Disjunctive LP+integrity constraints= stable model semantics

We show that stable models of logic programs may be viewed as minimal models of programs that satisfy certain additional constraints. To do so, we transform the normal programs into disjunctive logic programs and sets of integrity constraints. We show that the stable models of the normal program coincide with the minimal models of the disjunctive program thatsatisfy the integrity constraints. As a consequence, the stable model semantics can be characterized using theextended generalized closed world assumption for disjunctive logic programs. Using this result, we develop a bottomup algorithm for function-free logic programs to find all stable models of a normal program by computing the perfect models of a disjunctive stratified logic program and checking them for consistency with the integrity constraints. The integrity constraints provide a rationale as to why some normal logic programs have no stable models.     

Recognition of Simple Enlarged Horn Formulas and Simple Extended Horn Formulas

The enlarged Horn formulas generalize the extended Horn formulas introduced by Chandru and Hooker (1991). Their satisfying truth assignments can be generated with polynomial delay. Unfortunately no polynomial algorithm is known for recognizing enlarged Horn formulas or extended Horn formulas. In this paper we define the class of simple enlarged Horn formulas, a subclass of the enlarged Horn formulas, that contains the simple extended Horn formulas introduced by Swaminathan and Wagner (1995). We present recognition algorithms for the simple enlarged Horn formulas and the simple extended Horn formulas whose complexity is bounded by the complexity of the arborescence-realization problem.     

Incremental reasoning with lazy behavioral subtyping for multiple inheritance

Object-orientation supports code reuse and incremental programming. Multiple inheritance increases the possibilities for code reuse, but complicates the binding of method calls and thereby program analysis. Behavioral subtyping allows program analysis under an open world assumption; i.e., under the assumption that class hierarchies are extensible. However, method redefinition is severely restricted by behavioral subtyping, and multiple inheritance may lead to conflicting restrictions from independently designed superclasses. This paper presents a more liberal approach to incremental reasoning for multiple inheritance under an open world assumption. The approach, based on lazy behavioral subtyping, is well-suited for multiple inheritance, as it incrementally imposes context-dependent behavioral constraints on new subclasses. We first present the approach for a simple language and show how incremental reasoning can be combined with flexible code reuse. Then this language is extended with a hierarchy of interface types which is independent of the class hierarchy. In this setting, flexible code reuse can be combined with modular reasoning about external calls in the sense that each class is analyzed only once. We formalize the approach as a calculus and show soundness for both languages.     

On the Use of an Extended Relational Model to Handle Changing Incomplete Information

In this paper we consider approaches to updating databases containing null values and incomplete information. Our approach distinguishes between modeling incompletely known worlds and modeling changes in these worlds. As an alternative to the open and closed world assumptions, we propose the expanded closed world assumption. Under this assumption, we discuss how to perform updates on databases containing set nulls, marked nulls, and simple conditional tuples, and address some issues of refining incompletely specified information.     

On the computational cost of disjunctive logic programming: Propositional case

This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of well-known semantics, as well as the complexity of deciding whether a propositional formula is satisfied by all models according to a given semantics. We concentrate on finite propositional disjunctive programs with as well as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is ₂ ^p -complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is ₂ ^p -complete; analogous results are derived for the answer sets semantics of extended disjunctive logic programs. Besides, we generalize previously derived complexity results for the generalized closed world assumption and other more sophisticated variants of the closed world assumption. Furthermore, we use the close ties between the logic programming framework and other nonmonotonic formalisms to provide new complexity results for disjunctive default theories and disjunctive autoepistemic literal theories.Parts of the results in this paper appeared in form of an abstract in the Proceedings of the Twelfth ACM SIGACT SIGMOD-SIGART Symposium on Principles of Database Systems (PODS-93), pp. 158–167. Other parts appeared in shortened form in the Proceedings of the International Logic Programming Symposium, Vancouver, October 1993 (ILPS-93), pp. 266–278. MIT Press.     

H 2 design of one-degree-of-freedom decoupling controllers for square plants

Decoupling design of one-degree-of-freedom controllers is treated for the generalised plant model within the H ₂ framework. The class of all realisable closed loop transfer matrices is parametrised under a mild assumption on non-unity feedback sensors. A set of compact assumptions is presented to guarantee the existence of the optimal H ₂ controller. Together with the optimal one, the class of all H ₂ controllers that yield finite H ₂ cost is obtained. The optimal closed transfer matrix and its associated controller are shown to be strictly proper under the reasonable order assumptions on the generalised plant.     

Complexity and undecidability results for logic programming

This paper surveys complexity, degree of uncomputability, and expressive power results for logic programming. Some major decision problem complexity results and other results for logic programming are also covered. It also proves several new results filling in previous gaps in the literature. The paper considers seven logic programming semantics: the van Emden-Kowalski semantics for definite (Horn) logic programs; the perfect model semantics for stratified and for locally stratified logic programs; and the two- and three-valued program completion semantics, the well-founded semantics, and the stable semantics, all for normal logic programs, under skeptical inference. The main results concern expressibility and query complexity/uncomputability in five contexts: for propositional logic programs, for first order logic programs with infinite Herbrand universes on their Herbrand universes (a closed domain assumption), for first order logic programs with infinite Herbrand universes on those universes extended with infinitely many new elements (an open domain assumption), and for logic programs without function or constant symbols evaluated over varying extensional databases (DATALOG-type results, data complexity results only) under both closed and open domain assumptions. Several of the open domain assumption results are new to this paper. Other results surveyed are (1) results about the family of all stable models of a program and (2) decision questions about when a logic program has nice properties with respect to a semantics (e.g., a unique stable model). One decision result, for well-founded semantics, is new to this paper.Work supported in part by NSF grant IRI-8905166.     

Relaxing the homogeneity assumption in usability testing

Much attention has been paid to the question of how many subjects are needed in usability research. Virzi (1992) modelled the accumulation of usability problems with increasing numbers of subjects and claimed that five subjects are sufficient to find most problems. The current paper argues that this answer is based on an important assumption, namely that all types of users have the same probability of encountering all usability problems. If this homogeneity assumption is violated, then more subjects are needed. A modified version of Virzi's model demonstrates that the number of subjects required increases with the number of heterogeneous groups. The model also shows that the more distinctive the groups, the more subjects will be required. This paper will argue that the simple answer 'five' cannot be applied in all circumstances. It most readily applies when the probability that a user will encounter a problem is both high and similar for all users. It also only applies to simple usability tests that seek to detect the presence, but not the statistical prevalence, of usability problems.