By Jay C.B.
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Additional info for An introduction to categories in computing
Such a structure where the interpretation of worlds is not considered is sometimes called a K ripke frame. Traditionally, such structures served as interpretation structures for modal logics. The modal operators 0 and 0 have been put on top of traditional logic with the following meanings: • A formula Dcp states that cp must hold in all worlds that are reachable from the current world. • A formula Ocp states that there is a world w' reachable from the current world such that cp holds in w'. 48 3 Basic Notions of System Specification and Modeling Approaches The reachability relation can also be interpreted as a temporal relation: if a state w' is reachable from a state w, then this can be interpreted as w precedes w'.
A system is represented as a collection of interacting objects that evolve over time in a discrete, eventdriven way, and • support the abstract specification of systems according to that perspective. We are trying to combine characteristics of the approaches to the development of complex systems described above in order to come up with a new language that fulfills the following requirements: • The language shall support a problem-oriented way of modeling. That is, we want to model problems and their conceptual solution, but not the implementation of the solution.
Thus, we are able to distinguish instances in a state even if the values of all their observable properties are identical. We must also be able to refer to the same object in different states. • Classification Objects having the same properties and showing the same admissible behavior can be grouped into a class. A similar notion is that of typing although the direction is the opposite: a type describes the potential instances. The currently existing instances form a class of that particular type.
An introduction to categories in computing by Jay C.B.