56 research outputs found

    Set Unification

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    The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature--and properly revisited and analyzed--and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI1 unification and a new simpler algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of Logic Programming (TPLP

    Third International Conference on Technologies for Music Notation and Representation TENOR 2017

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    The third International Conference on Technologies for Music Notation and Representation seeks to focus on a set of specific research issues associated with Music Notation that were elaborated at the first two editions of TENOR in Paris and Cambridge. The theme of the conference is vocal music, whereas the pre-conference workshops focus on innovative technological approaches to music notation

    Abstract Representation of Music: A Type-Based Knowledge Representation Framework

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    The wholesale efficacy of computer-based music research is contingent on the sharing and reuse of information and analysis methods amongst researchers across the constituent disciplines. However, computer systems for the analysis and manipulation of musical data are generally not interoperable. Knowledge representation has been extensively used in the domain of music to harness the benefits of formal conceptual modelling combined with logic based automated inference. However, the available knowledge representation languages lack sufficient logical expressivity to support sophisticated musicological concepts. In this thesis we present a type-based framework for abstract representation of musical knowledge. The core of the framework is a multiple-hierarchical information model called a constituent structure, which accommodates diverse kinds of musical information. The framework includes a specification logic for expressing formal descriptions of the components of the representation. We give a formal specification for the framework in the Calculus of Inductive Constructions, an expressive logical language which lends itself to the abstract specification of data types and information structures. We give an implementation of our framework using Semantic Web ontologies and JavaScript. The ontologies capture the core structural aspects of the representation, while the JavaScript tools implement the functionality of the abstract specification. We describe how our framework supports three music analysis tasks: pattern search and discovery, paradigmatic analysis and hierarchical set-class analysis, detailing how constituent structures are used to represent both the input and output of these analyses including sophisticated structural annotations. We present a simple demonstrator application, built with the JavaScript tools, which performs simple analysis and visualisation of linked data documents structured by the ontologies. We conclude with a summary of the contributions of the thesis and a discussion of the type-based approach to knowledge representation, as well as a number of avenues for future work in this area

    Supporting the DSL Spectrum

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    A language tailored to the problem domain can focus on its idioms and jargon, avoiding clumsy, overly general constructs needed to support general-purpose language. The leverage provided by DSLs over conventional programming languages is often extreme; application engineers may specify as little as 2% of the code that one would need to program the same thing in a conventional programming language! But commitment to a DSL approach can be rather expensive. It is often difficult to know when to invest in exactly how much infrastructure support for a product or product family. All of the concerns that are germane to generalpurpose programming language design and support may become important in the support of a specific DSL. At the same time, there is a wide spectrum of approaches to providing DSL support. This paper relates the various DSL design approaches to alternatives for tool support, providing a kind of “DSL tool support selection framework,” indicating where one might expect to need to invest heavily to obtain adequate support and illustrating the spectrum of tradeoffs and situations in which each is appropriate

    Pseudo-contractions as Gentle Repairs

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    Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

    Topics in Programming Languages, a Philosophical Analysis through the case of Prolog

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    [EN]Programming languages seldom find proper anchorage in philosophy of logic, language and science. is more, philosophy of language seems to be restricted to natural languages and linguistics, and even philosophy of logic is rarely framed into programming languages topics. The logic programming paradigm and Prolog are, thus, the most adequate paradigm and programming language to work on this subject, combining natural language processing and linguistics, logic programming and constriction methodology on both algorithms and procedures, on an overall philosophizing declarative status. Not only this, but the dimension of the Fifth Generation Computer system related to strong Al wherein Prolog took a major role. and its historical frame in the very crucial dialectic between procedural and declarative paradigms, structuralist and empiricist biases, serves, in exemplar form, to treat straight ahead philosophy of logic, language and science in the contemporaneous age as well. In recounting Prolog's philosophical, mechanical and algorithmic harbingers, the opportunity is open to various routes. We herein shall exemplify some: - the mechanical-computational background explored by Pascal, Leibniz, Boole, Jacquard, Babbage, Konrad Zuse, until reaching to the ACE (Alan Turing) and EDVAC (von Neumann), offering the backbone in computer architecture, and the work of Turing, Church, Gödel, Kleene, von Neumann, Shannon, and others on computability, in parallel lines, throughly studied in detail, permit us to interpret ahead the evolving realm of programming languages. The proper line from lambda-calculus, to the Algol-family, the declarative and procedural split with the C language and Prolog, and the ensuing branching and programming languages explosion and further delimitation, are thereupon inspected as to relate them with the proper syntax, semantics and philosophical élan of logic programming and Prolog

    3D Composer: A Software for Micro-composition

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    The aim of this compositional research project is to find new paradigms of expression and representation of musical information, supported by technology. This may further our understanding of how artistic intention materialises during the production of a musical work. A further aim is to create a software device, which will allow the user to generate, analyse and manipulate abstract musical information within a multi-dimensional environment. The main intent of this software and composition portfolio is to examine the process involved during the development of a compositional tool to verify how transformations applied to the conceptualisation of musical abstraction will affect musical outcome, and demonstrate how this transformational process would be useful in a creative context. This thesis suggests a reflection upon various technological and conceptual aspects within a dynamic multimedia framework. The discussion situates the artistic work of a composer within the technological sphere, and investigates the role of technology and its influences during the creative process. Notions of space are relocated in the scope of a personal compositional direction in order to develop a new framework for musical creation. The author establishes theoretical ramifications and suggests a definition for micro-composition. The main aspect focuses on the ability to establish a direct conceptual link between visual elements and their correlated musical output, ultimately leading to the design of a software called 3D-Composer, a tool for the visualisation of musical information as a means to assist composers to create works within a new methodological and conceptual realm. Of particular importance is the ability to transform musical structures in three-dimensional space, based on the geometric properties of micro-composition. The compositions Six Electroacoustic Studies and Dada 2009 display the use of the software. The formalisation process was derived from a transposition of influences of the early twentieth century avant-garde period, to a contemporary digital studio environment utilising new media and computer technologies for musical expression

    Acta Cybernetica : Volume 16. Number 4.

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    Guide to Discrete Mathematics

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