The ghosts of forgotten things: A study on size after forgetting

Forgetting is removing variables from a logical formula while preserving the constraints on the other variables. In spite of being a form of reduction, it does not always decrease the size of the formula and may sometimes increase it. This article discusses the implications of such an increase and analyzes the computational properties of the phenomenon. Given a propositional Horn formula, a set of variables and a maximum allowed size, deciding whether forgetting the variables from the formula can be expressed in that size is $D^p$-hard in $\Sigma^p_2$. The same problem for unrestricted propositional formulae is $D^p_2$-hard in $\Sigma^p_3$. The hardness results employ superredundancy: a superirredundant clause is in all formulae of minimal size equivalent to a given one. This concept may be useful outside forgetting

Complexity of Prioritized Default Logics

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories

Complexity of Nested Circumscription and Nested Abnormality Theories

The need for a circumscriptive formalism that allows for simple yet elegant modular problem representation has led Lifschitz (AIJ, 1995) to introduce nested abnormality theories (NATs) as a tool for modular knowledge representation, tailored for applying circumscription to minimize exceptional circumstances. Abstracting from this particular objective, we propose L_{CIRC}, which is an extension of generic propositional circumscription by allowing propositional combinations and nesting of circumscriptive theories. As shown, NATs are naturally embedded into this language, and are in fact of equal expressive capability. We then analyze the complexity of L_{CIRC} and NATs, and in particular the effect of nesting. The latter is found to be a source of complexity, which climbs the Polynomial Hierarchy as the nesting depth increases and reaches PSPACE-completeness in the general case. We also identify meaningful syntactic fragments of NATs which have lower complexity. In particular, we show that the generalization of Horn circumscription in the NAT framework remains CONP-complete, and that Horn NATs without fixed letters can be efficiently transformed into an equivalent Horn CNF, which implies polynomial solvability of principal reasoning tasks. Finally, we also study extensions of NATs and briefly address the complexity in the first-order case. Our results give insight into the ``cost'' of using L_{CIRC} (resp. NATs) as a host language for expressing other formalisms such as action theories, narratives, or spatial theories.Comment: A preliminary abstract of this paper appeared in Proc. Seventeenth International Joint Conference on Artificial Intelligence (IJCAI-01), pages 169--174. Morgan Kaufmann, 200

Redundancy in Logic III: Non-Mononotonic Reasoning

Results about the redundancy of circumscriptive and default theories are presented. In particular, the complexity of establishing whether a given theory is redundant is establihsed.Comment: minor correction

Reason Maintenance - State of the Art

This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques

Proceedings of the Workshop on Linear Logic and Logic Programming

Declarative programming languages often fail to effectively address many aspects of control and resource management. Linear logic provides a framework for increasing the strength of declarative programming languages to embrace these aspects. Linear logic has been used to provide new analyses of Prolog\u27s operational semantics, including left-to-right/depth-first search and negation-as-failure. It has also been used to design new logic programming languages for handling concurrency and for viewing program clauses as (possibly) limited resources. Such logic programming languages have proved useful in areas such as databases, object-oriented programming, theorem proving, and natural language parsing. This workshop is intended to bring together researchers involved in all aspects of relating linear logic and logic programming. The proceedings includes two high-level overviews of linear logic, and six contributed papers. Workshop organizers: Jean-Yves Girard (CNRS and University of Paris VII), Dale Miller (chair, University of Pennsylvania, Philadelphia), and Remo Pareschi, (ECRC, Munich)