Defeasible Semantics for L4
The importance of defeasibility for legal reasoning has been investigated for a long time (see among other [10, 3, 11]). This notion mostly concerns the issue that textual provisions of (legal) norms typically provide prima facie conditions for their applicability, but to understand a norm in full, we have to evaluate the norms in the context in which the norm is used and to see if other norms prevent it either to apply or to be effective. In other words, when evaluating norms, we must account for possible (prima facie) conflicts and exceptions. Indeed, in general, norms first provide the basic conditions for their applicability. Then, they give the exceptions and exclusions (and they can go on, with exceptions/exclusions of the exceptions/exclusions and so on).
The first issue to address to model legal reasoning is how to model norms. Here, we follow the approach of [12, 4] and stipulate that a norm is represented by an “IF · · · THEN . . .” rule, where the IF part establishes the conditions of applicability of the norm and the THEN part specifies the legal effect of the norm. Where the legal effect of the norm is either that a proposition is taken to hold legally or that a legal requirement (obligation, prohibition, permission) is in force. Moreover, as we have alluded to, the norms are defeasible; thus, the IF/THEN conditional used to model legal norms does not correspond to the material implication of classical logic, and it has a non-monotonic nature. Several approaches have been proposed to reduce or compile the normative IF/THEN conditional. However, in general, as discussed by [13, 8], they suffer from some limitations; for example, the translation to classical propositional logic requires complete knowledge (for any atomic proposition, we have to determine whether it is true or not), it is not resilient to contradictions, and changes to the norms might require a complete rewriting of the translation.
In this work, we are going to examine how to provide an effective and constructive non-monotonic interpretation of (a restricted version of) L4 based on Answer Set Programming (ASP) meta-program. The meta-program gives the semantics of the underlying L4 constructs as well as a computational framework for them.