Pointers in Recursion: Exploring the Tropics

We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tiering is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras

Parallelism in Soft Linear Logic

We extend the Soft Linear Logic of Lafont with a new kind of modality, called parallel. Contractions on parallel modalities are only allowed in the cut and the left ? rules, in a controlled, uniformly distributive way. We show that SLL, extended with this parallel modality, is sound and complete for PSPACE. We propose a corresponding typing discipline for the ?-calculus, extending the STA typing system of Gaboardi and Ronchi, and establish its PSPACE soundness and completeness. The use of the parallel modality in the cut-rule drives a polynomial-time, parallel call-by-value evaluation strategy of the terms

Parsing Schemata

Parsing schemata provide a general framework for specication, analysis and comparison of (sequential and/or parallel) parsing algorithms. A grammar specifies implicitly what the valid parses of a sentence are; a parsing algorithm specifies explicitly how to compute these. Parsing schemata form a well-defined level of abstraction in between grammars and parsing algorithms. A parsing schema specifies the types of intermediate results that can be computed by a parser, and the rules that allow to expand a given set of such results with new results. A parsing schema does not specify the data structures, control structures, and (in case of parallel processing)\ud communication structures that are to be used by a parser.\ud Part I, Exposition, gives a general introduction to the ideas that are worked out in the following parts.\ud Part II, Foundation, unfolds a mathematical theory of parsing schemata. Different kinds of relations between parsing schemata are formally introduced and illustrated with examples drawn from the parsing literature.\ud Part III, Application, discusses a series of applications of parsing schemata.\ud - Feature percolation in unification grammar parsing can be described in an elegant, legible notation.\ud - Because of the absence of algorithmic detail, parsing schemata can be used to get a formal grip on highly complicated algorithms. We give substance to this claim by means of a thorough analysis of Left-Corner and Head-Corner chart parsing.\ud - As an example of structural similarity of parsers, despite differences in form and appearance, we show that the underlying parsing schemata of Earley's algorithm and Tomita's algorithm are virtually identical. Using this structural correspondence we can obtain a novel parallel parser by cross-fertilizing a parallel Earley parser with Tomita's graph-structured stack.\ud - Parsing schemata can be implemented straightforwardly by boolean circuits. This means that, in principle, parsing schemata can be coded directly into hardware.\ud Part IV, Perspective, discusses the prospects for natural language parsing applications and draws some conclusions. An important observation is that the theoretical and practical part of the book reinforce each other. The proposed framework is abstract enough to allow a thorough mathematical treatment and practical enough to allow rewriting a variety of real parsing algorithms (i.e. seriously proposed in the literature, not toy examples)\ud in a clear and coherent way

Superseded: Grammatical theory: From transformational grammar to constraint-based approaches. Second revised and extended edition.

This book is superseded by the third edition, available at http://langsci-press.org/catalog/book/255. This book introduces formal grammar theories that play a role in current linguistic theorizing (Phrase Structure Grammar, Transformational Grammar/Government & Binding, Generalized Phrase Structure Grammar, Lexical Functional Grammar, Categorial Grammar, Head-​Driven Phrase Structure Grammar, Construction Grammar, Tree Adjoining Grammar). The key assumptions are explained and it is shown how the respective theory treats arguments and adjuncts, the active/passive alternation, local reorderings, verb placement, and fronting of constituents over long distances. The analyses are explained with German as the object language. The second part of the book compares these approaches with respect to their predictions regarding language acquisition and psycholinguistic plausibility. The nativism hypothesis, which assumes that humans posses genetically determined innate language-specific knowledge, is critically examined and alternative models of language acquisition are discussed. The second part then addresses controversial issues of current theory building such as the question of flat or binary branching structures being more appropriate, the question whether constructions should be treated on the phrasal or the lexical level, and the question whether abstract, non-visible entities should play a role in syntactic analyses. It is shown that the analyses suggested in the respective frameworks are often translatable into each other. The book closes with a chapter showing how properties common to all languages or to certain classes of languages can be captured. The book is a translation of the German book Grammatiktheorie, which was published by Stauffenburg in 2010. The following quotes are taken from reviews: With this critical yet fair reflection on various grammatical theories, Müller fills what was a major gap in the literature. Karen Lehmann, Zeitschrift für Rezen­sio­nen zur ger­man­is­tis­chen Sprach­wis­senschaft, 2012 Stefan Müller’s recent introductory textbook, Gram­matik­the­o­rie, is an astonishingly comprehensive and insightful survey for beginning students of the present state of syntactic theory. Wolfgang Sternefeld und Frank Richter, Zeitschrift für Sprach­wissen­schaft, 2012 This is the kind of work that has been sought after for a while [...] The impartial and objective discussion offered by the author is particularly refreshing. Werner Abraham, Germanistik, 2012   This book is a new edition of http://langsci-press.org/catalog/book/25

