Implementation of Defeasible Deontic Logic in ASP (clingo).

This is the first working version of an ASP implementation of Defeasible Deontic Logic. The implementation covers Obligations, Permisions, and Compensatory Obligations. Currently, the language is restricted to defeasible rules (constitutive, prescriptive and permissive).

A rule

label: a_1, ... , a_n, OBL(o_1), ... OBL(o_m), PERM(p_1), ... PERM(p_k) =>X head

is represented by the clauses

<type>Rule(label, head).
applicable(label, head) :-
    defeasible(a_1), ...  defeasible(a_n),
    obligation(o_1), ...  obligation(o_m),
    permission(p_1), ...  permission(p_k).

where <type> is a placeholder for constitutive, prescriptive or permissive according to the value of X.

For a prescriptive rule if head is not a single element, i.e.,

head =  c_1, c_2, ..., c_w

The head is represented by a set of clauses

compensate(label, c_n, c_n+1, n).

For constitutiveRule, it is possible to add

convertObligation(label, head) :-
    obligatoin(a_1), ... obligation(a_n).
convertPermission(label, head) :-
    permission(a_1), ... permission(a_n).

provided {a_1, ..., a_n} is not empty and there are no obligations or permissions in the antecedent of the rule.

Instances of the superiority relation are caputured by

superior(r,s). 
inferior(r,s). 

All the atomic propositions appearing in a theory must be declared by

atom(atomic_proposition).