Forgetting complex propositions

This paper uses possible-world semantics to model the changes that may occur in an agent's knowledge as she loses information. This builds on previous work in which the agent may forget the truth-value of an atomic proposition, to a more general case where she may forget the truth-value of a propositional formula. The generalization poses some challenges, since in order to forget whether a complex proposition $\pi$ is the case, the agent must also lose information about the propositional atoms that appear in it, and there is no unambiguous way to go about this. We resolve this situation by considering expressions of the form $[\boldsymbol{\ddagger} \pi]\varphi$, which quantify over all possible (but minimal) ways of forgetting whether $\pi$. Propositional atoms are modified non-deterministically, although uniformly, in all possible worlds. We then represent this within action model logic in order to give a sound and complete axiomatization for a logic with knowledge and forgetting. Finally, some variants are discussed, such as when an agent forgets $\pi$ (rather than forgets whether $\pi$) and when the modification of atomic facts is done non-uniformly throughout the model

Demonstração da Adequação do Operador BPM aos Postulados de Fusão de Crenças

TCC(graduação) - Universidade Federal de Santa Catarina. Centro Tecnológico. Ciências da Computação.A manutenção de crenças é um grande desafio na concepção de agen- tes inteligentes. Em particular, a área de fusão de crenças tem por objetivo definir crenças e objetivos comuns para um grupo de agentes com objetivos individuais distintos e possivelmente conflitantes, man- tendo suas bases de crenças individuais consistentes e sem perda ex- cessiva de informação. Neste contexto, alguns operadores para fusão de crenças foram propostos nas últimas décadas, incluindo os pionei- ros: operadores de maioria e arbitração - que utilizam, como principal medida de mudança, o cálculo de distância entre as bases considerando como unidade de distância um símbolo proposicional. Grande parte dos operadores atuam sobre conjuntos de modelos, que podem cres- cer exponencialmente ao número de fórmulas descritas na base. Como alternativa, operadores sintáticos podem ser utilizados. Em particu- lar, o operador BPM (acrônimo de Bittencourt, Perrussel e Marchi) foi proposto utilizando a mesma ideia de medida mínima, mas atuando sobre uma representação dual enxuta da base de crenças, denominada formas normais primárias, obtendo resultados equivalentes. Contudo, permaneceu em aberto a demonstração de que tal operador respeita os postulados estabelecidos para guiar processos de fusão de crenças. Desta forma, o objetivo deste trabalho foi demonstrar que tal operador satisfaz os postulados de fusão, o que foi realizado com sucesso utili- zando as próprias definições de implicantes primários como estratégia para as provas. Assim sendo, o operador sintático BPM torna-se uma interessante ferramenta para determinadas situações em que lidamos com sistemas baseados em conhecimento.Maintenance of belief bases is a big challenge in the design of intelligent agents. In particular, the belief merging area aims to define common beliefs and goals for a group of agents with distinct and possibly con- flicting individual goals, keeping their individual belief bases consistent and without excessive loss of information. In this context, some belief merging operators have been proposed in the recent decades, including the pioneers: majority and arbitration operators - which use, as a me- asure of change, the calculation of distance between bases considering one propositional symbol as the unit of distance. Most operators act on model sets, which can grow exponentially on the number of formulas described in the belief base. As alternative, synthetic operators can be used. In particular, the BPM operator (acronym of Bittencourt, Perrussel and Marchi) was proposed using the same idea of minimum measure, but acting on a minimal dual representation of the belief ba- ses, called prime normal forms, obtaining equivalent results. However, the demonstration such this operator respect the postulates established to guide belief merging processes remains open. Thus, the objective of this work was to demonstrate that this operator satisfies the merging postulates, which was done successfully using the definitions of prime implicants as an strategy for the demonstrations. Thus, the synthetic operator BPM becomes an interesting tool to obtain situations that deal with basic knowledge systems

Prime Forms in Possibilistic Logic

Possibilistic logic is a weighted logic used to represent uncertain and inconsistent knowledge. Its semantics is often defined by a possibility distribution, which is a function from a set of interpretations to a totally ordered scale. In this paper, we consider a new semantic characteristics of knowledge bases in possibilistic logic (or possibilistic knowledge bases) by a generalized notion of propositional prime implicant, which we call prioritized prime implicant. We first consider several desirable properties of a prioritized prime implicant for characterizing possibilistic knowledge bases. Some examples show that existing generalizations of prime implicant in possibilistic logic do not satisfy all of these properties. We then provide a novel definition of prioritized prime implicant, which is a set of weighted literals that may be inconsistent. We show that the prioritized prime implicants satisfy all the desirable properties. Finally, we discuss the problem of computing prioritized prime implicants of a possibilistic knowledge base

