A Conditional Logic for Iterated Belief Revision

In this paper we (Laura Giordano, Nicola Olivetti and myself) propose a conditional logic to represent iterated belief revision systems. We propose a set of postulates for belief revision which are a small variant of Darwiche and Pearl's ones.The resulting conditional logic has a standard semantics in terms of selection function models, and provides a natural representation of epistemic states. A Representation Theorem establishes a correspondence between iterated belief revision systems and conditional models. Our Representation Theorem does not entail Gärdenfors' Triviality Result

On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general

On strengthening the logic of iterated belief revision: proper ordinal interval operators

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. However, most of the suggestions for doing so have been radical enough to result in a dubious ‘reductionist’ principle that identifies belief states with orderings of worlds. The present paper offers a more modest strengthening of Darwiche and Pearl’s proposal. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the family that these principles characterise, which subsumes both lexicographic and restrained revision, can be represented as relating belief states that are associated with a ‘proper ordinal interval’ assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of a large number of AGM era postulates

On strengthening the logic of iterated belief revision: Proper ordinal interval operators

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general

The lexicographic closure as a revision process

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing "if A is true then, normally, B is true" be said to follow from a given set of items of such information. Many answers to this question have been proposed but, surprisingly, virtually none have attempted any explicit connection to belief revision. The aim of this paper is to give an example of how such a connection can be made by showing how the lexicographic closure of a set of defaults may be conceptualised as a process of iterated revision by sets of sentences. Specifically we use the revision process of Nayak.Comment: 7 pages, Nonmonotonic Reasoning Workshop 2000 (special session on belief change), at KR200

RankPL: A Qualitative Probabilistic Programming Language

In this paper we introduce RankPL, a modeling language that can be thought of as a qualitative variant of a probabilistic programming language with a semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used to represent and reason about processes that exhibit uncertainty expressible by distinguishing "normal" from" surprising" events. RankPL allows (iterated) revision of rankings over alternative program states and supports various types of reasoning, including abduction and causal inference. We present the language, its denotational semantics, and a number of practical examples. We also discuss an implementation of RankPL that is available for download