Origins. The first type theory to appear in print appears to have been Xxxxxxx’x Doctrine of Types [122]. In Xxxxxxx’x own words, it was “put forward tentatively, as affording a possible solution to the contradiction”, the contradiction being what later became known as Xxxxxxx’x Paradox. Stated briefly and paraphrasing Xxxxxxx, “it is meaningless to assert something about all cases of some kind, if from what is said a new case is generated, which both is and is not of the same kind as the cases of which all were concerned”. The most celebrated example of Xxxxxxx’x Paradox is the set of all sets w that do not contain themselves as members, i.e. w ≡df {x : x /∈ x}. This fits Xxxxxxx’x description of a statement about all cases of some kind, the kind being sets. Furthermore, the new case that “seems to be generated” is w, which Xxxxxxx asserts “both is and is not of the same kind” as the set of all sets that do not contain themselves as members. In other words, w both is and is not a member of itself. If w is assumed to be a member of itself, it follows that w is not a member of itself, and vice versa: clearly a contradiction. Xxxxxxx eventually formulated a solution to the contradiction by introducing a hierarchy of types, where a type was defined as the collection of values for which a function has values, the principle being that “whatever contains an apparent variable must be of a different type from the possible values of that variable”, that is to say it must be of a higher type. As Xxxx describes in his excellent biography [91], Xxxxxxx’x preoccupation with the contradiction was an all consuming affair, which led to a long period of introspection and self doubt, and hampered his attempts to reconstruct the foundations of mathematics. In establishing the rules of type formation, it is important to consider whether or not it makes sense for a type to be an object of itself. Is it paradoxical? Xxxxxxx clearly thought it was. However, almost seventy years later, Xxxxxx-L¨of, the acknowledged founder of modern type theory, proposed a theory of types for the formalisation of intuitionistic mathematics (later revised in [85] and [83]), based on an “axiom of all types whatsoever, which is at the same time a type and an object of that type”, only to discover the following year, courtesy of a young French mathematician Xxxxxx [58], that his theory was inconsistent. Xxxxxxx’x Doctrine of Types evolved into the Ramified Theory of Types [123], and then thanks to Church, int...
Origins. The industry propelled the creation of a school for higher education in technical fields since the beginning, sponsoring the foundation of the Royal School. Thus, the relationship with the academic world has been always very strong. This has been particularly true between shipping and maritime worlds and the Royal School before and then the Department of Naval Architecture and Marine Engineering. It has been always natural a passage from Navy/Merchant Marine/Shipyards to the University and vice versa. The participation of former students to the life of the University as lecturers has always been a standard. However, since the '90s, this became more constant, in particular due to a strict cooperation with ATENA. ATENA members, being former managers of important shipyards, described to the students their experiences and what they were expected to do in the "outside world".
Origins. ❖ It first appears in Common Law legal systems as a kind of license agreement, based on the concept of «franchise». ❖ »Franchise» is a word coming from ancient franc, with the meaning of »free» or «freedom». To grant a franchise means to allow someone to do something. It implies wider rights than a mere license ❖ Even if embryonic franchising networks showed up in late 19° century (Singer sewing machines) and in the first decades of the 20° (General Motors), this contract type became widespread after WWII, as a consequence of the western economic growth
Origins. Blanchardstown has a strong history of effective interagency working. This has helped to build trust, xxxxxx understanding, develop a shared purpose to complex issues, leadership and clarify roles/responsibilities. This is aligned to best practice interagency co-operation (e.g. Children Acts Advisory Board Guidelines, 2009) In recent years, collaborations in Blanchardstown have become more formalised. A number of the collaborations in Blanchardstown have influenced national policy. For example, the Blanchardstown Interagency Protocol Initiative (BIPI) is acknowledged within the National Drugs Rehabilitation Strategy and the formulation of the National Drugs Rehabilitation Implementation Committee (NDRIC) implementation structure. This more structured approach emerged: To ensure that a clear recorded process of working collaboratively was developed, and To respond to increasing recognition at national level that children/families often require services and supports from different agencies in order to address complex issues To formalise working to prevent the escalation of issues. In early 2009, a number of agencies working with children at risk and their families in the Blanchardstown area identified the need for a formal Interagency Working Agreement (IWA) which would underpin the implementation of effective interagency working. This was to document and to strengthen collaborative approaches. The experience of working with the family focus groups established in Corduff and Mulhuddart in particular helped to inform the process. The focus of the agreement is on children and young people aged up to 18 years in the Mulhuddart/Corduff area of Blanchardstown. These communities were chosen because of the high levels of social exclusion that they experience which has led to a range of prevention and intervention services working with children and young people in these communities.
