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On the Logic of Theory Base Change: Reformulation of Belief Bases
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Introduces reformulation, a belief base change operation that makes an implicit consequence explicit while keeping the logical closure unchanged, built from AGM-style base contraction and characterized axiomatically.
Problem
Belief base change operations (AGM-style) treat logically equivalent bases alike, so they cannot model changes that only alter the explicit/implicit status of beliefs without changing consequences.
Approach
Define reformulation R(B,p) as base contraction by p followed by adding p explicitly, plus recovery sentences p→q, so that the logical closure is preserved while p becomes explicit and redundant derivations are removed; provide partial meet and kernel versions with representation theorems.
Key results
- Defines a reformulation operation R(B,p)=B-p ∪ {p→q} ∪ {p} when B⊢p, and shows it is characterized by postulates R2, R2b, R3, R4, R6, R6b iff the underlying contraction is partial meet (Theorem 12).
- Shows a kernel-based version is characterized by R2, R2b, R5, R4, R6, R6b iff the contraction is kernel base contraction (Theorem 13).
- Proposes three non-redundant variants (RM2, RM3, RM4) whose full axiomatic characterization is left to future work.
Limitations
- Full axiomatic characterization of the non-redundant variants RM2-RM4 is left open
- Reformulation as defined may retain redundant sentences (e.g., p→q recovery sentences) in some variants
- Purely theoretical; no computational evaluation or implementation
Experimental setup
Builds on: AGM model partial meet base contraction (Hansson 1992) kernel contraction (Hansson 1994) Nebel recovery construction
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