## The FaCT system (1998)

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### Other Repositories/Bibliography

Venue: | In Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX’98), volume 1397 in Lecture Notes in Artificial Intelligence |

Citations: | 143 - 15 self |

### BibTeX

@INPROCEEDINGS{Horrocks98thefact,

author = {Ian Horrocks},

title = {The FaCT system},

booktitle = {In Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX’98), volume 1397 in Lecture Notes in Artificial Intelligence},

year = {1998},

pages = {307--312},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. FaCT is a Description Logic classifier which has been implemented as a test-bed for a highly optimised tableaux satisfiability (subsumption) testing algorithm. The correspondence between modal and description logics also allows FaCT to be used as a theorem prover for the propositional modal logics K, KT, K4 and S4. Empirical tests have demonstrated the effectiveness of the optimised implementation and, in particular, of the dependency directed backtracking optimisation. 1

### Citations

768 |
A machine program for theorem proving
- Davis, Logemann, et al.
- 1962
(Show Context)
Citation Context ...FaCT deals with this problem by using a semantic branching technique adapted from the Davis-Putnam-Logemann-Loveland procedure (DPL) commonly used to solve propositional satisfiability (SAT) problems =-=[8, 10]-=-. Instead of choosing an unexpanded disjunction, a single disjunct φ is chosen from the set of unexpanded disjunctions, and the two possible tableaux obtained by adding either φ or ¬φ are then searche... |

271 | A correspondence theory for terminological logics
- Schild
- 1991
(Show Context)
Citation Context ...LC DL, and this means that FaCT can be used as a theorem prover for the propositional modal logic K (m) (K with multiple modalities) by exploiting the well known correspondence between the two logics =-=[17]-=-. Because ALCH R + supports transitive relations, FaCT can also be used as a prover for K4 (m), and it extends the range of logics it can deal with to include KT (m) and S4 (m) by embedding formulae i... |

191 | Decidable reasoning in terminological knowledge representation systems - Buchheit, Donini, et al. - 1993 |

183 |
Attributive concept descriptions with complements
- Schmidt-Schauß, Smolka
- 1991
(Show Context)
Citation Context ...odal Logics Description Logics support the logical description of concepts and roles (relationships) and their combination, using a variety of operators, to form more complex descriptions. The ALC DL =-=[18]-=- allows descriptions to be formed using 1 Fast Classification of Terminologies.standard logical connectives as well as both universally and existentially quantified relational operators: if C is a co... |

166 | Improvements to propositional satisfiability search algorithms
- Freeman
- 1995
(Show Context)
Citation Context ...m the set of unexpanded disjunctions, and the two possible tableaux obtained by adding either φ or ¬φ are then searched. During the DPL search, FaCT also performs boolean constraint propagation (BCP) =-=[9]-=-, a technique which maximises deterministic expansion, and thus pruning of the search via contradiction detection, before performing non-deterministic expansion. BCP works by deterministically expandi... |

149 | Attributive concept descriptions with complements - Schmidt-Schau, Smolka - 1991 |

143 | An empirical analysis of optimization techniques for terminological representation systems, or: Making KRIS get a move on
- Baader, Franconi, et al.
- 1994
(Show Context)
Citation Context ...l this strategy lazy unfolding. In fact it has been shown (in the Kris system) that a significant improvement in performance can be obtained simply by not deleting names when they are lazily unfolded =-=[2]-=-. This is because obvious contradictions can often be detected earlier by comparing names rather than unfolded definitions. FaCT takes this optimisation to its logical conclusion by lexically normalis... |

120 |
Optimising Tableaux Decision Procedures for Description Logics
- Horrocks
- 1997
(Show Context)
Citation Context ...x Algorithm The tableau algorithm for ALCH R + is extended from an algorithm for the ALC R + DL described in [16]. The full algorithm, along with a proof of its soundness and correctness, is given in =-=[14]-=-. The main features of the algorithm are: 1. it uses a “single pass” tableau construction and search method as is usual in DL tableaux algorithms where logics generally have the finite model property;... |

98 | Building decision procedures for modal logics from propositional decision procedures - the case study of modal K
- Giunchiglia, Sebastiani
- 1996
(Show Context)
Citation Context ...nefficient search technique for the non-deterministic expansion of disjunctive formulae—they choose an unexpanded disjunction and check the different tableaux obtained by adding each of the disjuncts =-=[11]-=-. As the alternative branches of the search are not disjoint, there is nothing to prevent the recurrence of unsatisfiable disjuncts. FaCT deals with this problem by using a semantic branching techniqu... |

62 | Cardinality restrictions on concepts
- Baader, Buchheit, et al.
- 1996
(Show Context)
Citation Context ...he finite model property; 2. transitive roles are dealt with simply by propagating □iφ terms along i relations; 3. termination is ensured by “blocking”—checking for cycles in the tableau construction =-=[7,1]-=-. 4 Optimisations To improve the performance of the ALCH R + satisfiability testing algorithm, a range of optimisations have been employed. These include lexical normalisation and encoding, semantic b... |

