3.1 CTT as the general framework: informal description
3.1.1 Formalization of knowledge and information
3.1.2 Contexts: formal explanation
The calculus of contexts and environments
There are two specific types
subject to the following rules:
Context formation rules
saying that contexts can be used as types and that we write contexts in brackets.
where , , and. This rule declares the formation of a type under a environment . It is an extension of a context in some environment.
Environment formation rules
where the first bracket expects environments and the second- expects contexts.
This rule can be derived from two rules of computation of environments whose genesis is conceptually crucial to this chapter:
Environment computation rule 1
Environment computation rule 2
To avoid the circularity arising in the formalization of contexts we need some inductive construction called updating. Contexts are hence built by successive updating of the elements in it:
Updating of contexts
Calculus of contexts
Updating of environments
3.2 Representation of knowledge and information
3.2.1 Presuppositions
3.2.2 Assumptions
3.2.3 Types and meaning declarations
3.2.4 Truths and the role of assumptions
3.2.5 Defining information
3.3 Contexts as constructive possible worlds
3.3.1 introducing orderings: Kripke models
3.4 The knowledge framework
3.4.1 Updating information, extending knowledge
3.4.2 The structure of knowledge
Revision on August 4, 2012 at 20:29:50 by
Stephan Alexander Spahn?.
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