Belief revision in the propositional closure of a qualitative algebra

Belief revision is an operation that aims at modifying old be-liefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily repre-sentable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional clo-sures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an al-gorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web

Belief revision in the propositional closure of a qualitative algebra

International audienceBelief revision is an operation that aims at modifying old be-liefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily repre-sentable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional clo-sures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an al-gorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web.La révision des croyances est une opération visant à modifier d'anciennes croyances afin qu'elles deviennent cohérentes avec de nouvelles croyances. La problématique de la révision des croyances a été étudiée dans divers formalismes, en particulier dans les algèbres qualitatives (AQ), dans lesquelles le résultat est une disjonction de bases de croyances, qui ne sont pas nécessairement représentables dans une AQ. Cela motive l'étude de la révision des croyances dans les clôtures propositionnelles des AQ, dans lesquels le résultat de la révision est représentable. Cette propriété rend possible la définition d'un opérateur de contraction, en s'appuyant sur l'identité de Harper. La révision des croyances dans les clôtures propositionnelles d'AQ est étudiée, un algorithme pour une famille d'opérateurs de révision dans ces formalismes est présenté et une implantation gratuite, avec code source ouvert et disponible sur la toile est décrite

Belief revision in the propositional closure of a qualitative algebra (extended version)

This is the extended version of an article originally presented at the 14th International Conference on Principles of Knowledge Representation and ReasoningBelief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily representable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional closures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an algorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web. (This is the extended version of an article originally presented at the 14th International Conference on Principles of Knowledge Representation and Reasoning.)La révision des croyances est une opération visant à modifier d'anciennes croyances afin qu'elles deviennent cohérentes avec de nouvelles croyances. La problématique de la révision des croyances a été étudiée dans divers formalismes, en particulier dans les algèbres qualitatives (AQ), dans lesquelles le résultat est une disjonction de bases de croyances, qui ne sont pas nécessairement représentables dans une AQ. Cela motive l'étude de la révision des croyances dans les clôtures propositionnelles des AQ, dans lesquels le résultat de la révision est représentable. Cette propriété rend possible la définition d'un opérateur de contraction, en s'appuyant sur l'identité de Harper. La révision des croyances dans les clôtures propositionnelles d'AQ est étudiée, un algorithme pour une famille d'opérateurs de révision dans ces formalismes est présenté et une implantation gratuite, avec code source ouvert et disponible sur la toile est décrite

To Preference via Entrenchment

We introduce a simple generalization of Gardenfors and Makinson's epistemic entrenchment called partial entrenchment. We show that preferential inference can be generated as the sceptical counterpart of an inference mechanism defined directly on partial entrenchment.Comment: 16 page

Belief as Willingness to Bet

We investigate modal logics of high probability having two unary modal operators: an operator $K$ expressing probabilistic certainty and an operator $B$ expressing probability exceeding a fixed rational threshold $c\geq\frac 12$. Identifying knowledge with the former and belief with the latter, we may think of $c$ as the agent's betting threshold, which leads to the motto "belief is willingness to bet." The logic $\mathsf{KB.5}$ for $c=\frac 12$ has an $\mathsf{S5}$ $K$ modality along with a sub-normal $B$ modality that extends the minimal modal logic $\mathsf{EMND45}$ by way of four schemes relating $K$ and $B$, one of which is a complex scheme arising out of a theorem due to Scott. Lenzen was the first to use Scott's theorem to show that a version of this logic is sound and complete for the probability interpretation. We reformulate Lenzen's results and present them here in a modern and accessible form. In addition, we introduce a new epistemic neighborhood semantics that will be more familiar to modern modal logicians. Using Scott's theorem, we provide the Lenzen-derivative properties that must be imposed on finite epistemic neighborhood models so as to guarantee the existence of a probability measure respecting the neighborhood function in the appropriate way for threshold $c=\frac 12$. This yields a link between probabilistic and modal neighborhood semantics that we hope will be of use in future work on modal logics of qualitative probability. We leave open the question of which properties must be imposed on finite epistemic neighborhood models so as to guarantee existence of an appropriate probability measure for thresholds $c\neq\frac 12$.Comment: Removed date from v1 to avoid confusion on citation/reference, otherwise identical to v