## Solving Advanced Reasoning Tasks using Quantified Boolean Formulas (2000)

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Citations: | 67 - 20 self |

### BibTeX

@INPROCEEDINGS{Egly00solvingadvanced,

author = {Uwe Egly and Thomas Eiter and Hans Tompits and Stefan Woltran},

title = {Solving Advanced Reasoning Tasks using Quantified Boolean Formulas},

booktitle = {},

year = {2000},

pages = {417--422},

publisher = {AAAI Press}

}

### Years of Citing Articles

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### Abstract

We consider the compilation of different reasoning tasks into the evaluation problem of quantified boolean formulas (QBFs) as an approach to develop prototype reasoning systems useful, e.g., for experimental purposes.

### Citations

2939 | Graph--based algorithms for boolean function manipulation
- Bryant
- 1986
(Show Context)
Citation Context ...ms using the reductions discussed above. QUIP employs as underlying QBFevaluator the publicly available propositional theorem prover boole (bddlib), which is based on binary decision diagrams (BDDs) (=-=Bryant 1986-=-). Choosing boole is motivated by the fact that it can handle arbitrary QBFs, and because it is a highly sophisticated package developed over many years. In order to evaluate the feasibility of the me... |

1498 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ... / P (r); N(r); where H(r) is a disjunction of variables, P (r) is a conjunction of variables, and N(r) is a conjunction of negated variables. A Herbrand interpretation I of V is a stable model of P (=-=Gelfond & Lifschitz 1988-=-; Przymusinski 1991), if it is a minimal model (with respect to set-inclusion) of the program P I resulting from P as follows: remove each clause r such that I j= a for some :a in N(r), and remove N(r... |

1424 |
A logic for default reasoning
- Reiter
- 1980
(Show Context)
Citation Context ...d (fl is concluded) if ff is provable and the justification fi can be consistently assumed. T is said to be finite iff W is finite. The semantics of T = (W; \Delta) is defined in terms of extensions (=-=Reiter 1980-=-). Following (Marek & Truszczy'nski 1993), extensions can be characterised thus. For any S ` L, let \Delta(S) be the monotonic rules f ff fl j ff : fi fl 2 \Delta; :fi = 2 Sg. Then, E ` L is an extens... |

816 |
Circumscription—a form of non-monotonic reasoning
- McCarthy
- 1980
(Show Context)
Citation Context ...the formalisms described above, propositional circumscription is already a quantified boolean formula, hence it does not require a separate reduction. We recall the basic concepts of circumscription (=-=McCarthy 1980-=-). In the propositional case, the parallel circumscription of a set of atoms P = {p1, . . . , pn} in a theory T , where the atoms Q are fixed and the remaining atoms Z = {z1, . . . , zm} = V \ (P ∪ Q)... |

322 | Pointwise circumscription
- Lifschitz
- 1987
(Show Context)
Citation Context ...atoms P = fp 1 ; : : : ; png in a theory T , where the atoms Q are fixed and the remaining atoms Z = fz 1 ; : : : ; z m g = V n (P [ Q) may vary, is given by the following QBF CIRC (T ; P ; Z ), cf. (=-=Lifschitz 1985-=-): T 8P 0 8Z 0 i (T [P=P 0 ; Z=Z 0 ]s(P 0sP )) ! (PsP 0 ) j : Here, P 0 = fp 0 1 ; : : : ; p 0 n g and Z 0 = fz 0 1 ; : : : ; z 0 m g are sets of new propositional variables corresponding to P and Z, ... |

191 |
Autoepistemic logic
- Marek, Truszczyński
- 1991
(Show Context)
Citation Context ... is provable and the justification fi can be consistently assumed. T is said to be finite iff W is finite. The semantics of T = (W; \Delta) is defined in terms of extensions (Reiter 1980). Following (=-=Marek & Truszczy'nski 1993-=-), extensions can be characterised thus. For any S ` L, let \Delta(S) be the monotonic rules f ff fl j ff : fi fl 2 \Delta; :fi = 2 Sg. Then, E ` L is an extension of T iff E = Cn \Delta(E) (W ), wher... |

141 | Constructing conditional plans by a theorem-prover
- Rintanen
- 1999
(Show Context)
Citation Context ...major reasoning problems from several propositional nonmonotonic reasoning (NMR) formalisms into QBFs. To the best of our knowledge, except for an encoding of conditional planning problems into QBFs (=-=Rintanen 1999-=-a), concrete transformations of KR tasks beyond NP into QBFs have not been presented so far. In particular, we provide polynomial-time translations of problems from abduction, default logic, autoepist... |

139 | An Algorithm to Evaluate Quantified Boolean Formulae - Cadoli, Giovanardi, et al. - 1998 |

137 | E cient implementation of the well-founded and stable model semantics
- Niemela, Simons
- 1996
(Show Context)
Citation Context ...ing NMR theorem provers. In particular, we compare the different translations of QUIP with Theorist (Poole 1989), DeRes (Cholewinski, Marek, & Truszcynski 1996), dlv (Eiter et al. 1998), and smodels (=-=Niemela & Simons 1996-=-). As shown by the experimental results, even with no optimization methods applied, our (ad hoc) NMR implementations via QBFs compare reasonably well to these systems, some of which represent the stat... |

130 | Explanation and prediction: an architecture for default and abductive reasoning
- Poole
- 1989
(Show Context)
Citation Context ...evaluate the feasibility of the method in practice, we compare the prototype system QUIP with existing NMR theorem provers. In particular, we compare the different translations of QUIP with Theorist (=-=Poole 1989-=-), DeRes (Cholewinski, Marek, & Truszcynski 1996), dlv (Eiter et al. 1998), and smodels (Niemela & Simons 1996). As shown by the experimental results, even with no optimization methods applied, our (a... |

