Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Theory of Relational Databases
Theory of Relational Databases
Counting pseudo-intents and #p-completeness
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
Some Computational Problems Related to Pseudo-intents
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
On the complexity of enumerating pseudo-intents
Discrete Applied Mathematics
Some notes on managing closure operators
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Computing premises of a minimal cover of functional dependencies is intractable
Discrete Applied Mathematics
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Pseudo-intents (also called pseudo-closed sets) of formal contexts have gained interest in recent years, since this notion is helpful for finding minimal representations of implicational theories. In particular, there are some open problems regarding complexity. In our paper, we compile some results about pseudo-intents which contribute to the understanding of this notion and help in designing optimized algorithms. We provide a characterization of pseudointents based on the notion of a formal context's incrementors. The latter are essentially non-closed sets which - when added to a closure system - do not enforce the presence of other new attribute sets. In particular, the provided definition is non recursive. Moreover we show that this notion coincides with the notion of a quasi-closed set that is not closed, which enables to reuse existing results and to formulate an algorithm that checks for pseudo-closedness. Later on, we provide an approach for further optimizing those algorithms based on a result which correlates the set of pseudo-intents of a formal context with the pseudo-intents of this context's reduced version.