122 research outputs found
Resource modalities in game semantics
The description of resources in game semantics has never achieved the
simplicity and precision of linear logic, because of a misleading conception:
the belief that linear logic is more primitive than game semantics. We advocate
instead the contrary: that game semantics is conceptually more primitive than
linear logic. Starting from this revised point of view, we design a categorical
model of resources in game semantics, and construct an arena game model where
the usual notion of bracketing is extended to multi- bracketing in order to
capture various resource policies: linear, affine and exponential
Reoccurring patterns in hierarchical protein materials and music: The power of analogies
Complex hierarchical structures composed of simple nanoscale building blocks
form the basis of most biological materials. Here we demonstrate how analogies
between seemingly different fields enable the understanding of general
principles by which functional properties in hierarchical systems emerge,
similar to an analogy learning process. Specifically, natural hierarchical
materials like spider silk exhibit properties comparable to classical music in
terms of their hierarchical structure and function. As a comparative tool here
we apply hierarchical ontology logs (olog) that follow a rigorous mathematical
formulation based on category theory to provide an insightful system
representation by expressing knowledge in a conceptual map. We explain the
process of analogy creation, draw connections at several levels of hierarchy
and identify similar patterns that govern the structure of the hierarchical
systems silk and music and discuss the impact of the derived analogy for
nanotechnology.Comment: 13 pages, 3 figure
Abstract Representation of Music: A Type-Based Knowledge Representation Framework
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
Definitional Functoriality for Dependent (Sub)Types
Dependently-typed proof assistant rely crucially on definitional equality,
which relates types and terms that are automatically identified in the
underlying type theory. This paper extends type theory with definitional
functor laws, equations satisfied propositionally by a large class of
container-like type constructors , equipped with a , such as lists or trees. Promoting these equations to
definitional ones strengthen the theory, enabling slicker proofs and more
automation for functorial type constructors. This extension is used to
modularly justify a structural form of coercive subtyping, propagating
subtyping through type formers in a map-like fashion. We show that the
resulting notion of coercive subtyping, thanks to the extra definitional
equations, is equivalent to a natural and implicit form of subsumptive
subtyping. The key result of decidability of type-checking in a dependent type
system with functor laws for lists has been entirely mechanized in Coq
From Normal Functors to Logarithmic Space Queries
We introduce a new approach to implicit complexity in linear logic, inspired by functional database query languages and using recent developments in effective denotational semantics of polymorphism. We give the first sub-polynomial upper bound in a type system with impredicative polymorphism; adding restrictions on quantifiers yields a characterization of logarithmic space, for which extensional completeness is established via descriptive complexity
Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
Materials in biology span all the scales from Angstroms to meters and typically consist of complex hierarchical assemblies of simple building blocks. Here we describe an application of category theory to describe structural and resulting functional properties of biological protein materials by developing so-called ologs. An olog is like a “concept web” or “semantic network” except that it follows a rigorous mathematical formulation based on category theory. This key difference ensures that an olog is unambiguous, highly adaptable to evolution and change, and suitable for sharing concepts with other olog. We consider simple cases of beta-helical and amyloid-like protein filaments subjected to axial extension and develop an olog representation of their structural and resulting mechanical properties. We also construct a representation of a social network in which people send text-messages to their nearest neighbors and act as a team to perform a task. We show that the olog for the protein and the olog for the social network feature identical category-theoretic representations, and we proceed to precisely explicate the analogy or isomorphism between them. The examples presented here demonstrate that the intrinsic nature of a complex system, which in particular includes a precise relationship between structure and function at different hierarchical levels, can be effectively represented by an olog. This, in turn, allows for comparative studies between disparate materials or fields of application, and results in novel approaches to derive functionality in the design of de novo hierarchical systems. We discuss opportunities and challenges associated with the description of complex biological materials by using ologs as a powerful tool for analysis and design in the context of materiomics, and we present the potential impact of this approach for engineering, life sciences, and medicine.Presidential Early Career Award for Scientists and Engineers (N000141010562)United States. Army Research Office. Multidisciplinary University Research Initiative (W911NF0910541)United States. Office of Naval Research (grant N000141010841)Massachusetts Institute of Technology. Dept. of MathematicsStudienstiftung des deutschen VolkesClark BarwickJacob Luri
Architectural abstraction as transformation of poset labelled graphs
The design of large, complex computer based systems, based on their architecture, will benefit from a formal system that is intuitive, scalable and accessible to practitioners. The work herein is based in graphs which are an efficient and intuitive way of encoding structure, the essence of architecture. A model of system architectures and architectural abstraction is proposed, using poset labelled graphs and their transformations. The poset labelled graph formalism closely models several important aspects of architectures, namely topology, type and levels of abstraction. The technical merits of the formalism are discussed in terms of the ability to express and use domain knowledge to ensure sensible refinements. An abstraction / refinement calculus is introduced and illustrated with a detailed usage scenario. The paper concludes with an evaluation of the formalism in terms of its rigour, expressiveness, simplicity and practicality. © J.UCS
Developing a Knowledge-based System for Complex Geometrical Product Specification (GPS) Data Manipulation.
Geometrical product specification and verification (GPS) matrix system is a universal tool for expressing
geometrical requirements on product design drawings. It benefits product designers through providing
detailed description of functional requirements for geometrical products, and through referring to corresponding
manufacturing and verification processes. In order to overcome current implementation problems
highlighted in this paper, a GPS knowledge base and a corresponding innovative inference
mechanism have been researched, which led to the development of an integrated GPS knowledge-based
system to facilitate rapid and flexible manufacturing requirements. This paper starts with a brief introduction
of GPS, GPS application problems and the project background. It then moves on to demonstrate
a unified knowledge acquisition and representation mechanism based on the category theory (CT) with
five selected examples of this project. The paper concludes with a discussion on the future works for this
projec
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