R-Calculus: A Logic of Belief Revision

This book introduces new models based on R-calculus and theories of belief revision for dealing with large and changing data. It extends R-calculus from first-order logic to propositional logic, description logics, modal logic and logic programming, and from minimal change semantics to subset minimal change, pseudo-subformula minimal change and deduction-based minimal change (the last two minimal changes are newly defined). And it proves soundness and completeness theorems with respect to the minimal changes in these logics. To make R-calculus computable, an approximate R-calculus is given which uses finite injury priority method in recursion theory. Moreover, two applications of R-calculus are given to default theory and semantic inheritance networks.

This book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners in the field of logic. Also it is very useful for all those who are interested in data, digitization and correctness and consistency of information, in modal logics, non monotonic logics, decidable/undecidable logics, logic programming, description logics, default logics and semantic inheritance networks.

本書介紹了基於R-計算和信念修正理論的新模型，用於處理大型且不斷變化的數據。它將R-計算從一階邏輯擴展到命題邏輯、描述邏輯、模態邏輯和邏輯編程，並從最小變化語義擴展到子集最小變化、偽子公式最小變化和基於推理的最小變化（最後兩種最小變化是新定義的）。並且證明了這些邏輯中最小變化的完備性和一致性定理。為了使R-計算可計算，提出了一種使用有限損傷優先方法的近似R-計算。此外，還提供了R-計算在默認理論和語義繼承網絡中的兩個應用。

本書結合了理論和實踐，適合邏輯領域的學生、研究人員和從業人員閱讀。對於所有對數據、數字化以及信息的正確性和一致性感興趣的人，以及對模態邏輯、非單調邏輯、可判定/不可判定邏輯、邏輯編程、描述邏輯、默認邏輯和語義繼承網絡感興趣的人來說，本書非常有用。