Superseded: Grammatical theory: From transformational grammar to constraint-based approaches. Second revised and extended edition.

This book is superseded by the third edition, available at http://langsci-press.org/catalog/book/255. This book introduces formal grammar theories that play a role in current linguistic theorizing (Phrase Structure Grammar, Transformational Grammar/Government & Binding, Generalized Phrase Structure Grammar, Lexical Functional Grammar, Categorial Grammar, Head-​Driven Phrase Structure Grammar, Construction Grammar, Tree Adjoining Grammar). The key assumptions are explained and it is shown how the respective theory treats arguments and adjuncts, the active/passive alternation, local reorderings, verb placement, and fronting of constituents over long distances. The analyses are explained with German as the object language. The second part of the book compares these approaches with respect to their predictions regarding language acquisition and psycholinguistic plausibility. The nativism hypothesis, which assumes that humans posses genetically determined innate language-specific knowledge, is critically examined and alternative models of language acquisition are discussed. The second part then addresses controversial issues of current theory building such as the question of flat or binary branching structures being more appropriate, the question whether constructions should be treated on the phrasal or the lexical level, and the question whether abstract, non-visible entities should play a role in syntactic analyses. It is shown that the analyses suggested in the respective frameworks are often translatable into each other. The book closes with a chapter showing how properties common to all languages or to certain classes of languages can be captured. The book is a translation of the German book Grammatiktheorie, which was published by Stauffenburg in 2010. The following quotes are taken from reviews: With this critical yet fair reflection on various grammatical theories, Müller fills what was a major gap in the literature. Karen Lehmann, Zeitschrift für Rezen­sio­nen zur ger­man­is­tis­chen Sprach­wis­senschaft, 2012 Stefan Müller’s recent introductory textbook, Gram­matik­the­o­rie, is an astonishingly comprehensive and insightful survey for beginning students of the present state of syntactic theory. Wolfgang Sternefeld und Frank Richter, Zeitschrift für Sprach­wissen­schaft, 2012 This is the kind of work that has been sought after for a while [...] The impartial and objective discussion offered by the author is particularly refreshing. Werner Abraham, Germanistik, 2012   This book is a new edition of http://langsci-press.org/catalog/book/25

Superseded: Grammatical theory: From transformational grammar to constraint-based approaches. Second revised and extended edition.

This book is superseded by the third edition, available at http://langsci-press.org/catalog/book/255. This book introduces formal grammar theories that play a role in current linguistic theorizing (Phrase Structure Grammar, Transformational Grammar/Government & Binding, Generalized Phrase Structure Grammar, Lexical Functional Grammar, Categorial Grammar, Head-​Driven Phrase Structure Grammar, Construction Grammar, Tree Adjoining Grammar). The key assumptions are explained and it is shown how the respective theory treats arguments and adjuncts, the active/passive alternation, local reorderings, verb placement, and fronting of constituents over long distances. The analyses are explained with German as the object language. The second part of the book compares these approaches with respect to their predictions regarding language acquisition and psycholinguistic plausibility. The nativism hypothesis, which assumes that humans posses genetically determined innate language-specific knowledge, is critically examined and alternative models of language acquisition are discussed. The second part then addresses controversial issues of current theory building such as the question of flat or binary branching structures being more appropriate, the question whether constructions should be treated on the phrasal or the lexical level, and the question whether abstract, non-visible entities should play a role in syntactic analyses. It is shown that the analyses suggested in the respective frameworks are often translatable into each other. The book closes with a chapter showing how properties common to all languages or to certain classes of languages can be captured. The book is a translation of the German book Grammatiktheorie, which was published by Stauffenburg in 2010. The following quotes are taken from reviews: With this critical yet fair reflection on various grammatical theories, Müller fills what was a major gap in the literature. Karen Lehmann, Zeitschrift für Rezen­sio­nen zur ger­man­is­tis­chen Sprach­wis­senschaft, 2012 Stefan Müller’s recent introductory textbook, Gram­matik­the­o­rie, is an astonishingly comprehensive and insightful survey for beginning students of the present state of syntactic theory. Wolfgang Sternefeld und Frank Richter, Zeitschrift für Sprach­wissen­schaft, 2012 This is the kind of work that has been sought after for a while [...] The impartial and objective discussion offered by the author is particularly refreshing. Werner Abraham, Germanistik, 2012   This book is a new edition of http://langsci-press.org/catalog/book/25

