Recently, the old logical notion of forgetting propositional symbols (or reducing the logical vocabulary) has been generalized to a new notion: forgetting literals. The aim was to help the automatic computation of various formalisms which are currently used in knowledge representation, particularly for nonmonotonic reasoning. We develop here a further generalization, allowing propositional symbols to vary while forgetting literals. We describe the new notion, on the syntactical and the semantical side. We provide various manipulations over the basic definitions involved, including for the original version, which hopefully should help improving again the efficiency of the computation. This work concerns especially circumscription, since it is known that one way of computing circumscription uses the forgetting of literals.
[1]
Yan Zhang,et al.
Reasoning about Knowledge by Variable Forgetting
,
2004,
KR.
[2]
Teodor C. Przymusinski.
An Algorithm to Compute Circumscription
,
1989,
Artif. Intell..
[3]
Yves Moinard,et al.
Forgetting Literals with Varying Propositional Symbols
,
2007,
J. Log. Comput..
[4]
R. Reiter,et al.
Forget It !
,
1994
.
[5]
John McCarthy,et al.
Applications of Circumscription to Formalizing Common Sense Knowledge
,
1987,
NMR.
[6]
Fangzhen Lin,et al.
On strongest necessary and weakest sufficient conditions
,
2000,
Artif. Intell..