The AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. We generalize K&M's approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of ``base'' (such as belief sets, arbitrary or finite sets of sentences, or single sentences). The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain ``assignments'': functions mapping belief bases to total - yet not transitive - ``preference'' relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M's original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence.
%0 Journal Article
%1 Falakh2021-vo
%A Falakh, Faiq Miftakhul
%A Rudolph, Sebastian
%A Sauerwald, Kai
%D 2021
%I arXiv
%K
%T Semantic characterizations of general belief base revision
%X The AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. We generalize K&M's approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of ``base'' (such as belief sets, arbitrary or finite sets of sentences, or single sentences). The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain ``assignments'': functions mapping belief bases to total - yet not transitive - ``preference'' relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M's original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence.
@article{Falakh2021-vo,
abstract = {The AGM postulates by Alchourr{\'o}n, G{\"a}rdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K\&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. We generalize K\&M's approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of ``base'' (such as belief sets, arbitrary or finite sets of sentences, or single sentences). The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain ``assignments'': functions mapping belief bases to total - yet not transitive - ``preference'' relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K\&M's original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence.},
added-at = {2024-09-10T11:56:37.000+0200},
author = {Falakh, Faiq Miftakhul and Rudolph, Sebastian and Sauerwald, Kai},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2f52af0bb69f766de283374a52172774b/scadsfct},
interhash = {18372371a398db8e4085941dc88c9cf8},
intrahash = {f52af0bb69f766de283374a52172774b},
keywords = {},
publisher = {arXiv},
timestamp = {2024-09-10T15:15:57.000+0200},
title = {Semantic characterizations of general belief base revision},
year = 2021
}
