Pseudo-intent is one of the significant notions of formal concept analysis.Pseudo-intents of formal contexts have gained interest in recent years

since this notion is helpful for finding minimal representations of implicational theories.In order to obtain all pseudo-intents from a given formal context

the existing approaches need to examine all combinations of attributes

which are not intents of formal concepts.However

the number of attribute combinations can be exponential in the number of attributes

which may easily leads to the explosion of search space.To address this problem

this paper provides characterizations of pseudo-intents from the point of view of minimal generators of concept intents.The necessary and sufficient conditions of pseudo-intents are derived.Based on these results

an algorithm

called GPI

is designed to generate all pseudo-intents from a formal context.The efficiency of the algorithm is analyzed and several optimizations are presented.The algorithm computes pseudo-intents starting from minimal generators of concept intents and is helpful to reduce the search space of non-intents.Thus it improves the computational efficiency of pseudo-intents.Theory analysis and experimental results show the feasibility and effectiveness of the algorithm.