Dimensions of Neural-symbolic Integration - A Structured Survey

Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks) has reached a critical mass which enables the community to strive for applicable implementations and use cases. Recent work has covered a great variety of logics used in artificial intelligence and provides a multitude of techniques for dealing with them within the context of artificial neural networks. We present a comprehensive survey of the field of neural-symbolic integration, including a new classification of system according to their architectures and abilities.Comment: 28 page

Institutionalising Ontology-Based Semantic Integration

We address what is still a scarcity of general mathematical foundations for ontology-based semantic integration underlying current knowledge engineering methodologies in decentralised and distributed environments. After recalling the first-order ontology-based approach to semantic integration and a formalisation of ontological commitment, we propose a general theory that uses a syntax-and interpretation-independent formulation of language, ontology, and ontological commitment in terms of institutions. We claim that our formalisation generalises the intuitive notion of ontology-based semantic integration while retaining its basic insight, and we apply it for eliciting and hence comparing various increasingly complex notions of semantic integration and ontological commitment based on differing understandings of semantics

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Neurons and symbols: a manifesto

We discuss the purpose of neural-symbolic integration including its principles, mechanisms and applications. We outline a cognitive computational model for neural-symbolic integration, position the model in the broader context of multi-agent systems, machine learning and automated reasoning, and list some of the challenges for the area of neural-symbolic computation to achieve the promise of effective integration of robust learning and expressive reasoning under uncertainty

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration

On the mathematical and foundational significance of the uncountable

We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindel\"of lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindel\"of property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. $[0,1]$ as 'almost finite', while the latter allows one to treat uncountable sets like e.g. $\mathbb{R}$ as 'almost countable'. This reduction of the uncountable to the finite/countable turns out to have a considerable logical and computational cost: we show that the aforementioned lemmas, and many related theorems, are extremely hard to prove, while the associated sub-covers are extremely hard to compute. Indeed, in terms of the standard scale (based on comprehension axioms), a proof of these lemmas requires at least the full extent of second-order arithmetic, a system originating from Hilbert-Bernays' Grundlagen der Mathematik. This observation has far-reaching implications for the Grundlagen's spiritual successor, the program of Reverse Mathematics, and the associated G\"odel hierachy. We also show that the Cousin lemma is essential for the development of the gauge integral, a generalisation of the Lebesgue and improper Riemann integrals that also uniquely provides a direct formalisation of Feynman's path integral.Comment: 35 pages with one figure. The content of this version extends the published version in that Sections 3.3.4 and 3.4 below are new. Small corrections/additions have also been made to reflect new development

Designing Improved Sediment Transport Visualizations

Monitoring, or more commonly, modeling of sediment transport in the coastal environment is a critical task with relevance to coastline stability, beach erosion, tracking environmental contaminants, and safety of navigation. Increased intensity and regularity of storms such as Superstorm Sandy heighten the importance of our understanding of sediment transport processes. A weakness of current modeling capabilities is the ability to easily visualize the result in an intuitive manner. Many of the available visualization software packages display only a single variable at once, usually as a two-dimensional, plan-view cross-section. With such limited display capabilities, sophisticated 3D models are undermined in both the interpretation of results and dissemination of information to the public. Here we explore a subset of existing modeling capabilities (specifically, modeling scour around man-made structures) and visualization solutions, examine their shortcomings and present a design for a 4D visualization for sediment transport studies that is based on perceptually-focused data visualization research and recent and ongoing developments in multivariate displays. Vector and scalar fields are co-displayed, yet kept independently identifiable utilizing human perception\u27s separation of color, texture, and motion. Bathymetry, sediment grain-size distribution, and forcing hydrodynamics are a subset of the variables investigated for simultaneous representation. Direct interaction with field data is tested to support rapid validation of sediment transport model results. Our goal is a tight integration of both simulated data and real world observations to support analysis and simulation of the impact of major sediment transport events such as hurricanes. We unite modeled results and field observations within a geodatabase designed as an application schema of the Arc Marine Data Model. Our real-world focus is on the Redbird Artificial Reef Site, roughly 18 nautical miles offshor- Delaware Bay, Delaware, where repeated surveys have identified active scour and bedform migration in 27 m water depth amongst the more than 900 deliberately sunken subway cars and vessels. Coincidently collected high-resolution multibeam bathymetry, backscatter, and side-scan sonar data from surface and autonomous underwater vehicle (AUV) systems along with complementary sub-bottom, grab sample, bottom imagery, and wave and current (via ADCP) datasets provide the basis for analysis. This site is particularly attractive due to overlap with the Delaware Bay Operational Forecast System (DBOFS), a model that provides historical and forecast oceanographic data that can be tested in hindcast against significant changes observed at the site during Superstorm Sandy and in predicting future changes through small-scale modeling around the individual reef objects

Reclaiming human machine nature

Extending and modifying his domain of life by artifact production is one of the main characteristics of humankind. From the first hominid, who used a wood stick or a stone for extending his upper limbs and augmenting his gesture strength, to current systems engineers who used technologies for augmenting human cognition, perception and action, extending human body capabilities remains a big issue. From more than fifty years cybernetics, computer and cognitive sciences have imposed only one reductionist model of human machine systems: cognitive systems. Inspired by philosophy, behaviorist psychology and the information treatment metaphor, the cognitive system paradigm requires a function view and a functional analysis in human systems design process. According that design approach, human have been reduced to his metaphysical and functional properties in a new dualism. Human body requirements have been left to physical ergonomics or "physiology". With multidisciplinary convergence, the issues of "human-machine" systems and "human artifacts" evolve. The loss of biological and social boundaries between human organisms and interactive and informational physical artifact questions the current engineering methods and ergonomic design of cognitive systems. New developpment of human machine systems for intensive care, human space activities or bio-engineering sytems requires grounding human systems design on a renewed epistemological framework for future human systems model and evidence based "bio-engineering". In that context, reclaiming human factors, augmented human and human machine nature is a necessityComment: Published in HCI International 2014, Heraklion : Greece (2014