102 | A Deductive System for Nonmonotonic Reasoning
- Eiter, Leone, et al.
- 1997
(Show Context)
Citation Context ...tice, we compare the prototype system QUIP with existing NMR theorem provers. In particular, comparisons are performed with Theorist (Poole 1989), DeRes (Cholewinski, Marek, & Truszczyński 1996),dlv (=-=Eiter et al. 1997-=-), and smodels (Niemelä & Simons 1996). As shown by the experimental results, even with no optimization methods applied, our (ad hoc) NMR implementations via QBFs compare reasonably well to these syst... |

77 | Resolution for Quantified Boolean Formulas - Büning, Karpinski, et al. - 1995 |

74 |
B.Selman, Pushing the Envelope
- Kautz
(Show Context)
Citation Context ...opositional logic. Thus, efficient algorithms for sat can be used to solve such problems. Successful applications of this idea include, e.g., reductions of constrained-based planning problems to sat (=-=Kautz & Selman 1996-=-). The feasibility of this approach relies on the proviso that the considered problem is in NP, i.e., that it can be solved by a nondeterministic Turing machine working in polynomial time, and on the ... |

73 | Improvements to the Evaluation of Quantified Boolean Formulae
- Rintanen
- 1999
(Show Context)
Citation Context ...major reasoning problems from several propositional nonmonotonic reasoning (NMR) formalisms into QBFs. To the best of our knowledge, except for an encoding of conditional planning problems into QBFs (=-=Rintanen 1999-=-a), concrete transformations of KR tasks beyond NP into QBFs have not been presented so far. In particular, we provide polynomial-time translations of problems from abduction, default logic, autoepist... |

71 | Default reasoning system deres - Cholewinski, Marek, et al. - 1996 |

64 |
Nonmonotonic Logics
- Marek, Truszczyński
- 1993
(Show Context)
Citation Context ...) if α is provable and the justification β can be consistently assumed. T is said to be finite iff W is finite. The semantics of T = (W, ∆) is defined in terms of extensions (Reiter 1980). Following (=-=Marek & Truszczyński 1993-=-), extensions can be characterised thus. For any S ⊆ L, let ∆(S) be the monotonic rules { α α : β γ | γ ∈ ∆, ¬β /∈ S}. Then, E ⊆ L is an extension of T iff E = Cn ∆(E) (W ), where Cn ∆(E) (W ) is the ... |

35 | Experimenting with nonmonotonic reasoning
- Cholewinski, Marek, et al.
- 1995
(Show Context)
Citation Context ...e tools are DeReS (Cholewinski, Marek, & Truszcynski 1996), dlv (Eiter et al. 1998), smodels (Niemela & Simons 1996), and Theorist (Poole 1989). Three of the four test sets are taken from TheoryBase (=-=Cholewinski et al. 1995-=-), a well-known testbed for nonmonotonic formalisms; the other test set consists of abductive diagnosis problems for n-bit full adders. The latter problem is used to compare the abduction part of QUIP... |

34 |
Stable semantics for disjunctive programs. New generation computing
- Przymusinski
- 1991
(Show Context)
Citation Context ... is a disjunction of variables, P (r) is a conjunction of variables, and N(r) is a conjunction of negated variables. A Herbrand interpretation I of V is a stable model of P (Gelfond & Lifschitz 1988; =-=Przymusinski 1991-=-), if it is a minimal model (with respect to set-inclusion) of the program P I resulting from P as follows: remove each clause r such that I j= a for some :a in N(r), and remove N(r) from all remainin... |

28 | Towards efficient default reasoning
- Niemelä
- 1995
(Show Context)
Citation Context ... extension iff T dl (T ) evaluates to true. An alternative (and more succinct) translation of default logic into QBFs is possible using Niemela's characterisation of extensions in terms of full sets (=-=Niemela 1995-=-). To this end, for a set \Delta of defaults and a set S of formulas, define j (\Delta) = ffi j ff : fi fl 2 \Deltag and \Delta p (S) = f ff fl j ff : fi fl 2 \Delta; fi 2 Sg. Rephrasing a definition ... |

7 |
The complexity of propositional default reasoning under the stationary semantics
- Gottlob
- 1992
(Show Context)
Citation Context ....e., Cn \Delta(E) (W ) j= ffl i j d 0 i = true g). This amounts to checking whether V n i=1 (d 0 i ! fl i ) 2 Cn \Delta(E) (W ), i.e., whether (D 0sG) 2 Cn \Delta(E) (W ). Applying a result shown in (=-=Gottlob 1995-=-), OE = 2 Cn \Delta(E) (W ) iff there exists a subset C ` G = ffl 1 ; : : : ; fl n g such that 1 For simplicity, we omit multiple justifications here. Our QBF translations can be easily extended to th... |

4 |
On the decidability and complexity of autoepistemic reasoning. Fundamenta Informaticae
- Niemelä
- 1992
(Show Context)
Citation Context ...fLOE j OE 2 E) [ f:LOE j OE = 2 Eg); where Cn(\Delta) is the classical consequence operator with respect to the extended language LL . The existence of a stable expansion can be expressed as follows (=-=Niemela 1992-=-). Let T ` LL be an autoepistemic theory, M be the set of all modal atoms occurring in T , and V be the set of ordinary (non-modal) atoms in T . We say thats` M [ f:OE j OE 2 Mg is T -full iff, for al... |