Multi-valued logic and Gröner bases with applications to modal logic
Journal of Symbolic Computation
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Homogenization and the polynomial calculus
Computational Complexity
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family
Journal of Automated Reasoning
Conservative Extensions in the Lightweight Description Logic $\mathcal{EL}$
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
An equational approach to theorem proving in first-order predicate calculus
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
A formally verified prover for the ALC description logic
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Semantic matching: algorithms and implementation
Journal on data semantics IX
Extension of ontologies assisted by automated reasoning systems
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
Confidence-based reasoning with local temporal formal contexts
IWANN'11 Proceedings of the 11th international conference on Artificial neural networks conference on Advances in computational intelligence - Volume Part II
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We present a specialised (polynomial-based) rule for the propositional logic called the Independence Rule , which is useful to compute the conservative retractions of propositional logic theories. In this paper we show the soundness and completeness of the logical calculus based on this rule, as well as other applications. The rule is defined by means of a new kind of operator on propositional formulae. It is based on the boolean derivatives on the polynomial ring ${\mathbb F}_2[{\bf x}]$.