Variants of Temporal Defeasible Logics for Modelling Norm Modifications Guido Governatori 1∗ , Antonino Rotolo 2† , Régis Riveret 2† , Monica Palmirani 2† , Giovanni Sartor 2† 1 School of ITEE, The University of Queensland, Brisbane, Australia 2 CIRSFID and Law Faculty, University of Bologna, Italy guido@itee.uq.edu.au,{rotolo, rriveret, palmiran,sartor}@cirsfid.unibo.it ABSTRACT This paper proposes some variants of Temporal Defeasible Logic (TDL) to reason about normative modifications. These variants make it possible to differentiate cases in which, for example, mod- ifications at some time change legal rules but their conclusions per- sist afterwards from cases where also their conclusions are blocked. 1. BACKGROUND AND MOTIVATION This paper presents some variants of Temporal Defeasible Logic (TDL) [5, 4] to reason about different aspects of norm modifica- tions. The issues discussed in this paper are similar to those as- sumed in [5], namely: (1) to reason about conditional modifica- tions of conditional normative provisions, where the former ones apply under, and are conditioned to, the occurrence of some uncer- tain events; (2) to identify criteria for detecting and solving con- flicts between textual modifications; (3) to clarify the specific role played by the temporal dimension in modelling norm modification processes. The novelty of this work is that we are interested in defining different temporal constraints according to which the ele- ments of a normative system, and the conclusions that follow from them, can, or cannot persist over time. Indeed, several options are available, and each of them corresponds to a specific way through which norm modifications can take place and behave. Norm applications and modifications take place along the axis of time. In particular, a rule is represented at least as (a t ⇒ b t ′ ) : t ′′ , where instants t and t ′ indicate the time at which a and b hold, while t ′′ is the time when the rule is in force. A temporal model should allow us to give an accurate account of the dynamics of norms and therefore to manage legal modifications consistently with le- gal principles [10]. A legal system is defined as a set of documents fixed at a time t and which have been issued by an authority and whose validity de- ∗ Supported by the Australian Research Council under the Discov- ery Project DP0558854. † Supported by the European project for Standardized Transpar- ent Representations in order to Extend Legal Accessibility (ES- TRELLA, IST-4-027655). Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ICAIL ’07, June 4-8, 2007, Palo Alto, CA USA. Copyright 2007 ACM 978-1-59593-680-6 ...$5.00. pends on rules that determine, for any given time, whether a single document belongs to the system. Formally: LS(t )= D 1 (t ), D 2 (t ), D 3 (t ),..., D m (t ) where m ∈ N, D i denotes documents and t is a fixed time in a dis- crete representation. A normative system, in turn, takes the doc- uments belonging to a legal system and organises them to reflect their evolution over time. A normative system should therefore be defined as a particular discrete time-series of legal systems that evolves over time. In formal terms: NS = LS(t 1 ), LS(t 2 ), LS(t 3 ),..., LS(t j ), j ∈ N. The passage from a legal system to another legal system is ef- fected either by normative modifications or by simple persistence. However, norm-modifying provisions, too, belong to legal systems, and, as other legal provisions, they can be seen as conditional state- ments. Accordingly, also modifications have three temporal dimen- sions, these being attached to the conditions, to the effects, and to the overall conditional. These temporal dimensions refer to the effi- cacy, applicability, and force of the provision, respectively. Further- more, one has to consider the time of observability of the normative system. Consider a law r of 2001 nullified in 2005: the change af- fects the entire normative system because the legal text is removed from the system as if it had never been there in the first place (ex- tunc removal). The same would happen, e.g., with a temporary law decree that does not pass into law or with a retroactive abrogation [7]. The peculiarity of system changes shows up when we query the system to retrieve information from it: if today (e.g., 2007) we ask for all the laws in force in 2001, law r will not turn up and the system will look as if that law had never been in force in the first place. But if we enter the query as if we were in 2001, when the an- nulment had not yet occurred, law r will show up as being in force, and the entire system will reflect that fact. This difference depends on the temporal point of view from which we query the system and this refers to the time of observability of a normative system. It is possible to identify different kinds of normative conditional in a temporal setting, and so different ways of how normative mod- ifications temporally affect the normative system [6, 5]. For ex- ample, we can distinguish between persistent and transient rules: the former, if applicable, permit to infer literals that persist unless some other, subsequent, and incompatible events or states of affairs terminate them; the latter allow for the inference of literals which hold on the condition and only while the antecedents of these rules hold. But these characterisation of transiency and persistency pro- vides only a partial picture of how things can or cannot evolve over time. Persistency is a notion which need to be linked with a specific temporal perspective. Consider the following legal provisions r 1 : (a 10 ⇒ b 10 ) : 10 r 2 : (b 10 ⇒ c 10 ) : 10 © ACM 2007. This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 11th International Conference on Artificial Intelligence and Law. June 4–8 2007, Palo Alto, CA, USA. ISBN: 1-59593-303-4.www.acm.org