57 | A SAT-based Decision Procedure for ALC
- Giunchiglia, Sebastiani
- 1996
(Show Context)
Citation Context ...nique was employed in the HARP theorem prover [15]. 5 Performance FaCT’s performance as a modal logic theorem prover has been tested using both randomly generated formulae, a test method described in =-=[12]-=- and derived from a widely used procedure for testing SAT decision procedures [10], and a corpus of carefully designed benchmark formulae [13]. FaCT performs well in tests using randomly generated for... |

52 | Implementing and testing expressive description logics: A preliminary report
- Bresciani, Franconi, et al.
- 1995
(Show Context)
Citation Context ... Figure 1, for example, shows CPU time plotted against problem size for 2 classes of formulae from the K benchmark suite, k-dum-p and k-grz-p. FaCT’s performance is compared with that of the Crack DL =-=[6]-=-, the KSAT K (m) theorem prover [11] and the Kris DL [4]. The performance of FaCT with the backjumping optimisation disabled is also shown, indicated in the graphs by FaCT ∗ . All the systems use comp... |

51 | Intelligent Backtracking on Constraint Satisfaction Problems: Experimental and Theoretical Results
- Baker
- 1995
(Show Context)
Citation Context ... ♦i(φ ∧ ϕ) ∧ □i¬φ is discovered. This problem is addressed by adapting a form of dependency directed backtracking called backjumping, which has been used in solving constraint satisfiability problems =-=[5]-=-. Backjumping works by labeling formulae with a dependency set indicating the branching choices on which they depend. When a contradiction is discovered, the dependency sets of the contradictory formu... |

49 | Terminological knowledge representation: A proposal for a terminological logic. German Research Center for Artificial Intelligence (DFKI
- Baader, Bürckert, et al.
- 1991
(Show Context)
Citation Context ...: if C is a concept and R is a role then an ALC concept expression is of the form C | ⊤ | ⊥ | ¬C | C ⊓D | C ⊔D | ∃R.C | ∀R.C. A Tarski style model theoretic semantics is used to interpret expressions =-=[3]-=-. Table 1 shows how propositional K (m) formulae correspond to ALC concept expressions. Note that the modal operators □ and ♦ correspond to ∃R.C and ∀R.C expressions, with different roles correspondin... |

49 | A concept language extended with different kinds of transitive roles
- Sattler
- 1996
(Show Context)
Citation Context ...ae in K (m) and K4 (m): □iφ becomes φ ∧ □iφ and ♦iφ becomes φ ∨ ♦iφ. 3 The ALCH R + Tableaux Algorithm The tableau algorithm for ALCH R + is extended from an algorithm for the ALC R + DL described in =-=[16]-=-. The full algorithm, along with a proof of its soundness and correctness, is given in [14]. The main features of the algorithm are: 1. it uses a “single pass” tableau construction and search method a... |

44 | A benchmark method for the propositional modal logics K, KT, S4
- Heuerding, Schwendimann
- 1996
(Show Context)
Citation Context ...h randomly generated formulae, a test method described in [12] and derived from a widely used procedure for testing SAT decision procedures [10], and a corpus of carefully designed benchmark formulae =-=[13]-=-. FaCT performs well in tests using randomly generated formulae [14], but its advantages are more clearly demonstrated by the benchmark formulae, and in particular by the provable formulae. 2 This is ... |

40 |
A Tableau-Based Theorem Prover
- Oppacher, Suen, et al.
- 1988
(Show Context)
Citation Context ... cause of the contradiction. The algorithm can then jump back over intervening branching points without exploring any alternative branches. A similar technique was employed in the HARP theorem prover =-=[15]-=-. 5 Performance FaCT’s performance as a modal logic theorem prover has been tested using both randomly generated formulae, a test method described in [12] and derived from a widely used procedure for ... |

36 |
Knowledge Representation and Inference System
- KRIS
- 1991
(Show Context)
Citation Context ...roblem size for 2 classes of formulae from the K benchmark suite, k-dum-p and k-grz-p. FaCT’s performance is compared with that of the Crack DL [6], the KSAT K (m) theorem prover [11] and the Kris DL =-=[4]-=-. The performance of FaCT with the backjumping optimisation disabled is also shown, indicated in the graphs by FaCT ∗ . All the systems use compiled Lisp code (Allegro CL 4.3), and the tests were perf... |

17 |
Random 3-SAT Problems and the Davis-Putnam Procedure
- Hard
- 1996
(Show Context)
Citation Context ...FaCT deals with this problem by using a semantic branching technique adapted from the Davis-Putnam-Logemann-Loveland procedure (DPL) commonly used to solve propositional satisfiability (SAT) problems =-=[8, 10]-=-. Instead of choosing an unexpanded disjunction, a single disjunct φ is chosen from the set of unexpanded disjunctions, and the two possible tableaux obtained by adding either φ or ¬φ are then searche... |