Instantiation Theory

Instantiation Theory

Author: James G. Williams

Publisher: Springer Science & Business Media

Published: 1991-08-07

Total Pages: 148

ISBN-13: 9783540543336

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Instantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic programming systems. Instantiation theory is the study of instantiation in an abstract context that is applicable to most commonly studied logical formalisms. The volume begins with a survey of general approaches to the study of instantiation, as found in tree systems, order-sorted algebras, algebraic theories, composita, and instantiation systems. A classification of instantiation systems is given, based on properties of substitutions, degree of type strictness, and well-foundedness of terms. Equational theories and the use of typed variables are studied in terms of quotient homomorphisms and embeddings, respectively. Every instantiation system is a quotient system of a subsystem of first-order term instantiation. The general unification algorithm is developed as an application of the basic theory. Its soundness is rigorously proved, and its completeness and efficiency are verfied for certain classes of instantiation systems. Appropriate applications of the algorithm include unification of first-order terms, order-sorted terms, and first-order formulas modulo alpha-conversion, as well as equational unification using simple congruences.


A Metaphysics of Platonic Universals and their Instantiations

A Metaphysics of Platonic Universals and their Instantiations

Author: José Tomás Alvarado

Publisher: Springer Nature

Published: 2020-10-27

Total Pages: 361

ISBN-13: 303053393X

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This book offers a detailed defense of a metaphysics of Platonic universals and a conception of particular objects that is coherent with said metaphysics. The work discusses all the main alternatives in metaphysics of properties and tries to show why universals are the entities that best satisfy the theoretical roles required for a property. The work also explains the advantages of Platonic over Aristotelian universals in the metaphysics of modality and natural laws. Moreover, it is argued that only Platonic universals are coherent with the grounding profile required for universals. The traditional objections against Platonism are discussed and answered. The third part of the book, finally, offers a conception of particular objects as nuclear bundles of tropes that is coherent with the Platonic ontology of universals. This book is of interest to anyone that wants to understand the current –and intricate– debate in metaphysics of properties and its incidence in many other areas in philosophy.


Instantiation

Instantiation

Author: Greg Egan

Publisher: Greg Egan

Published: 2020-01-23

Total Pages: 336

ISBN-13: 1922240311

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Instantiation is a collection of 11 stories by the Hugo award winning author Greg Egan: “The Discrete Charm of the Turing Machine” “Zero For Conduct” “Uncanny Valley” “Seventh Sight” “The Nearest” “Shadow Flock” “Bit Players” “Break My Fall” “3-adica” “The Slipway” “Instantiation”


The Unity of the Proposition

The Unity of the Proposition

Author: Richard Gaskin

Publisher: OUP Oxford

Published: 2008-10-30

Total Pages: 473

ISBN-13: 019155362X

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Richard Gaskin presents a work in the philosophy of language. He analyses what is distinctive about sentences and the propositions they express—what marks them off from mere lists of words and mere aggregates of word-meanings respectively. Since he identifies the world with all the true and false propositions, his account of the unity of the proposition has significant implications for our understanding of the nature of reality. He argues that the unity of the proposition is constituted by a certain infinitistic structure known in the tradition as 'Bradley's regress'. Usually, Bradley's regress has been regarded as vicious, but Gaskin argues that it is the metaphysical ground of the propositional unity, and gives us an important insight into the fundamental make-up of the world.


The Complexity of Creativity

The Complexity of Creativity

Author: Ake E. Andersson

Publisher: Springer Science & Business Media

Published: 2013-12-14

Total Pages: 156

ISBN-13: 9401587884

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This is a volume on the concepts, theories, models and social consequences of creativity. It contains articles by well-known cognitive scientists, economists, mathematicians, philosophers and psychologists.


