The logic of enactment (abstract)

In the article, we present a logic of enactment with local reasoning. The basic idea behind this treatment is that sets of aurhorities may enact conilicting normative rules, depending on the frame of reference. The main strength of the presented theory is that we are now able to resson consistently in the presence of inconsistent enacted norms. In most legal support/expert systems only the applicable norms are considered. It is impossible in these systems to talk about the rules that select applicable norms explicitly. This is the main disadvantage of using non-monotonic logic logics with minimal models and argumentation approaches. In these theories we can reason with inconsistent information, but the level is always of applicable norms. One cannot reason about enacted norms which are not applicable. Any derivation using these norms is blocked through the implicit consistency requirement of the non-monotonic modus panens rule. In the paper we give a theory to describe enacted norms and applicable norms separately. This can be seen as naming the minimal models with sets of nuthorifies. Making this explicit in a modal op erator enables us also to reason about enacted norms that are not applicable (within a non-preferred minimal logic). Therefore, we introduce the logic for enactment with local reasoning. In the logic for enactment we treat NA, as a modal operator, with Ai E NA and NA the set of normative authorities. The formula NAP : B is read as ‘the set Ai of normative authorities enacted the norm 8’. The system Ent for enactment with respect to set NA is a restricted version of the system weak 55 or I-D45 (Chellas 1980), in the sense that we are not dealing with nested enactment. On the other hand we add an extra rule to express the relation between sets of authorities: ,,t$ . @. %In system Ent there is a property that is very unrealistic, which nevertheless holds: NA, : B -) ~NA, : 10: consistency of enactments. As we already mentioned in the introduction, it is a frequent phenomenon that authorities enacted conflicting norms. Frank Dignum Eindhoven University of Technology Dept. of Mathematics and Computer Science P.O. box 513, 5600 MB Eindhoven The Netherlands email: dignum@win.tue.nl In the logic of local reasoning (Fagin SC Halpern 1988), there is not necessarily one set of worlds that a set of authorities thinks possible, but rather a number of sets, each one corresponding to a different set of enacted norms. In a given situation, such a set of enacted norms by A; is a ma&ma1 consistent sei of the set EA, of explicitly enacted norms by Ai. The basic idea is that a set of authorities may enact inconsistent norms, but these conflicting norms are not applicable at the same time (depending on the situation). We view a cluster as representing the worlds the set of authorities thinks are possible in a given frame of reference, when he is focusing on a certain set of issues (Royakkers and Dignum 1997). We distinguish weak and strong enactment: Nz, : 8: the set Ai of authorities enacted 0 in a weak sense, i.e. within some cluster considered by A;; N& : 8: the set Ai of authorities enacted B in a strong sense, i.e. within all clusters considered by Ai. A set of authorities may now enact inconsistent norms: Nxi : 0 A Ni : 70 is satisfiable, since in one cluster the set Ai conkiders that 0 is applicable, while in another the set considers 10 applicable. N;, : 0 represents that the set Ai of authorities considers that 0 is applicable in any frame of reference. Thii means that 0 is not conflicting with any other norm enacted by the set Ai of authorities. However, the norm can be conflicting with a norm enacted by a superset Ai of Ai (Ai C Ai)The main advantage of this theory is that expert Systerns can now reason with the use of normal first-order logic within a cluster instead of using nonmonotonic