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Strong generative capacity. The semantics of linguistic formalism. (English) Zbl 0959.68121
CSLI Lecture Notes. 103. Stanford, CA: CSLI Publications. x, 158 p. (1999).
The classical notions of Weak Generative Capacity (WGC) and Strong Generative Capacity (SGC) have been introduced by Noam Chomsky, and they generally correspond to what our intuition tends to linguistically assign to sentences (e.g. strings) and to their corresponding structural descriptions (e.g. trees). The main problem is that two linguistic theories may provide (formal) sentences and/or their structural descriptions which are quite difficult (or merely impossible) to be compared on the basis of Chomsky’s classical definitions of WGC and/or SGC.
One major purpose of the present book is to propose an appropriate SGC definition as the semantic interpretation of a linguistic formalism (theory), in the classical model-theoretical sense. For the new SGC concept, the structural descriptions generated by different formalisms, i.e. linguistic theories, should be interpreted in terms of abstract entities, independent of the considered formalisms, by assigning to a sentence within a given formalism, a certain structural description. Using interpretations on abstract entities, the structural descriptions of linguistic formalisms with crucially different notations may become comparable. Thus, the author offers a semantically-based conception of SGC as the solution to the problem of incommensurability of the structural description sets specified by different linguistic formalisms (theories), and provides appropriate hierarchies for evaluating SGC.
Chapter 2 (Constituency, Dependency, Labeling and Ordering) discusses the SGC equivalence in terms of isomorphisms and introduces a semantics-based technique for analyzing SGC. Notions and results on Dependency Grammars (DGs), Context-Free Grammars (CFGs), their expressibility and dependency aspects are included. Chapter 3 (SGC: the Semantics of Linguistic Formalism) introduces the SGC new definition based on interpretation domains and interpretation functions. There are defined the SGC of a grammar and of theory with respect to a finite number of interpretation domains, pointing out the analogy with the model-theoretic semantics, and showing how grammars and theories can be described in the new SGC context.
Chapter 4 (Constituency, Dependency, Ordering, and Endocentricity in Phrase Structure Grammars – PSGs) considers a number of interesting variants to the classical CFGs and investigates their SGC with respect to constituency, dependency, endocentricity and ordering. Marked CFGs, Weakly Marked CFGs, Strongly Marked CFGs, and X-Bar Grammars (XBGs) are designed to support interpretations in terns of dependency. The expressive power of Liberation Grammars (LGs), Transformational Grammars (TGs), and ID/LP (Immediate Dominance/Linear Precedence) grammars is examined. Chapter 5 (Aspects of SGC of Categorial Grammars – CGs) is devoted to various forms of Generalized CGs and their relationships through SGC. The final Chapter 6 (Linking Systems) introduces a new interpretation domain to be used for linking systems (defined by a structural description as a relation on the constituent structure which it expresses). There are discussed linking systems for filler-gap dependencies in several linguistic theories such as GPSG (Generalized PSGs), parenthesis-free CGs, TGs, LFG (Lexical Functional Grammars), HPSG (Head-driven PSGs), and Extended PSGs with stacks and slash features.
This book is addressed to all those interested in the fundamental aspects of artificial intelligence, computational linguistics, mathematical linguistics, linguistic theories: computer scientists and engineers, mathematicians, linguists, logicians, language philosophers.

68T50 Natural language processing
68-02 Research exposition (monographs, survey articles) pertaining to computer science
03B65 Logic of natural languages
68Q55 Semantics in the theory of computing
68Q42 Grammars and rewriting systems