Reconstructing a single-head formula to facilitate logical forgetting

Logical forgetting is removing some variables from a logical formula while preserving its information regarding the others [LLM03]. Seen from a different angle, it is restricting a formula to keep only its information about some of its variables [Del17]. Each of the two interpretations has its own applications. Removing information allow reducing memory requirements [EKI19], simplifying reasoning [DW15, EF07, WSS05] and clarifying the relationship about variables [Del17]. Restricting a formula on some variables allows formalizing the limited knowledge of agents [FHMV95, RHPT14], ensuring privacy [GKLW17] and removing inconsistency [LM10].