Structuring Sense: Volume III: Taking Form

Structuring Sense: Volume III: Taking Form

Author: Hagit Borer

Publisher: OUP Oxford

Published: 2013-10-03

Total Pages: 698

ISBN-13: 0191643459

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Structuring Sense explores the difference between words however defined and structures however constructed. It sets out to demonstrate over three volumes that the explanation of linguistic competence should be shifted from lexical entry to syntactic structure, from memory of words to manipulation of rules. Its reformulation of how grammar and lexicon interact has profound implications for linguistic, philosophical, and psychological theories about human mind and language. Hagit Borer departs from language specific constructional approaches and from lexicalist approaches to argue that universal hierarchical structures determine interpretation, and that language variation emerges from the morphological and phonological properties of inflectional material. Taking Form, the third and final volume of Structuring Sense, applies this radical approach to the construction of complex words. Integrating research in syntax and morphology, the author develops a new model of word formation, arguing that on the one hand the basic building blocks of language are rigid semantic and syntactic functions, while on the other hand they are roots, which in themselves are but packets of phonological information, and are devoid of both meaning and grammatical properties of any kind. Within such a model, syntactic category, syntactic selection and argument structure are all mediated through syntactic structures projected from rigid functions, or alternatively, constructed through general combinatorial principles of syntax, such as Chomsky's Merge. The meaning of 'words', in turn, does not involve the existence of lexemes, but rather the matching of a well-defined and phonologically articulated syntactic domain with conceptual Content, itself outside the domain of language as such. In a departure from most current models of syntax but in line with many philosophical traditions, then, the Exo-Skeletal model partitions 'meaning' into formal functions, on the one hand, and Content, on the other hand. While the former are read off syntactico-semantic structures as is usually assumed, Content is crucially read off syntactico-phonological structures.


Radical Construction Grammar

Radical Construction Grammar

Author: William Croft

Publisher: OUP Oxford

Published: 2001-10-25

Total Pages: 448

ISBN-13: 0191544795

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This book is based on the results of research in language typology, and motivated by the need for a theory to explain them. The essence of the approach is (a) that almost all aspects of grammatical structure are language specific, and (b) that language universals are to be found in conceptual structure and in the mapping of conceptual structure on to linguistic form. It proposes intimate links between syntactic and semantic structures, and argues that the basic elements of any language are not syntactic but syntactic-semantic 'Gestalts'. Professor Croft puts forward a new approach to syntactic representation and a new model of how language and languages work. He covers a wide range of syntactic phenomena, illustrating these with examples that show the varied grammatical structures of the world's languages. The book will be accessible all linguists at graduate level and beyond.


The Mathematical Career of Pierre de Fermat, 1601-1665

The Mathematical Career of Pierre de Fermat, 1601-1665

Author: Michael Sean Mahoney

Publisher: Princeton University Press

Published: 1994

Total Pages: 458

ISBN-13: 9780691036663

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Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.


Kinesemiotics

Kinesemiotics

Author: Arianna Maiorani

Publisher: Routledge

Published: 2020-11-30

Total Pages: 147

ISBN-13: 1000264335

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This innovative work introduces the interdisciplinary field of research of kinesemiotics, offering a new adaptable model and means of analysis for understanding forms of movement-based communication, such as dance, that use a codified language shared by a community of users. It begins with a theoretical overview and review of existing literature on the main approaches to movement-based communication, specifically dance, which underpin kinesemiotics as an area of study. It reaffirms previous work which established dance as a form of embodied communication in that it encompasses a wide range of semiotic styles and forms shared by communities of "speakers." In collaboration with the English National Ballet, Maiorani employs the genre of ballet as a means through which to understand and analyse some of the key concepts of kinesemiotics, mainly that of space as a semiotic dimension and "motivated movement," or movement with meaning. Supported by automated movement recognition tools from the fields of bio-robotics engineering and computer science, Maiorani argues for ballet’s capacity, when movements are projected into meaningful space, to extend beyond sequences of physical movements to become a meaning making practice. Kinesemiotics advances interdisciplinary research in the fields of social semiotics, media and communication, multimodality, linguistics, and performance studies and will be of particular interest to students and scholars in these areas.