## Knowledge Representation with Logic Programs (1996)

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Venue: | DEPT. OF CS OF THE UNIVERSITY OF KOBLENZ-LANDAU |

Citations: | 32 - 6 self |

### BibTeX

@INPROCEEDINGS{Brewka96knowledgerepresentation,

author = {Gerhard Brewka and Jürgen Dix},

title = {Knowledge Representation with Logic Programs},

booktitle = {DEPT. OF CS OF THE UNIVERSITY OF KOBLENZ-LANDAU},

year = {1996},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this tutorial-overview, which resulted from a lecture course given by the authors at

### Citations

2343 | Computational Complexity - Papadimitriou - 1994 |

1855 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...that A\Theta 1 is identical to B \Theta 2 ; or if we can decide that this is not possible at all. In fact, if the two atoms are unifiable we can indeed compute a most general unifier, called mgU (see =-=[Llo87]-=-). The mgU \Theta is a substitution defined on the set of variables occurring in both A and B such that A\Theta is identical to B \Theta. This will be important in our framework because if an atom app... |

1492 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ... ([BD97a]). The underlying idea of STABLE is that any atom in an intended model should have a definite reason to be true or false. This idea was made explicit in [BF91a, BF91b] and, independently, in =-=[GL88]-=-. We use the latter terminology and introduce the Gelfond-Lifschitz transformation: for a program P and a model N ` BP we define P N := frule N : rule 2 Pg 11 With the help of a regular move, given by... |

1423 | A Logic for Default Reasoning - Reiter - 1980 |

960 |
Negation as failure
- Clark
- 1978
(Show Context)
Citation Context ...re 1 the leftmost branch is also failing but infinite. Although this idea of Finite-Failure is very procedural in nature, there is a nice modeltheoretical counterpart --- Clark's completion comp(P ) (=-=[Cla78]). The ide-=-a of Clark was that a program P consists not only of the implications, but also of the information that these are the only ones. Roughly speaking, he argues that one should interpret the "/"... |

847 | Classical negation in logic programs and disjunctive databases
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...ramming Semantics Semantics Reference Domain Taut. GPPE Red. Non-Min. Rel. comp [Cla78] Nondis. --- ffl ffl ffl --- GCWA [Min82] Pos. ffl ffl ffl ffl ffl WGCWA [RT88] Pos. --- ffl ffl --- ffl DSTABLE =-=[GL91]-=- Dis. ffl ffl ffl ffl --- WFS [vGRS91] Nondis. ffl ffl ffl ffl ffl ST N [Prz91b] Dis. ffl ffl ffl ffl ffl STATIC [Prz95] Dis. ffl ffl ffl ffl ffl D-WFS [BD95d] Dis. ffl ffl ffl ffl ffl DWFS [Dix92b] D... |

844 | The well-founded semantics for general logic programs - Gelder, Ross, et al. - 1991 |

815 |
Circumscription: A Form of Nonmonotonic Reasoning
- McCarthy
- 1980
(Show Context)
Citation Context ...ENDIX 84 e1 e2 e3 e4 C C e1 e2 e3 e4 p1 -> e1 p2 -> e2 p3 -> e3 p4 -> e4 Model M1 Model M2 Figure 5: Two Models of a Theory with the Same Valuation. functions. Since its first formulation by McCarthy =-=[McC80]-=-, it has taken on several different forms, including domain circumscription [McC79] (minimizing the elements in the universe of models), and the most popular and useful version, parallel predicate cir... |

709 | The semantics of predicate logic as a programming language - Emden, Kowalski - 1976 |

529 | A lattice-theorethic Fixpoint Theorem and its applications - Tarski - 1955 |

502 | Artificial Intelligence: A Modern Approach - Russel, Norvig - 2003 |

486 | Applications of circumscription to formalizing common sense knowledge - McCarthy |

416 | Introduction to Logic Programming - Apt - 1990 |

381 | Bilattices and the semantics of logic programming
- Fitting
- 1991
(Show Context)
Citation Context ...Theorem 3.2 we already related a restricted form of finite failure to Clark's completion. We will see later that comp(P ) is inconsistent even in cases where we would not expect it. Therefore Fitting =-=[Fit85]-=- introduced a three-valued formulation comp 3 (P ) of the original completion. Kunen ([Kun87]) then proved in the propositional case SLDNF is sound and complete with respect to comp 3 (P ). In the pre... |

331 | A catalog of complexity classes - Johnson - 1990 |

322 | Pointwise circumscription, in
- Lifschitz
- 1988
(Show Context)
Citation Context ...RENCES 51 The relevance of preferences is well-recognized in nonmonotonic reasoning, and prioritized versions for most of the nonmonotonic logics have been proposed, e.g., prioritized circumscription =-=[Lif85], hierarch-=-ic autoepistemic logic [Kon88], prioritized default logic [Bre94]. In these approaches preferences are handled in an "external" manner in the following sense: some ordering among defaults is... |

309 | Classical Recursion Theory - Odifreddi - 1989 |

258 | Tabled evaluation with delaying for general logic programs
- Chen, Warren
- 1996
(Show Context)
Citation Context ...cial eye on complexity. The most advanced system has been implemented by David Warren and his group in Stony Brook based on OLDT-algorithm of [TS86]. They first developed a meta-interpreter (SLG, see =-=[CW96]-=-) in PROLOG and then directly modified the WAM for a direct implementation of WFS (XSB). They use tabling-methods and a mixture of Top-Down and bottom-up evaluation to detect loops. Their system is co... |

