Communications of the ACM
Information Processing Letters
Algorithms for testing the satisfiability of propositional formulae
Journal of Logic Programming
A note on Dowling and Gallier's top-down algorithm for propositional horn satisfiability
Journal of Logic Programming
Gentzen-type systems and resolution rules. Part I. Propositional logic
COLOG-88 Proceedings of the international conference on Computer logic
Minimizing the number of clauses by renaming
CADE-10 Proceedings of the tenth international conference on Automated deduction
Extended Horn sets in propositional logic
Journal of the ACM (JACM)
A linear control algorithm for a class of rule-based systems
Journal of Logic Programming
Optimizing the clausal normal form transformation
Journal of Automated Reasoning
Dissolution: making paths vanish
Journal of the ACM (JACM)
A Complexity Index for Satisfiability Problems
SIAM Journal on Computing
Recognition of q-Horn formulae in linear time
Discrete Applied Mathematics
On finding solutions for extended Horn formulas
Information Processing Letters
Polarity guided tractable reasoning
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Unit Refutations and Horn Sets
Journal of the ACM (JACM)
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
Theorem Proving via General Matings
Journal of the ACM (JACM)
Completeness for Linear Regular Negation Normal Form Inference Systems
ISMIS '97 Proceedings of the 10th International Symposium on Foundations of Intelligent Systems
Non-clausal Reasoning with Propositional Definite Theories
AISC '98 Proceedings of the International Conference on Artificial Intelligence and Symbolic Computation
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Some applications of non clausal deduction
Some applications of non clausal deduction
Model-theoretic semantics and tractable algorithm for CNF-BCP
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
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Many applications in Computer Science require to represent knowledge and to reason with non normal form formulas. However, most of the advances in tractable reasoning are applied only to CNF formulas. In this paper, we extend tractability to several classes of non normal formulas which are of high practical interest. Thus, we first define three non normal Horn-like classes of formulas F1ΛF2Λ...ΛFn where each Fi is constituted by a disjunction of two optional terms Fi = N N Fi- V Ci+: the first one is in Negation Normal Form (NNF) composed exclusively with negative literals and the second one is a conjunction of positive propositions. These formulas codify the same problems that the Horn formulas but with significantly, even exponentially, less propositional symbols. Second, we define sound and refutational complete inference rule sets for each class. Our third contribution consists in the design of a sound, complete and strictly linear running time algorithm for each class. As a result, the time required by our linear algorithms running on the defined non normal Horn-like formulas can be exponentially less than that required by the existing linear Horn-SAT algorithms.