Results 1 
6 of
6
The Complexity of LogicBased Abduction
, 1993
"... Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minima ..."
Abstract

Cited by 163 (26 self)
 Add to MetaCart
Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.
Nogood Recording for Static and Dynamic Constraint Satisfaction Problems
 International Journal of Artificial Intelligence Tools
, 1993
"... Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, fo ..."
Abstract

Cited by 111 (5 self)
 Add to MetaCart
Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The problem we consider here is the solution maintenance problem in such a dynamic CSP (DCSP). We propose a new class of constraint recording algorithms called Nogood Recording that may be used for solving both static and dynamic CSPs. It offers an interesting compromise, polynomially bounded in space, between an ATMSlike approach and the usual static constraint satisfaction algorithms. 1 Introduction The constraint satisfaction problem (CSP) model is widely used to represent and solve various AI related problems and provides fundamental tools in areas such as truth...
The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions
 In: Proceedings of International Joint Conference on Artificial Intelligence
, 1993
"... We consider the computational complexity of evaluating nested counterfactuals over a propositional knowledge base. Counterfactual implication p ? q models a statement "if p, then q," where p is known or expected to be false, and is different from material implication p ) q. A nested counterfact ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
We consider the computational complexity of evaluating nested counterfactuals over a propositional knowledge base. Counterfactual implication p ? q models a statement "if p, then q," where p is known or expected to be false, and is different from material implication p ) q. A nested counterfactual is a counterfactual statement where the conclusion q is a (possibly negated) counterfactual. Statements of the form p 1 ? (p 2 ? \Delta \Delta \Delta (p n ? q) \Delta \Delta \Delta) intuitively correspond to hypothetical queries involving a sequence of revisions. We show that evaluating such statements is \Pi P 2 complete, and that this task becomes PSPACEcomplete if negation is allowed in the nesting. We also consider nesting a counterfactual in the premise, i.e. (p ? q) ? r and show that evaluating such statements is most likely much harder than evaluating p ? (q ? r). 1 Introduction A counterfactual is a conditional statement "if p, then q," where the premise p is eit...
Belief Revision and Dialogue Management in Information Retrieval
, 1994
"... This report describes research to evaluate a theory of belief revision proposed by Galliers in the context of informationseeking interaction as modelled by Belkin, Brooks and Daniels and illustrated by userlibrarian dialogues. The work covered the detailed assessment and development, and computati ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
This report describes research to evaluate a theory of belief revision proposed by Galliers in the context of informationseeking interaction as modelled by Belkin, Brooks and Daniels and illustrated by userlibrarian dialogues. The work covered the detailed assessment and development, and computational implementation and testing, of both the belief revision theory and the information retrieval model. Some features of the belief theory presented problems, and the original `multiple expert' retrieval model had to be drastically modified to support rational dialogue management. But the experimental results showed that the characteristics of literatureseeking interaction could be successfully captured by the belief theory, exploiting important elements of the retrieval model. Thus though the system's knowledge and dialogue performance were very limited, it provides a useful base for further research. The report presents all aspects of the research in detail, with particular emphasis on the implementation of belief and intention revision, and the integration of revision with domain reasoning and dialogue interaction.
Penalty logic and its link with DempsterShafer theory
 In Proc. of the 10 th Conf. on Uncertainty in Artificial Intelligence
, 1994
"... Penalty logic, introduced by Pinkas [?], associates to each formula of a knowledge base the price to pay if this formula is violated. Penalties may be used as a criterion for selecting preferred consistent subsets in an inconsistent knowledge base, thus inducing a nonmonotonic inference relation. A ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
Penalty logic, introduced by Pinkas [?], associates to each formula of a knowledge base the price to pay if this formula is violated. Penalties may be used as a criterion for selecting preferred consistent subsets in an inconsistent knowledge base, thus inducing a nonmonotonic inference relation. A precise formalization and the main properties of penalty logic and of its associated nonmonotonic inference relation are given in the first part. We also show that penalty logic and DempsterShafer theory are related, especially in the infinitesimal case. 1 Introduction The problem of inconsistency handling appears when the available knowledge base  KB for short  (here a set of propositional formulas) is inconsistent. Most approaches come up with the inconsistency by selecting among the consistent subsets of KB some preferred subsets; the selection criterion generally makes use of uncertainty considerations, sometimes by using explicitly uncertainty measures (such as Wilson [?], Benfer...
Two Approaches to the Solution Maintenance Problem in Dynamic Constraint Satisfaction Problems
 In Proceedings of the IJCAI93/SIGMAN Workshop on Knowledgebased Production Planning, Scheduling and Control
, 1993
"... Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The notion of dynamic CSP (DCSP) [DD88] has been proposed to represent such evolutions. The problem we consider here is the solution maintenance problem in a DCSP. Naively applying usual satisfaction algorithms to this problem results in redundant search and inefficiency. Two distinct approaches to this problem are proposed in this paper. The first one, called the Local Changes approach, reuses the previous solution (if any) to compute a new solution. The second one, called the Nogood Recording approach, tries to store in a concise way, an approximate description of the front...