In this paper, the logical development of Euclidean geometry as presented in Euclid’s Elements, has been studied. Pointing out some gaps in the Euclid arguments, the need for modern axiomatic systems has been explored.

Axiomatic design is one of the design approaches. This approach is established on two axioms: Independence and information axioms. In this approach design matrix is a key concept. It is categorized to three types matrix with name uncoupled, decoupled and coupled design matrix. The uncoupled design matrix satisfies independence axiom. In this paper a new problem is presented in axiomatic design that is named Design Matrix Reconstruction. The recostructability of design relation matrix is investigated in this paper. Design relation matrix is used for presenting the relation between functional requirements and design parameters. For design relation matrix reconstruction, existence of some projections from unknown design matrix is supposed and on this basis some proofs are presented. These proofs show design relation matrix is reconstructible when the projections are consistence together. The design matrix reconstruction is applicable for reverse engineering, design evaluation and design improvement.

Ontological arguments are those arguments which prove God's existence by a preori method through analyzing the concept of God. The first one who represented this kind of arguments was Anselm, the medieval theologian and philosopher. Anselm's argument has always been marked from its proposal (11th century) until now, because of its complexity and ambiguity. There are various versions of this argument, contemporary one of the most important versions of which belongs to Alvin Platinga, the contemporary philosopher and epistemologist. Since axiomatic method is a suitable way to evaluate and criticize an argument through explaining its logical format and specifying its premises, this article is going to introduce it and show the sufficiency of Plantinga's version in proving God's existence through using this method and presenting its exact logical format (by employing both ancient and symbolic logic).

Today, product design has experienced fundamental changes. Design criteria have changed from focusing on product performance to sustainable criteria. This has increased the contrast between traditional and new requirements and consequently increases the design complexity. In this regard, traditional methods are incapable of solving the problems of product design. Therefore, many efforts have been made to solve these challenges to improve the design process. As a result of these efforts, various design methodologies such as multidisciplinary design optimization and knowledge-based engineering were developed. These approaches could support the evolutionary improvement of current product designs or the study of the novel complex product or could reduce the coupling between various FRs and design parameters (DPs). In this article, the authors discuss the effect of using the Axiomatic Design approach in the aircraft conceptual design process. The results obtained in this study indicate the high efficiency of this method in reducing the coupling between the FRs defined for the aircraft, as well as in reducing repetitive activities, thus optimizing the time and cost of the aircraft design process.

Development of virtual research management enterprise architecture (EA) can provide solutions to the current challenges of research management in academic institutions and create necessary capabilities to manage and control the flow of research process among individuals, groups, and institutes. As a new approach to organizational operation, virtual enterprises (VE) introduce new business models and management techniques. The aim of this study is to provide architecture for designing and developing virtual research management based on axiomatic design method. For this purpose, first the design framework has been developed by investigating theoretical principles and using content analysis method. In the next step, the components of research management architecture have been extracted based on proposed framework and using axiomatic design method. Finally by surveying experts, the proposed architecture is validated and its application in an Iranian academic institute has been studied as a case. Proposed architecture in this paper can be used in distributed and dynamic academic research environment. Proposing new methodology for research management enterprise architecture, integrating virtual organization concepts in enterprise architecture design, introducing a methodology for identifying research management system requirements, introducing key components in designing and developing research management based on virtual enterprise are innovation aspects of this research.

In 20th century, Classic Logic allowed logicians to look at Aristotelian Logic from a broader perspective. With the fruition of the studies and research of Lukasiewicz about Aristotelian Logic in the first half of the 20th century, a new path opened for logicians. In the framework of Classic Logic and using its rules and principles, Lukasiewicz introduced Aristotelian syllogisms as Axiomatic System, providing a detailed explanation of his method. In this approach, Barbara and Datisi beside the Identity are axioms; therefore, other moods are deducible by applying these two and borrowing inference rules from Propositional Logic. Later, in the early 1970s, Smiley and Corcoran disagreed with Lukasiewicz’s view. Smiley and Corcoran introduced Aristotelian syllogism as Natural Deduction System, The upcoming research aim is to present reasons based on the deductive nature of the Aristotelian Logical System after introducing each approach and comparing them with Aristotle's statements .

The calculative foundation of mathematical logic is propositional calculus. Propositional calculus consists of two layers: the surface layer which is the approach of truth foundation; and the underlying layer which is the approach of the axiomatic method. In this paper, the underlying layer of interpreting calculus which is the approach to the axiomatic method will be analyzed. In this article, in addition to introducing the axiomatic method, its two fundamental characters are also examined. The first is the common inferential rule. I have tried to make clearer in this part that modus ponens is the inferential essence of retional system on the one hand and is common for all of them on the other. The other characteristic is its ability of plurality. In this article I have also declared that logic as reasoning not only doesnt need axiomatic method but also this approach discard logic its inferential essence and determines it as a special science.

A new algorithm for reconstruction of design relation matrix(DRM) is presented. The reconstruction of an unknown DRM is discussed based on some design matrix projections, which was expressed by design experts. The reconstruction algorithm has been formed based on the new concept of DRM. It shows the relation between functional requirements and design parameters that exists in the related design matrix. The specifications of uncoupled, decoupled and coupled design matrices are scrutinizable by the DRM and related concepts such as design set (DS), design row set (DRS) and design column set (DCS). Then, the DRM reconstruction algorithm and algorithm for selecting the unbiased reconstruction from reconstruction family members are presented based on reconstruct ability analysis. The DRM reconstruction algorithm is applicable in reverse engineering, design evaluation and improvement.