Forgetting Atoms and Arguments

From International Center for Computational Logic

Forgetting Atoms and Arguments

Talk by Matti Berthold
Whereas the operation of forgetting has recently seen a considerable amount of attention in the context of Answer Set Programming (ASP), most of it has focused on theoretical aspects, leaving the practical issues largely untouched. Recent studies include results about what sets of properties operators should satisfy, as well as the abstract characterization of several operators and their theoretical limits. However, no concrete operators have been investigated.

We address this issue by presenting the first concrete operator that satisfies strong persistence (SP) - a property that seems to best capture the essence of forgetting in the context of ASP - whenever this is possible, and many other important properties. The operator is syntactic, limiting the computation of the forgetting result to manipulating the rules in which the atoms to be forgotten occur, naturally yielding a forgetting result that is close to the original program. Whenever (SP) cannot be satisfied, it is inevitable to break some relations between the atoms not to be forgotten. Therefore, an alternative to satisfying (SP) only when possible is to enhance the logical language so that all such relations can be maintained after the forgetting operation. We borrow from the recently introduced notion of fork – a conservative extension of Equilibrium Logic and its monotonic basis, the logic of Here-and-There – which has been shown to be sufficient to overcome the problems related to satisfying (SP). We map this notion into the language of logic programs, enhancing it with so-called anonymous cycles, and we introduce a concrete syntactical forgetting operator over this enhanced language that we show to always obey strong persistence. Research of forgetting in the context of Dung-style argumentation frameworks (AFs) is much less developed. For example, properties that forgetting operators over AFs should satisfy have only been compiled this year. We provide a summery of relevant results and preliminary thoughts on how to proceed in the field.


Short-Bio: Matti Berthold received his B.Sc. in Computer Science at the University of Leipzig, before studying Computational Logic at TU Dresden and FCT NOVA Lisbon. During his studies he had the chance to assist and conduct teaching and publish and present the results of both his theses.


The talk will take place online. If there is any interest in attending, please send an e-mail to thomas.feller@tu-dresden.de.