Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Model, Metamodel and Topology

This reply to Gash’s (Found Sci 2013) commentary on Nescolarde-Selva and Usó-Doménech (Found Sci 2013) answers the three questions raised and at the same time opens up new questions.

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses.

An investigation of pretend play, mental state terms and false belief understanding: In search of a metarepresentational link

The aim of this study was to investigate the association between false belief comprehension, the exhibition of pretend play and the use of mental state terms in pre-school children. Ferry children, aged between 36 and 54 months were videotaped engaging in free play with each parent. The exhibit-ion of six distinct acts of pretend play and the expression of 16 mental sr:ate terms were coded during play. Each child was also administered a pantomime task and three standard false belief casks. Reliable associations were also found between false belief performance and the pretence categories of object substitution and role assignment, and the exhibition of imaginary object pantomimes. Moreover, the use of mental state terms was positively correlated with false belief and the pretence categories of object substitution, imaginary play and role assignment, and negatively correlated with the exhibition of body part object pantomimes. These findings indicate that the development of a mental state lexicon and some, bur not all, components of pretend play are dependent on the capacity for metarepresentational cognition.

Drawing insight from pictures: The development of concepts of false drawing and false belief in children with deafness, normal hearing, and autism

Theory-of-mind concepts in children with deafness, autism, and normal development (N = 154) were examined in three experiments using a set of standard inferential false-belief tasks and matched sets of tasks involving false drawings. Results of all three experiments replicated previously published findings by showing that primary school children with deafness or autism, aged 6 to 13 years, scored significantly lower than normal-developing 4-year-old preschoolers on standard misleading-container and unseen-change tests of false-belief understanding. Furthermore, deaf and autistic children generally scored higher on drawing-based tests than on corresponding standard tests and, on the most challenging of the false-drawing tests in Experiment 2, they significantly outperformed the normal-developing preschoolers by clearly understanding their own false intentions and another person's false beliefs about an actively misleading drawing. In Experiment 3, preschoolers; outperformed older deaf and autistic children on standard tasks, but did less well on a task that required the drawing of a false belief. Methodological factors could not fully explain the findings, but early social and conversational experiences in the family were deemed likely contributors.

Corporate rumor activity, belief and accuracy

An integrated model relating workplace rumor activity, belief, and accuracy is proposed and tested. Senior VPs of Communications from a sample of Fortune-500 corporations and CEOs of established public relations firms were surveyed regarding rumor episodes that they had experienced. Results confirmed previous research on the role of uncertainty, anxiety, and belief in rumor activity. In addition, a reduced sense of control mediated the effects of uncertainty on anxiety, and anxiety mediated the effects of importance on rumor activity. Evidence was found for the roles of group bias in how strongly a rumor is believed. Rumor activity was also implicated in the formation of more accurate rumors. The significance of these results for rumor theory and for Public Relations practitioners is presented. (C) 2002 Elsevier Science Inc. All rights reserved.

Reason Maintenance Systems: Tools for Foundations-based Belief Revision

Dynamic and distributed environments are hard to model since they suffer from unexpected changes, incomplete knowledge, and conflicting perspectives and, thus, call for appropriate knowledge representation and reasoning (KRR) systems. Such KRR systems must handle sets of dynamic beliefs, be sensitive to communicated and perceived changes in the environment and, consequently, may have to drop current beliefs in face of new findings or disregard any new data that conflicts with stronger convictions held by the system. Not only do they need to represent and reason with beliefs, but also they must perform belief revision to maintain the overall consistency of the knowledge base. One way of developing such systems is to use reason maintenance systems (RMS). In this paper we provide an overview of the most representative types of RMS, which are also known as truth maintenance systems (TMS), which are computational instances of the foundations-based theory of belief revision. An RMS module works together with a problem solver. The latter feeds the RMS with assumptions (core beliefs) and conclusions (derived beliefs), which are accompanied by their respective foundations. The role of the RMS module is to store the beliefs, associate with each belief (core or derived belief) the corresponding set of supporting foundations and maintain the consistency of the overall reasoning by keeping, for each represented belief, the current supporting justifications. Two major approaches are used to reason maintenance: single-and multiple-context reasoning systems. Although in the single-context systems, each belief is associated to the beliefs that directly generated it—the justification-based TMS (JTMS) or the logic-based TMS (LTMS), in the multiple context counterparts, each belief is associated with the minimal set of assumptions from which it can be inferred—the assumption-based TMS (ATMS) or the multiple belief reasoner (MBR).

