Babatunde Opeoluwa Akinkunmi

Babatunde Opeoluwa Akinkunmi, Moyin Florence Babalola

Most of the knowledge Representation formalisms developed for representing prescriptive norms can be categorized as either suitable for representing either low level or high level norms.We argue that low level norm representations do not advance the cause of autonomy in agents in the sense that it is not the agent itself that determines the normative position it should be at a particular time, on the account of a more general rule. In other words an agent on some external system for a nitty gritty prescriptions of its obligations and prohibitions. On the other hand, high level norms which have an explicit description of a norm's precondition and have some form of implication, do not as they exist in the literature do not support generalized inferences about violation like low level norm representations do. This paper presents a logical formalism for the representation of high level norms in open societies that enable violation inferences that detail the situation in which the norm violation took place and the identity of the norm violation. Norms are formalized as logic programs whose heads specify what an agent is obliged or permitted to do when a situation arises and within what time constraint of the situation.Each norm is also assigned an identity using some reification scheme. The body of each logic program describes the nature of the situation in which the agent is expected to act or desist from acting. This kind of violation is novel in the literature.

Babatunde Opeoluwa Akinkunmi, Adesoji A. Adegbola

Let two sequences of eventualities x (signifying the sequence, x0,x1, x2,...,xn-1) and y (signifying the sequence, y0, y1, y2,..,yn-1) both recur over the same time interval and it is required to determine whether or not a subinterval exists within the said interval which is a common subinterval of the intervals of occurrence of xp and yq. This paper presents two algorithms for solving the problem. the first explores an arbitrary cycle of the double recurrence for the existence of such an interval. its worst case running time is quadratic. The other algorithm is based on the novel notion of gcd-partitions and has a linear worst case running time. If the eventuality sequence pair (W,z) is a gcd-partition for the double recurrence (x, y),then, from a certain property of gcd-partitions, within any cycle of the double recurrence, there exists r and s such that intervals of occurrence of xp and yq are non-disjoint with the interval of co-occurrence of wr and zs. As such, a coincidence between xp and yq occurs within a cycle of the double recurrence if and only if such r and s exist so that the interval of co-occurrence of wr and zs shares a common interval with the common interval of occurrences of xp and yq. The algorithm systematically reduces the number of wr and zs pairs to be explored in the process of finding the existence of the coincidence.