# Tractable Databases : How to Make Propositional Unit ResolutionComplete through CompilationAlvaro

@inproceedings{DelVal1994TractableD, title={Tractable Databases : How to Make Propositional Unit ResolutionComplete through CompilationAlvaro}, author={Alvaro Del Val}, year={1994} }

We present procedures to compile any propo-sitional clausal database into a logically equivalent \compiled" database ? such that, for any clause C, j = C if and only if there is a unit refutation of ? :C. It follows that once the compilation process is complete any query about the logical consequences of can be correctly answered in time linear in the sum of the sizes of ? and the query. The compiled database ? is for all but one of the procedures a subset of the set PI(() of prime implicates…

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## 4 Citations

Compilation for Critically Constrained Knowledge Bases

- Computer ScienceAAAI/IAAI, Vol. 1
- 1996

An aggressive hybrid approach is developed which attempts to compile a KB exactly until a given resource limit is reached, then falls back to approximate compilation into unit clauses, with average savings of an order of magnitude over the brute-force approach.

Extending the Knowledge Compilation Map: Krom, Horn, Affine and Beyond

- Computer ScienceAAAI
- 2008

The knowledge compilation map introduced by Darwiche and Marquis is extended with three influential propositional fragments, the Krom CNF one, the Hom CNF fragment and the affine fragment as well as seven additional languages based on them.

Implicates and Prime Implicates in Random 3-SAT

- Mathematics, Computer ScienceArtif. Intell.
- 1996

This paper looks beyond satisfiability to implicates and prime implicates of non-zero length and shows experimentally that, for any given length, these exhibit their own phase transitions, which appear to share the same critical point as the well-known satisfiability phase transition.

D2.1.1 Survey of Scalability Techniques for Reasoning with Ontologies

- 2004

EU-IST Network of Excellence (NoE) IST-2004-507482 KWEB Deliverable D2.1.1 (WP2.1) This deliverable gives an overview of methods necessary for achieving scalability. This includes general methods for…

## References

SHOWING 1-10 OF 22 REFERENCES

Unit Refutations and Horn Sets

- Mathematics, Computer ScienceJACM
- 1974

It is proved that, if S is an unsatisfiable Horn set, there exists a strictly-unit refutation of S employing binary resolution alone, thus eliminating the need for factoring and a theorem similar to Theorem 1 for paramodulation-based inference systems is proven in Theorem 3 but with the inclusion of factoring as an inference rule.

An Improved Incremental Algorithm for Generating Prime Implicates

- Computer ScienceAAAI
- 1992

A method based on a simplification of Kean and Tsiknis' algorithm using an entirely different data structure to represent the data base of clauses which produces an improvement in running time on all known examples with a dramatic improvement inrunning time on larger examples.

Knowledge Compilation using Horn Approximations

- Computer ScienceAAAI
- 1991

This work introduces a knowledge compilation method that allows the user to enter statements in a general, unrestricted representation language, which the system compiles into a restricted language that allows for efficient inference.

Consequence-Finding Based on Ordered Linear Resolution

- Computer ScienceIJCAI
- 1991

This paper shows how adding a skip rule to ordered linear resolution makes it complete for consequence-finding in this general sense and compares with set-of-support resolution, which generates fewer clauses to find such a subset of consequences.

An Incremental Method for Generating Prime Implicants/Impicates

- Computer Science, MathematicsJ. Symb. Comput.
- 1990

The correctness proof and complexity analysis of the incremental method and the role of prime implicants in the CMS is mentioned and the intricacy of subsumptions in the incremental process is examined.

Making Believers out of Computers

- Computer ScienceArtif. Intell.
- 1986

This chapter discusses the knowledge-based systems or KBS, the idea is not just to construct systems that exhibit knowledge, but to represent that knowledge somehow in the data structures of the program, and to have the system perform whatever it is doing by manipulating that knowledge explicitly.

A Tractable Class of Abduction Problems

- Mathematics, Computer ScienceIJCAI
- 1993

It is shown that when the background theory is acyclic Horn and its pseudo-completion is unit refutable, there is a polynomial time algorithm for finding minimal explanations.

Two Results on Ordering for Resolution with Merging and Linear Format

- Mathematics, Computer ScienceJACM
- 1971

A new kind of ordering, called C-ordering, is introduced and shown to be compatible with merge, linear format, and set of support resolution, that the literal to be resolved upon in the near parent is uniquely specified.

On the number of prime implicants

- Mathematics, Computer ScienceDiscret. Math.
- 1978

It is shown that any Boolean expression in disjunctive normal form having k conjuncts, can have at most 2k prime implicants. However, there exist such expressions that have 2k2 prime implicants. It…

A Note on Linear Resolution Strategies in Consequence-Finding

- Computer ScienceArtif. Intell.
- 1972

It is argued that the incompleteness of this latter strategy for consequence-finding recommends it above the other two as a complete strategy for theorem-proving.