Results 1  10
of
46
Logic Programming and Knowledge Representation
 Journal of Logic Programming
, 1994
"... In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and sh ..."
Abstract

Cited by 242 (20 self)
 Add to MetaCart
(Show Context)
In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten sions of the language of definite logic programs by classical (strong) negation, disjunc tion, and some modal operators and show how each of the added features extends the representational power of the language.
On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals
 ARTIFICIAL INTELLIGENCE
, 1992
"... We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or ..."
Abstract

Cited by 215 (11 self)
 Add to MetaCart
(Show Context)
We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... 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 wellknown semantics, as well as the complexity of deciding whethe ..."
Abstract

Cited by 140 (26 self)
 Add to MetaCart
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 wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells 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 P 2 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 P 2 complete; analogous results are derived for the an
Propositional Circumscription and Extended Closed World Reasoning are $\Pi^P_2$complete
 Theoretical Computer Science
, 1993
"... Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction prob ..."
Abstract

Cited by 108 (20 self)
 Add to MetaCart
(Show Context)
Circumscription and the closed world assumption with its variants are wellknown nonmonotonic techniques for reasoning with incomplete knowledge. Their complexity in the propositional case has been studied in detail for fragments of propositional logic. One open problem is whether the deduction problem for arbitrary propositional theories under the extended closed world assumption or under circumscription is $\Pi^P_2$complete, i.e., complete for a class of the second level of the polynomial hierarchy. We answer this question by proving these problems $\Pi^P_2$complete, and we show how this result applies to other variants of closed world reasoning.
Disjunctive Deductive Databases
, 1994
"... Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Al ..."
Abstract

Cited by 59 (7 self)
 Add to MetaCart
Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Algorithms are developed to compute answers to queries in the alternative theories using the concept of a model tree. Open problems in this area are discussed.
Is Intractability of NonMonotonic Reasoning a Real Drawback?
 Artificial Intelligence
, 1996
"... Several studies about computational complexity of nonmonotonic reasoning (NMR) showed that nonmonotonic inference is significantly harder than classical, monotonic inference. This contrasts with the general idea that NMR can be used to make knowledge representation and reasoning simpler, not harde ..."
Abstract

Cited by 47 (8 self)
 Add to MetaCart
(Show Context)
Several studies about computational complexity of nonmonotonic reasoning (NMR) showed that nonmonotonic inference is significantly harder than classical, monotonic inference. This contrasts with the general idea that NMR can be used to make knowledge representation and reasoning simpler, not harder. In this paper we show that, to some extent, NMR fulfills the representation goal. In particular, we prove that nonmonotonic formalisms such as circumscription and default logic allow for a much more compact and natural representation of propositional knowledge than propositional calculus. Proofs are based on a suitable definition of compilable inference problem, and on nonuniform complexity classes. Some results about intractability of circumscription and default logic can therefore be interpreted as the price one has to pay for having such an extracompact representation. On the other hand, intractability of inference and compactness of representation are not equivalent notions: we ex...
Logic Programming and Reasoning with Incomplete Information
 Annals of Mathematics and Artificial Intelligence
, 1994
"... The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and neg ..."
Abstract

Cited by 40 (4 self)
 Add to MetaCart
The purpose of this paper is to expand the syntax and semantics of logic programs and disjunctive databases to allow for the correct representation of incomplete information in the presence of multiple extensions. The language of logic programs with classical negation, epistemic disjunction, and negation by failure is further expanded by new modal operators K and M (where for the set of rules T and formula F , KF stands for "F is known to be true by a reasoner with a set of premises T " and MF means " F may be believed to be true" by the same reasoner). Sets of rules in the extended language will be called epistemic specifications. We will define the semantics of epistemic specifications (which expands the semantics of disjunctive databases from [GL91]) and demonstrate their applicability to formalization of various forms of commonsense reasoning. In particular, we suggest a new formalization of the closed world assumption which seems to better correspond to the assumption's intuitive...
On Compact Representations of Propositional Circumscription
 Theoretical Computer Science
, 1997
"... . We prove that  unless the polynomial hierarchy collapses at the second level  the size of a purely propositional representation of the circumscription CIRC(T ) of a propositional formula T grows faster than any polynomial as the size of T increases. We then analyze the significance of this res ..."
Abstract

Cited by 36 (13 self)
 Add to MetaCart
(Show Context)
. We prove that  unless the polynomial hierarchy collapses at the second level  the size of a purely propositional representation of the circumscription CIRC(T ) of a propositional formula T grows faster than any polynomial as the size of T increases. We then analyze the significance of this result in the related field of closedworld reasoning. Appeared on the Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science (STACS'95) March 24, 1995, Munchen, Germany Lecture Notes in Computer Science, 900, pages 205216, SpringerVerlag 1 Introduction Reasoning with selected (or intended) models of a logical formula is a common reasoning technique used in Databases, Logic Programming, Knowledge Representation and Artificial Intelligence (AI). One of the most popular criteria for selecting intended models is minimality wrt the set of true atoms. The idea behind minimality is to assume that a fact is false whenever possible. Such a criterion allows one to represent o...