07351 Abstracts Collection -- Formal Models of Belief Change in Rational Agents

From 26.08. to 30.08.2007, the Dagstuhl Seminar 07351 ``Formal Models of Belief Change in Rational Agents\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Prime Forms in Possibilistic Logic

Possibilistic logic is a weighted logic used to represent uncertain and inconsistent knowledge. Its semantics is often defined by a possibility distribution, which is a function from a set of interpretations to a totally ordered scale. In this paper, we consider a new semantic characteristics of knowledge bases in possibilistic logic (or possibilistic knowledge bases) by a generalized notion of propositional prime implicant, which we call prioritized prime implicant. We first consider several desirable properties of a prioritized prime implicant for characterizing possibilistic knowledge bases. Some examples show that existing generalizations of prime implicant in possibilistic logic do not satisfy all of these properties. We then provide a novel definition of prioritized prime implicant, which is a set of weighted literals that may be inconsistent. We show that the prioritized prime implicants satisfy all the desirable properties. Finally, we discuss the problem of computing prioritized prime implicants of a possibilistic knowledge base

Fetishism and the social value of objects.

The idea of the fetish has a particular presence in the writings of both Marx and Freud. It implies for these two theorists of the social, a particular form of relation between human beings and objects. In the work of both the idea of the fetish involves attributing properties to objects that they do not 'really' have and that should correctly be recognised as human. While Marx's account of fetishism addresses the exchange-value of commodities at the level of the economic relations of production, it fails to deal in any detail with the use-value or consumption of commodities. In contrast Freud's concept of the fetish as a desired substitute for a suitable sex object explores how objects are desired and consumed. Drawing on both Marx and Freud, Baudrillard breaks with their analyses of fetishism as demonstrating a human relation with unreal objects. He explores the creation of value in objects through the social exchange of sign values, showing how objects are fetishised in ostentation. This paper argues that while Baudrillard breaks with the realism characteristic of Marx's and Freud's analyses of fetishism, he does not go far enough in describing the social and discursive practices in which objects are used and sometimes transformed into fetishes. It is proposed that the fetishisation of objects involves an overdetermination of their social value through a discursive negotiation of the capacities of objects that stimulates fantasy and desire for them

Handling Incoming Beliefs

International audienceMost logic-based approaches to knowledge and belief change in artificial intelligence assume that when a new piece of information comes up, it should be merely added to the current beliefs or knowledge when this does not lead to inconsistency. This paper addresses situations where this assumption does not hold. The focus is on the construction of Boolean standard-logic knowledge and belief bases in this context. We propose an approach to handle incoming beliefs that can require some formulas reconstruction or a form of preemption to be performed

A Computational Model and Convergence Theorem for Rumor Dissemination in Social Networks

The spread of rumors, which are known as unverified statements of uncertain origin, may cause tremendous number of social problems. If it would be possible to identify factors affecting spreading a rumor (such as agents' desires, trust network, etc.), then this could be used to slowdown or stop its spreading. A computational model that includes rumor features and the way a rumor is spread among society's members, based on their desires, is therefore needed. Our research is centering on the relation between the homogeneity of the society and rumor convergence in it and result shows that the homogeneity of the society is a necessary condition for convergence of the spreading rumor.Comment: 29 pages, 7 figure

Early Settlement in European Merger Control

We analyse the determinants of early settlement between merging parties and the European Commission over remedies that remove concerns of anticompetitive effects. This extends the previously narrow range of econometric literature on early settlement. Consistent with the theory of early settlement, our results confirm the importance of delay costs and of uncertainty, measured by the complexity of the economic analysis required for each merger. We also find a non-monotonic effect of agency resourcing, which raises questions about the Commission's efficiency in times of high case load. Econometrically, we select a sample of merger decisions in which the European Commission intervened due to concerns of anticompetitive effects, and our selection model provides estimates of the factors determining intervention by the Commission. Conclusions are drawn for public policy