Embodiment and Grammatical Structure: An Approach to the Relation of Experience, Assertion and Truth

In this thesis I address a concern in both existential phenomenology and embodied cognition, namely, the question of how ‘higher’ cognitive abilities such as language and judgements of truth relate to embodied experience. I suggest that although our words are grounded in experience, what makes this grounding and our higher abilities possible is grammatical structure. The opening chapter contrasts the ‘situated’ approach of embodied cognition and existential phenomenology with Cartesian methodological solipsism. The latter produces a series of dualisms, including that of language and meaning, whereas the former dissolves such dualisms. The second chapter adapts Merleau-Ponty’s arguments against the perceptual constancy hypothesis in order to undermine the dualism of grammar and meaning. This raises the question of what grammar is, which is addressed in the third chapter. I acknowledge the force of Chomsky’s observation that language is structure dependent and briefly introduce a minimal grammatical operation which might be the ‘spark which lit the intellectual forest fire’ (Clark: 2001, 151). Grammatical relations are argued to make possible the grounding of our symbols in chapters 4 and 5, which attempt to ground the categories of determiner and aspect in spatial deixis and embodied motor processes respectively. Chapter 6 ties the previous three together, arguing that we may understand a given lexeme as an object or as an event by subsuming it within a determiner phrase or aspectualising it respectively. I suggest that such modification of a word’s meaning is possible because determiners and aspect schematise, i.e. determine the temporal structure, of the lexeme. Chapter 7 uses this account to take up Heidegger’s claim that the relation between being and truth be cast in terms of temporality (2006, H349), though falls short of providing a complete account of the ‘origin of truth’. Chapter 8 concludes and notes further avenues of research

Grammatical theory

This book introduces formal grammar theories that play a role in current linguistic theorizing (Phrase Structure Grammar, Transformational Grammar/Government & Binding, Generalized Phrase Structure Grammar, Lexical Functional Grammar, Categorial Grammar, Head-​Driven Phrase Structure Grammar, Construction Grammar, Tree Adjoining Grammar). The key assumptions are explained and it is shown how the respective theory treats arguments and adjuncts, the active/passive alternation, local reorderings, verb placement, and fronting of constituents over long distances. The analyses are explained with German as the object language. The second part of the book compares these approaches with respect to their predictions regarding language acquisition and psycholinguistic plausibility. The nativism hypothesis, which assumes that humans posses genetically determined innate language-specific knowledge, is critically examined and alternative models of language acquisition are discussed. The second part then addresses controversial issues of current theory building such as the question of flat or binary branching structures being more appropriate, the question whether constructions should be treated on the phrasal or the lexical level, and the question whether abstract, non-visible entities should play a role in syntactic analyses. It is shown that the analyses suggested in the respective frameworks are often translatable into each other. The book closes with a chapter showing how properties common to all languages or to certain classes of languages can be captured. The book is a translation of the German book Grammatiktheorie, which was published by Stauffenburg in 2010. The following quotes are taken from reviews: With this critical yet fair reflection on various grammatical theories, Müller fills what was a major gap in the literature. Karen Lehmann, Zeitschrift für Rezen­sio­nen zur ger­man­is­tis­chen Sprach­wis­senschaft, 2012 Stefan Müller’s recent introductory textbook, Gram­matik­the­o­rie, is an astonishingly comprehensive and insightful survey for beginning students of the present state of syntactic theory. Wolfgang Sternefeld und Frank Richter, Zeitschrift für Sprach­wissen­schaft, 2012 This is the kind of work that has been sought after for a while [...] The impartial and objective discussion offered by the author is particularly refreshing. Werner Abraham, Germanistik, 201