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Partial monotonicity and a new version of the Ramsey test

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Abstract

We introduce two new belief revision axioms: partial monotonicity and consequence correctness. We show that partial monotonicity is consistent with but independent of the full set of axioms for a Gärdenfors belief revision sytem. In contrast to the Gärdenfors inconsistency results for certain monotonicity principles, we use partial monotonicity to inform a consistent formalization of the Ramsey test within a belief revision system extended by a conditional operator. We take this to be a technical dissolution of the well-known Gärdenfors dilemma.

In addition, we present the consequential correctness axiom as a new measure of minimal revision in terms of the deductive core of a proposition whose support we wish to excise. We survey several syntactic and semantic belief revision systems and evaluate them according to both the Gärdenfors axioms and our new axioms. Furthermore, our algebraic characterization of semantic revision systems provides a useful technical device for analysis and comparison, which we illustrate with several new proofs.

Finally, we have a new inconsistency result, which is dual to the Gärdenfors inconsistency results. Any elementary belief revision system that is consequentially correct must violate the Gärdenfors axiom of strong boundedness (K*8), which we characterize as yet another monotonicity condition.

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Authors and Affiliations

  1. McDonnell Douglas Research Laboratories Dept. 225, Bldg. 105/2, Mailcode 1065165, P.O.Box 516, 63166, St. Louis, MO, USA

    John Pais & Peter Jackson

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  1. John Pais
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  2. Peter Jackson
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This work was supported by the McDonnell Douglas Independent Research and Development program.

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Pais, J., Jackson, P. Partial monotonicity and a new version of the Ramsey test. Studia Logica 51, 21–47 (1992). https://doi.org/10.1007/BF00370330

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