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

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

Extending the Harper Identity to Iterated Belief Change

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators

Mind-reading versus neuromarketing: how does a product make an impact on the consumer?

Purpose – This research study aims to illustrate the mapping of each consumer’s mental processes in a market-relevant context. This paper shows how such maps deliver operational insights that cannot be gained by physical methods such as brain imaging. Design/methodology/approach – A marketed conceptual attribute and a sensed material characteristic of a popular product were varied across presentations in a common use. The relative acceptability of each proposition was rated together with analytical descriptors. The mental interaction that determined each consumer’s preferences was calculated from the individual’s performance at discriminating each viewed sample from a personal norm. These personal cognitive characteristics were aggregated into maps of demand in the market for subpanels who bought these for the senses or for the attribute. Findings – Each of 18 hypothesized mental processes dominated acceptance in at least a few individuals among both sensory and conceptual purchasers. Consumers using their own descriptive vocabulary processed the factors in appeal of the product more centrally. The sensory and conceptual factors tested were most often processed separately, but a minority of consumers treated them as identical. The personal ideal points used in the integration of information showed that consumers wished for extremes of the marketed concept that are technologically challenging or even impossible. None of this evidence could be obtained from brain imaging, casting in question its usefulness in marketing. Research limitations/implications – Panel mapping of multiple discriminations from a personal norm fills three major gaps in consumer marketing research. First, preference scores are related to major influences on choices and their cognitive interactions in the mind. Second, the calculations are completed on the individual’s data and the cognitive parameters of each consumer’s behavior are aggregated – never the raw scores. Third, discrimination scaling puts marketed symbolic attributes and sensed material characteristics on the same footing, hence measuring their causal interactions for the first time. Practical implications – Neuromarketing is an unworkable proposition because brain imaging does not distinguish qualitative differences in behavior. Preference tests are operationally effective when designed and analyzed to relate behavioral scores to major influences from market concepts and sensory qualities in interaction. The particular interactions measured in the reported study relate to the major market for healthy eating. Originality/value – This is the first study to measure mental interactions among determinants of preference, as well as including both a marketed concept and a sensed characteristic. Such an approach could be of great value to consumer marketing, both defensively and creatively

IASME: Information Security Management Evolution for SMEs

Most of the research in information risk and risk management has focused on the needs of larger organisations. In the area of standards accreditation, the ISO/IEC 27001 Information Risk Management standard has continued to grow in acceptance and popularity with such organisations, although not to a significant extent with SMEs. An interesting product recently developed for ENISA (European Nations Information Security Association) based on the Carnegie-Mellon maturity model and aimed at SMEs has not so far filled the gap. In this paper, a researcher and two practitioners from the UK discuss an innovative development in the UK for addressing the information assurance needs of smaller organisations. They also share their perceptions about the security of national information infrastructures, and concerns that SMEs do not get the priority that their position in the supply chain would suggest they should have. The authors also explore the development and roll out of IASME (Information Assurance for SMEs), which they have developed in the context of a tight market, where spare cash is in short supply, and many SMEs are still in survival mode. The question for the business is therefore not seen as “can we afford to spend on information security” but “can we afford not to spend…” As well as the effect on being able to do business at all of having an SMEs systems compromised, there are also matters of reputation, and the growing threat of fines as a result of not complying with laws and regulations. The paper concludes with achievements of real businesses using the IASME process to cost-effectively achieve information assurance levels appropriate for themselves

Lagrangian Matroids: Representations of Type BnB_n

We introduce the concept of orientation for Lagrangian matroids represented in the flag variety of maximal isotropic subspaces of dimension N in the real vector space of dimension 2N+1. The paper continues the study started in math.CO/0209100.Comment: Requires amssymb.sty; 17 page

Lagrangian Pairs and Lagrangian Orthogonal Matroids

Represented Coxeter matroids of types $C_n$ and $D_n$, that is, symplectic and orthogonal matroids arising from totally isotropic subspaces of symplectic or (even-dimensional) orthogonal spaces, may also be represented in buildings of type $C_n$ and $D_n$, respectively. Indeed, the particular buildings involved are those arising from the flags or oriflammes, respectively, of totally isotropic subspaces. There are also buildings of type $B_n$ arising from flags of totally isotropic subspaces in odd-dimensional orthogonal space. Coxeter matroids of type $B_n$ are the same as those of type $C_n$ (since they depend only upon the reflection group, not the root system). However, buildings of type $B_n$ are distinct from those of the other types. The matroids representable in odd dimensional orthogonal space (and therefore in the building of type $B_n$) turn out to be a special case of symplectic (flag) matroids, those whose top component, or Lagrangian matroid, is a union of two Lagrangian orthogonal matroids. These two matroids are called a Lagrangian pair, and they are the combinatorial manifestation of the ``fork'' at the top of an oriflamme (or of the fork at the end of the Coxeter diagram of $D_n$). Here we give a number of equivalent characterizations of Lagrangian pairs, and prove some rather strong properties of them.Comment: Requires amssymb.sty; 12 pages, 2 LaTeX figure