5 Some extensions of the model

5.1 Negation

Negation can be captured in two ways. There is the weak negation of simply not being activated (

) and the strong negation of being forced into an inactive state by the structure of the network (

). Weak negation is already included by just taking those parts of the network that are not activated.

Strong negation can be introduced with the introduction of a special node - the absurdum or bottom (). This is a simply a node that must not be activated, acting rather like the ground terminal in electrical circuits. It can either be seen as forcing all nodes that lead to it as inactive or that is activation implies a negative feedback to the present structure (thus weakening or eliminating relations). Negation can now be defined as . This sort of negation is a sort of intuitionistic negation so that, for example, the law of the excluded middle, , does not hold in general.

Bottom here could be used to symbolise different things: falsehood or an action representing negative feedback. In the first instance it could be used to merely indicate strong negation, in the second if bottom was ever activated this could indicate that the arcs leading to it could be removed. This could be done in a variety of ways, consistency resolution (like the "fixes in [6]), negative endorsement [1] or in a manner similar to some neural networks (as surveyed in [5]).

A Simple-Minded Network Model with Context-like Objects - Bruce Edmonds - 13 FEB 97

[Next] [Previous] [Up] [Top] [Contents]

Generated with CERN WebMaker