Evidence Propagation and Consensus Formation in Noisy Environments

We study the effectiveness of consensus formation in multi-agent systems where there is both belief updating based on direct evidence and also belief combination between agents. In particular, we consider the scenario in which a population of agents collaborate on the best-of-n problem where the aim is to reach a consensus about which is the best (alternatively, true) state from amongst a set of states, each with a different quality value (or level of evidence). Agents' beliefs are represented within Dempster-Shafer theory by mass functions and we investigate the macro-level properties of four well-known belief combination operators for this multi-agent consensus formation problem: Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging operator. The convergence properties of the operators are considered and simulation experiments are conducted for different evidence rates and noise levels. Results show that a combination of updating on direct evidence and belief combination between agents results in better consensus to the best state than does evidence updating alone. We also find that in this framework the operators are robust to noise. Broadly, Yager's rule is shown to be the better operator under various parameter values, i.e. convergence to the best state, robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen

A probabilistic analysis of argument cogency

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align

Formalized Conceptual Spaces with a Geometric Representation of Correlations

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define various operations for our formalization, both for creating new concepts from old ones and for measuring relations between concepts. We present an illustrative toy-example and sketch a research project on concept formation that is based on both our formalization and its implementation.Comment: Published in the edited volume "Conceptual Spaces: Elaborations and Applications". arXiv admin note: text overlap with arXiv:1706.06366, arXiv:1707.02292, arXiv:1707.0516

Fragmentation and logical omniscience

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient