Formalizing GDPR provisions in reified I/O logic: the DAPRECO knowledge base

in Journal of Logic, Language and Information (2019)

AGM Contraction and Revision of Rules

in Journal of Logic, Language and Information (2016), 25(3), 273-297

In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas ... [more ▼]

In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator Cn by an input/output logic. The results in this paper suggest that, in general, results from belief base dynamics can be transferred to rule base dynamics, but that a similar transfer of AGM theory change to rule change is much more problematic. First, we generalise belief base contraction to rule base contraction, and show that two representation results of Hansson still hold for rule base contraction. Second, we show that the six so-called basic postulates of AGM contraction are consistent only for some input/output logics, but not for others. In particular, we show that the notorious recovery postulate can be satisfied only by basic output, but not by simple-minded output. Third, we show how AGM rule revision can be defined in terms of AGM rule contraction using the Levi identity. We highlight various topics for further research. [less ▲]

A Theory of Hierarchical Consequence and Conditionals

in Journal of Logic, Language and Information (2010), 19(1), 332

We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked preferential structures are intermediate between sim- ple preferential structures and ranked ... [more ▼]

We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked preferential structures are intermediate between sim- ple preferential structures and ranked structures. The additional accessibility relation allows us to consider only parts of the overall A-ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved. [less ▲]