Argumentation as Distributed Belief Revision: Conflict Resolution in Decentralised Multi-agent Systems

Decentralised co-operative multi-agent systems are computational systems where conflicts are frequent due to the nature of the represented knowledge. Negotiation methodologies, in this case argumentation based negotiation methodologies, were developed and applied to solve unforeseeable and, therefore, unavoidable conflicts. The supporting computational model is a distributed belief revision system where argumentation plays the decisive role of revision. The distributed belief revision system detects, isolates and solves, whenever possible, the identified conflicts. The detection and isolation of the conflicts is automatically performed by the distributed consistency mechanism and the resolution of the conflict, or belief revision, is achieved via argumentation. We propose and describe two argumentation protocols intended to solve different types of identified information conflicts: context dependent and context independent conflicts. While the protocol for context dependent conflicts generates new consensual alternatives, the latter chooses to adopt the soundest, strongest argument presented. The paper shows the suitability of using argumentation as a distributed decentralised belief revision protocol to solve unavoidable conflicts.

Solving Conflicting Beliefs with a Distributed Belief Revision Approach

The ability to solve conflicting beliefs is crucial for multi- agent systems where the information is dynamic, incomplete and dis- tributed over a group of autonomous agents. The proposed distributed belief revision approach consists of a distributed truth maintenance sy- stem and a set of autonomous belief revision methodologies. The agents have partial views and, frequently, hold disparate beliefs which are au- tomatically detected by system’s reason maintenance mechanism. The nature of these conflicts is dynamic and requires adequate methodolo- gies for conflict resolution. The two types of conflicting beliefs addressed in this paper are Context Dependent and Context Independent Conflicts which result, in the first case, from the assignment, by different agents, of opposite belief statuses to the same belief, and, in the latter case, from holding contradictory distinct beliefs. The belief revision methodology for solving Context Independent Con- flicts is, basically, a selection process based on the assessment of the cre- dibility of the opposing belief statuses. The belief revision methodology for solving Context Dependent Conflicts is, essentially, a search process for a consensual alternative based on a “next best” relaxation strategy.

Belief Revision in Multi-Agent Systems

The ability to respond sensibly to changing and conflicting beliefs is an integral part of intelligent agency. To this end, we outline the design and implementation of a Distributed Assumption-based Truth Maintenance System (DATMS) appropriate for controlling cooperative problem solving in a dynamic real world multi-agent community. Our DATMS works on the principle of local coherence which means that different agents can have different perspectives on the same fact provided that these stances are appropriately justified. The belief revision algorithm is presented, the meta-level code needed to ensure that all system-wide queries can be uniquely answered is described, and the DATMS’ implementation in a general purpose multi-agent shell is discussed.

Improving Assumption based Distributed Belief Revision

Belief revision is a critical issue in real world DAI applications. A Multi-Agent System not only has to cope with the intrinsic incompleteness and the constant change of the available knowledge (as in the case of its stand alone counterparts), but also has to deal with possible conflicts between the agents’ perspectives. Each semi-autonomous agent, designed as a combination of a problem solver – assumption based truth maintenance system (ATMS), was enriched with improved capabilities: a distributed context management facility allowing the user to dynamically focus on the more pertinent contexts, and a distributed belief revision algorithm with two levels of consistency. This work contributions include: (i) a concise representation of the shared external facts; (ii) a simple and innovative methodology to achieve distributed context management; and (iii) a reduced inter-agent data exchange format. The different levels of consistency adopted were based on the relevance of the data under consideration: higher relevance data (detected inconsistencies) was granted global consistency while less relevant data (system facts) was assigned local consistency. These abilities are fully supported by the ATMS standard functionalities.