242 | Logic programming and negation: a survey
- Apt, Bol
- 1994
(Show Context)
Citation Context ...le to SLDResolution and treat negation as "Finite-Failure". This resulted in an extension of SLD, called SLDNF-Resolution, a procedural mechanism for query answering. For a nice overview, we=-= refer to [AB94]. NML-Appr-=-oach: This is the approach suggested by non-monotonic reasoning people. Here the main question is "What is the right semantics?" I.e. we are looking first for a semantics that correctly fits... |

237 | Principles of Database and - Ullman - 1987 |

234 |
Negation in Logic Programming
- Kunen
- 1987
(Show Context)
Citation Context ...will see later that comp(P ) is inconsistent even in cases where we would not expect it. Therefore Fitting [Fit85] introduced a three-valued formulation comp 3 (P ) of the original completion. Kunen (=-=[Kun87]-=-) then proved in the propositional case SLDNF is sound and complete with respect to comp 3 (P ). In the predicate logic case, SLDNF is not complete but it is always correct [She88, Theorem 39]) with r... |

221 | Unfounded Sets and Well-founded Semantics for General Logic - Gelder, Ross, et al. - 1989 |

218 | OLD resolution with tabulation - Tamaki, Sato - 1986 |

206 | Principles of Database and Knowledge Base Systems - Ullman - 1989 |

191 | Admissible Sets and Structures - Barwise - 1975 |

171 | Structural Complexity I - Balcázar, Díaz, et al. - 1988 |

169 | Elementary Induction on Abstract Structures - Moschovakis - 1974 |

162 | The complexity of logic-based abduction - Eiter, Gottlob - 1995 |

157 | Inconsistency management and prioritized syntax-based entailment - Benferhat, Cayrol, et al. - 1993 |

153 | Logic and the challenge of computer science - Gurevich - 1988 |

145 | Propositional semantics for disjunctive logic programs - Ben-Eliyahu, Dechter - 1994 |

142 | Consistency of clark's completion and existence of stable models - Fages - 1994 |

135 |
On indefinite databases and the closed world assumption
- Minker
- 1982
(Show Context)
Citation Context ...it in Section 6.3. We mention some other attempts to define disjunctive semantics in Section 6.4. Finally we discuss complexity and expressibility in Section 6.5. 6.1 GCWA GCWA was defined by Minker (=-=[Min82]-=-) and can bee seen as a refined version of the CWA introduced by Reiter ([Rei78]): Definition 6.1 (CWA) CWA(DB) = DB [ f:P (t) : DB 6j= P (t)g ; where P (t) is a ground predicate instance. That is, if... |

129 | Constructive negation based on the completed database - Chan - 1988 |

125 | A clash of intuitions: the current state of nonmonotonic multiple inheritance systems - Touretzky, Horty, et al. - 1987 |

122 | Well founded semantics for logic programs with explicit negation - Pereira, Alferes, et al. - 1992 |

107 | A skeptical theory of inheritance in non-monotonic semantic nets - Horty, Thomason, et al. - 1990 |

103 | The Pleadings Game: An Artificial Intelligence Model of Procedural Justice
- Gordon
- 1995
(Show Context)
Citation Context ...g Example In this section we want to show that the additional expressiveness provided by our approach actually helps representing real world problems. We will use an example first discussed by Gordon =-=[Gor93]-=-. We somewhat simplified it for our purposes. Example 5.8 (Legal Reasoning) Assume a person wants to find out if her security interest in a certain ship is perfected. She currently has possession of t... |

102 | A Deductive System for Nonmonotonic Reasoning - Eiter, Leone, et al. - 1997 |

101 | On the Comparison of Theories: Preferring the Most Specific Explanation - Poole - 1985 |

99 | Propositional circumscription and extended closed world reasoning are Π P 2 -complete - Eiter, Gottlob - 1993 |

93 | Logical tools for modelling legal argument - Prakken - 1993 |

91 | Well-founded semantics for extended logic programs with dynamic preferences
- Brewka
- 1996
(Show Context)
Citation Context ... would like to have, therefore, is an approach that allows us to represent preference information in the language and derive such information dynamically. The presentation in this section is based on =-=[Bre96b]-=-. A similar treatment of prioritized logic programs under answer set semantics is described in [Bre97]. 5.2 Handling Preferences In order to handle preferences we need to be able to express preference... |

88 | Dualities between Alternative Semantics for Logic Programming and Non-monotonic Reasoning - Baral, Subrahmanian - 1991 |

86 |
Linear Time Algorithms for testing the Satisfiability of Propositional Horn formulae
- Downing, Gallier
- 1984
(Show Context)
Citation Context ...a proof see [Wit91a]), while STABLE is co-NP-complete. The low complexity of WFS can be traced back to Dowling and Gallier's result whereby satisfiability of Horn clauses can be tested in linear time(=-=[DG84]-=-). In Dowling and Gallier's approach it is actually a minimal model of a Horn theory that 3 ADDING DEFAULT-NEGATION 39 is computed in linear time. Since minimal models of Horn theories are equivalent ... |

84 | A logic programming system for non-monotonic reasoning - Alferes, Damásio, et al. - 1995 |

84 | The expressive powers of logic programming semantics - Schlipf - 1995 |

82 | A survey on complexity results for nonmonotonic logics - Cadoli, Schaerf - 1993 |

81 | Efficient top-down computation of queries under the well-founded semantics - Chen, Swift, et al. - 1995 |

81 | How to progress a database - Lin, Reiter - 1997 |