicability	15	(1)
Labeled Constituent Structure	15	(2)
Linear Order	17	(1)
An Interpretation Domain for Dependency	18	(2)
Simple Dependency Grammars	20	(1)
An Interpretation Function for Dependency for DGs	21	(1)
Ordering properties of DGs	22	(1)
Constituent Structures Expressed by DGs	22	(2)
Interdependence of Constituency and Dependency Interpretations for DGs	24	(1)
Expressibility of Dependency by CFGs	25	(1)
Legitimate Interpretation Functions	26	(5)
Strong Generative Capacity: the Semantics of Linguistic Formalism	31	(20)
SGC of a Grammar G with respect to an Interpretation Domain IDi	31	(1)
SGC of a Theory T with respect to an Interpretation Domain IDi	32	(2)
SGC of Grammar G with respect to a Tuple of Interpretation Domain ⟨ID1,...,IDn⟩	34
SGC of a Theory T with respect to a Tuple of Interpretation Domains ⟨ID1,...,IDn⟩	35
Analogy with Model-theoretic Semantics	35	(1)
Comparing Grammars and Theories in SGC	36	(5)
Equivalence	36	(3)
Inclusion	39	(2)
Interpreting Sets of Structural Descriptions vs. Interpreting Grammars: Ordering in ID/LP Grammars vs. Classical CFGs	41	(3)
What is a Structural Description?	44	(5)
Structural Descriptions in TAGs	45	(2)
The Configurational Definition of Grammatical Relations	47	(2)
Conclusion	49	(2)
Constituency, Dependency, Ordering, and Endocentricity in Phrase Structure Grammars	51	(40)
Phrase Structure Grammars and Dependency	51	(24)
Marked Context Free Grammars (MCFGs)	51	(4)
Weakly Marked CFGs (WMCFGs)	55	(2)
Strongly Marked CFGs (SMCFGs)	57	(9)
X-bar Grammars	66	(8)
The Expressive Power of DGs and CFGs	74	(1)
Discontinuous Constituency in Phrase Structure Grammars	75	(8)
Introduction	75	(5)
Liberation Grammars	80	(1)
Comparison in SGC	81	(2)
Endocentricity	83	(8)
Expression of Endocentricity in CFGs	83	(3)
Expression of Endocentricity in MCFGs	86	(2)
Expression of endocentricity in XBGs	88	(1)
A Note on Adjunction and Rule-Schemata with Kleene Stars in CFGs	88	(3)
Aspects of the Strong Generative Capacity of Categorial Grammars	91	(14)
Legitimate Interpretations of Simple Categorial Grammars	91	(5)
Simple Categorial Grammars	91	(1)
Constituency and Labeling	92	(1)
Endocentricity	93	(1)
Functor-Argument Structure	94	(1)
Dependency	95	(1)
The SGC of Simple Categorial Grammars	96	(9)
Constituency	97	(4)
Dependency	101	(2)
Endocentricity	103	(2)
Linking System	105	(34)
Introduction	105	(5)
Constituent Addresses and Node Addresses	107	(1)
Empty Constituents	108	(1)
Constraints between Linking and Constituency	109	(1)
Command Constraints on Links	109	(1)
Linking Systems for Filler-gap Dependencies	110	(1)
Linking Systems for Filler-gap Dependencies in GPSG	111	(6)
Linking Systems for Filler-gap Dependencies in Parenthesis-free CGs	117	(4)
Linking Systems for Filler-gap Dependencies in TGs	121	(2)
Linking Systems without Gaps: LFG and HPSG-3	123	(3)
Linking Systems for Filler-gap Dependencies in EPSGs with Stacks of Slash Features	126	(11)
Introduction	126	(4)
Indexed Grammars of Type IGa	130	(2)
Indexed Grammars of Type IGb	132	(3)
Indexed Grammars of Type IGc	135	(2)
Multisets as Values for SLASH Features	137	(1)
Some Further Perspectives on Linking Systems	137	(2)
Conclusion	139	(6)
References	145	(8)
Index of Subjects and Abbreviations	153	(6)
Index of Names	159