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The course timetabling problem can be generally defined as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety of soft constraints and objective functions. Furthermore, the resulting encoding is required to be extensible for capturing new constraints and for switching them between hard and soft, and to be flexible enough to deal with different formulations. In this paper, we propose to make effective use of ASP as a modeling language for course timetabling. We show that our ASP-based approach can naturally satisfy the above requirements, through an ASP encoding of the curriculum-based course timetabling problem proposed in the third track of the second international timetabling competition (ITC-2007). Our encoding is compact and human-readable, since each constraint is individually expressed by either one or two rules. Each hard constraint is expressed by using integrity constraints and aggregates of ASP. Each soft constraint S is expressed by rules in which the head is the form of penalty (S, V, C), and a violation V and its penalty cost C are detected and calculated respectively in the body. We carried out experiments on four different benchmark sets with five different formulations. We succeeded either in improving the bounds or producing the same bounds for many combinations of problem instances and formulations, compared with the previous best known bounds.

Significant inferences
(2000)

Circumscribing inconsistency
(1997)

Compressions and extensions
(1998)

Reiter's default logic is one of the best known and most studied of the approaches to nonmonotonic reasoning. Several variants of default logic have subsequently been proposed to give systems with properties differing from the original. In this paper, we examine the relationship between default logic and its major variants. We accomplish this by translating a default theory under a variant interpretation into a second default theory, under the original Reiter semantics, wherein the variant interpretation is respected. That is, in each case we show that, given an extension of a translated theory, one may extract an extension of the original variant default logic theory. We show how constrained, rational, justified, and cumulative default logic can be expressed in Reiter's default logic. As well, we show how Reiter's default logic can be expressed in rational default logic. From this, we suggest that any such variant can be similarly treated. Consequently, we provide a unification of default logics, showing how the original formulation of default logic may express its variants. Moreover, the translations clearly express the relationships between alternative approaches to default logic. The translations themselves are shown to generally have good properties. Thus, in at least a theoretical sense, we show that these variants are in a sense superfluous, in that for any of these variants of default logic, we can exactly mimic the behaviour of a variant in standard default logic. As well, the translations lend insight into means of classifying the expressive power of default logic variants; specifically we suggest that the property of semi-monotonicity represents a division with respect to expressibility, whereas regularity and cumulativity do not

We present a general approach for representing and reasoning with sets of defaults in default logic, focusing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory, consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritized versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. Also, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semimonotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of a standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension