Temporary Unavailability Logic and General Modification Logic
Wouter Koolen

Abstract:
Modal logics are simple yet expressive devices to talk about
relational structures.  Dynamic modal logics extend standard modal
logics with new operators that upon evaluation alter the subject
relational structure. Sabotage logics are dynamic modal logics,
that crumble the relational structure under the effect of certain new
operators.

This paper first considers the simplest instance of non-caustic
sabotage, namely temporary removal of arbitrary single edges. This
results in the Temporary Unavailability Logic. The complexity of TUL
is subsequently analysed along the lines of [Rhode]. In the next
section we present and motivates a generalisation of TUL called
General Modification Logic or GML. Where TUL deals with temporary
removal of single edges, allowing any individual edge to be removed,
GML abstracts away from the actual way in which the model is altered,
and introduces restricted accessibility between dierent
alterations. The actual underlying mechanism is a variation of product
update. We conclude with a comparison of all treated sabotage logics
and a list of open problems.