Distributed First Order Logic

Distributed First Order Logic (DFOL) has been introduced more than ten years ago with the purpose of formalising distributed knowledge-based systems, where knowledge about heterogeneous domains is scattered into a set of interconnected modules. DFOL formalises the knowledge contained in each module by means of first-order theories, and the interconnections between modules by means of special inference rules called bridge rules. Despite their restricted form in the original DFOL formulation, bridge rules have influenced several works in the areas of heterogeneous knowledge integration, modular knowledge representation, and schema/ontology matching. This, in turn, has fostered extensions and modifications of the original DFOL that have never been systematically described and published. This paper tackles the lack of a comprehensive description of DFOL by providing a systematic account of a completely revised and extended version of the logic, together with a sound and complete axiomatisation of a general form of bridge rules based on Natural Deduction. The resulting DFOL framework is then proposed as a clear formal tool for the representation of and reasoning about distributed knowledge and bridge rules

A framework for developing engineering design ontologies within the aerospace industry

This paper presents a framework for developing engineering design ontologies within the aerospace industry. The aim of this approach is to strengthen the modularity and reuse of engineering design ontologies to support knowledge management initiatives within the aerospace industry. Successful development and effective utilisation of engineering ontologies strongly depends on the method/framework used to develop them. Ensuring modularity in ontology design is essential for engineering design activities due to the complexity of knowledge that is required to be brought together to support the product design decision-making process. The proposed approach adopts best practices from previous ontology development methods, but focuses on encouraging modular architectural ontology design. The framework is comprised of three phases namely: (1) Ontology design and development; (2) Ontology validation and (3) Implementation of ontology structure. A qualitative research methodology is employed which is composed of four phases. The first phase defines the capture of knowledge required for the framework development, followed by the ontology framework development, iterative refinement of engineering ontologies and ontology validation through case studies and experts’ opinion. The ontology-based framework is applied in the combustor and casing aerospace engineering domain. The modular ontologies developed as a result of applying the framework and are used in a case study to restructure and improve the accessibility of information on a product design information-sharing platform. Additionally, domain experts within the aerospace industry validated the strengths, benefits and limitations of the framework. Due to the modular nature of the developed ontologies, they were also employed to support other project initiatives within the case study company such as role-based computing (RBC), IT modernisation activity and knowledge management implementation across the sponsoring organisation. The major benefit of this approach is in the reduction of man-hours required for maintaining engineering design ontologies. Furthermore, this approach strengthens reuse of ontology knowledge and encourages modularity in the design and development of engineering ontologies

Modelling the Strategic Alignment of Software Requirements using Goal Graphs

This paper builds on existing Goal Oriented Requirements Engineering (GORE) research by presenting a methodology with a supporting tool for analysing and demonstrating the alignment between software requirements and business objectives. Current GORE methodologies can be used to relate business goals to software goals through goal abstraction in goal graphs. However, we argue that unless the extent of goal-goal contribution is quantified with verifiable metrics and confidence levels, goal graphs are not sufficient for demonstrating the strategic alignment of software requirements. We introduce our methodology using an example software project from Rolls-Royce. We conclude that our methodology can improve requirements by making the relationships to business problems explicit, thereby disambiguating a requirement's underlying purpose and value.Comment: v2 minor updates: 1) bitmap images replaced with vector, 2) reworded related work ref[6] for clarit

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