204 research outputs found

    Isabelle/DOF: Design and Implementation

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    This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record17th International Conference, SEFM 2019 Oslo, Norway, September 18–20, 2019DOF is a novel framework for defining ontologies and enforcing them during document development and evolution. A major goal of DOF is the integrated development of formal certification documents (e. g., for Common Criteria or CENELEC 50128) that require consistency across both formal and informal arguments. To support a consistent development of formal and informal parts of a document, we provide Isabelle/DOF, an implementation of DOF on top of the formal methods framework Isabelle/HOL. A particular emphasis is put on a deep integration into Isabelleâs IDE, which allows for smooth ontology development as well as immediate ontological feedback during the editing of a document. In this paper, we give an in-depth presentation of the design concepts of DOFâs Ontology Definition Language (ODL) and key aspects of the technology of its implementation. Isabelle/DOF is the first ontology language supporting machine-checked links between the formal and informal parts in an LCF-style interactive theorem proving environment. Sufficiently annotated, large documents can easily be developed collabo- ratively, while ensuring their consistency, and the impact of changes (in the formal and the semi-formal content) is tracked automatically.IRT SystemX, Paris-Saclay, Franc

    Logical operators for ontological modeling

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    We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment needed for their formalization, and even simplify their logical formulation

    A type-theoretical approach for ontologies: The case of roles

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    International audienceIn the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem. Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this gap, we present in this paper a theory for representing ontologies in a dependently-typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation

    A Monadic Second-Order Version of Tarski’s Geometry of Solids

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    In this paper, we are concerned with the development of a general set theory using the single axiom version of Leśniewski’s mereology. The specification of mereology, and further of Tarski’s geometry of solids will rely on the Calculus of Inductive Constructions (CIC). In the first part, we provide a specification of Leśniewski’s mereology as a model for an atomless Boolean algebra using Clay’s ideas. In the second part, we interpret Leśniewski’s mereology in monadic second-order logic using names and develop a full version of mereology referred to as CIC-based Monadic Mereology (λ-MM) allowing an expressive theory while involving only two axioms. In the third part, we propose a modeling of Tarski’s solid geometry relying on λ-MM. It is intended to serve as a basis for spatial reasoning. All parts have been proved using a translation in type theory

    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

    Isabelle/DOF. User and Implementation Manual

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    The software for which this is the manual is available via the DOI in this recordIsabelle/DOF provides an implementation of DOF on top of Isabelle/HOL. DOF itself is a novel framework for defining ontologies and enforcing them during document development and document evolution. Isabelle/DOF targets use-cases such as mathematical texts referring to a theory development or technical reports requiring a particular structure. A major application of DOF is the integrated development of formal certification documents (e.g., for Common Criteria or CENELEC 50128) that require consistency across both formal and informal arguments. Isabelle/DOF is integrated into Isabelle’s IDE, which allows for smooth ontology development as well as immediate ontological feedback during the editing of a document. Its checking facilities leverage the collaborative development of documents required to be consistent with an underlying ontological structure. In this user-manual, we give an in-depth presentation of the design concepts of DOF’s Ontology Definition Language (ODL) and describe comprehensively its major commands. Many examples show typical best-practice applications of the system. Isabelle/DOF is the first ontology language supporting machine-checked links between the formal and informal parts in an LCF-style interactive theorem proving environment.IRT System

    Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

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    A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure

    Handling domain knowledge in system design models. An ontology based approach.

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    Complex systems models are designed in heterogeneous domains and this heterogeneity is rarely considered explicitly when describing and validating processes. Moreover, these systems usually involve several domain experts and several design models corresponding to different analyses (views) of the same system. However, no explicit information regarding the characteristics neither of the domain nor of the performed system analyses is given. In our thesis, we propose a general framework offering first, the formalization of domain knowledge using ontologies and second, the capability to strengthen design models by making explicit references to the domain knowledgeformalized in these ontology. This framework also provides resources for making explicit the features of an analysis by formalizing them within models qualified as ‘’points of view ‘’. We have set up two deployments of our approach: a Model Driven Engineering (MDE) based deployment and a formal methods one based on proof and refinement. This general framework has been validated on several no trivial case studies issued from system engineering

    -ilities Tradespace and Affordability Project – Phase 3

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    One of the key elements of the SERC’s research strategy is transforming the practice of systems engineering and associated management practices – “SE and Management Transformation (SEMT).” The Grand Challenge goal for SEMT is to transform the DoD community’s current systems engineering and management methods, processes, and tools (MPTs) and practices away from sequential, single stovepipe system, hardware-first, document-driven, point- solution, acquisition-oriented approaches; and toward concurrent, portfolio and enterprise- oriented, hardware-software-human engineered, model-driven, set-based, full life cycle approaches.This material is based upon work supported, in whole or in part, by the U.S. Department of Defense through the Office of the Assistant Secretary of Defense for Research and Engineering (ASD(R&E)) under Contract H98230-08- D-0171 (Task Order 0031, RT 046).This material is based upon work supported, in whole or in part, by the U.S. Department of Defense through the Office of the Assistant Secretary of Defense for Research and Engineering (ASD(R&E)) under Contract H98230-08- D-0171 (Task Order 0031, RT 046)
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