An incremental method for generating prime implicants/implicates
Journal of Symbolic Computation
Optimizing the clausal normal form transformation
Journal of Automated Reasoning
Characterizing diagnoses and systems
Artificial Intelligence
Functional dependencies in Horn theories
Artificial Intelligence
Reductions for non-clausal theorem proving
Theoretical Computer Science
Implicates and reduction techniques for temporal logics
Annals of Mathematics and Artificial Intelligence
Extending abduction from propositional to first-order logic
FAIR '91 Proceedings of the International Workshop on Fundamentals of Artificial Intelligence Research
Temporal Reasoning over Linear Discrete Time
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
Proceedings of the 10th International Conference on Automated Deduction
Fuzzy logic programming via multilattices
Fuzzy Sets and Systems
Non-deterministic ideal operators: An adequate tool for formalization in Data Bases
Discrete Applied Mathematics
Congruence relations on some hyperstructures
Annals of Mathematics and Artificial Intelligence
A coalgebraic approach to non-determinism: Applications to multilattices
Information Sciences: an International Journal
Non-deterministic algebraic structures for soft computing
IWANN'11 Proceedings of the 11th international conference on Artificial neural networks conference on Advances in computational intelligence - Volume Part II
Multi-lattices as a basis for generalized fuzzy logic programming
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
Multi-adjoint relation equations: Definition, properties and solutions using concept lattices
Information Sciences: an International Journal
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The concepts of implicates and implicants are widely used in several fields of “Automated Reasoning”. Particularly, our research group has developed several techniques that allow us to reduce efficiently the size of the input, and therefore the complexity of the problem. These techniques are based on obtaining and using implicit information that is collected in terms of unitary implicates and implicants. Thus, we require efficient algorithms to calculate them. In classical propositional logic it is easy to obtain efficient algorithms to calculate the set of unitary implicants and implicates of a formula. In temporal logics, contrary to what we see in classical propositional logic, these sets may contain infinitely many members. Thus, in order to calculate them in an efficient way, we have to base the calculation on the theoretical study of how these sets behave. Such a study reveals the need to make a generalization of Lattice Theory, which is very important in “Computational Algebra”. In this paper we introduce the multisemilattice structure as a generalization of the semilattice structure. Such a structure is proposed as a particular type of poset. Subsequently, we offer an equivalent algebraic characterization based on non-deterministic operators and with a weakly associative property. We also show that from the structure of multisemilattice we can obtain an algebraic characterization of the multilattice structure. This paper concludes by showing the relevance of the multisemilattice structure in the design of algorithms aimed at calculating unitary implicates and implicants in temporal logics. Concretely, we show that it is possible to design efficient algorithms to calculate the unitary implicants/implicates only if the unitary formulae set has the multisemilattice structure.