Evidence and plausibility in neighborhood structures

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood $N$ indicates that the agent has reason to believe that the true state of the world lies in $N$. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this evidence structure, yielding our intended models for evidence-based beliefs. In addition, we also consider a second more general flavor, where belief and plausibility are modeled using additional primitive relations, and we prove a representation theorem showing that each such general model is a $p$-morphic image of an intended one. This semantics invites a number of natural special cases, depending on how uniform we make the evidence sets, and how coherent their total structure. We give a structural study of the resulting `uniform' and `flat' models. Our main result are sound and complete axiomatizations for the logics of all four major model classes with respect to the modal language of evidence, belief and safe belief. We conclude with an outlook toward logics for the dynamics of changing evidence, and the resulting language extensions and connections with logics of plausibility change

Implementation with Evidence: Complete Information

We study full-implementation in Nash equilibrium under complete information. We generalize the canonical model (Maskin, 1977) by allowing agents to send evidence or discriminatory signals. A leading case is where evidence is hard information that proves something about the state of the world. In this environment, an implementable social choice rule need not be Maskin-monotonic. We formulate a weaker property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation if there are three or more agents and the social choice rule satisfies two other properties—no veto power and non-satiation—that are reasonable in various settings, including “economic environments”. We discuss how natural conditions on the cost of discriminatory signals yield possibility results, in contrast with traditional negative results. Additional results are provided for the case of one and two agents.

Algorithmic parameterization of mixed treatment comparisons

Mixed Treatment Comparisons (MTCs) enable the simultaneous meta-analysis (data pooling) of networks of clinical trials comparing ≥2 alternative treatments. Inconsistency models are critical in MTC to assess the overall consistency between evidence sources. Only in the absence of considerable inconsistency can the results of an MTC (consistency) model be trusted. However, inconsistency model specification is non-trivial when multi-arm trials are present in the evidence structure. In this paper, we define the parameterization problem for inconsistency models in mathematical terms and provide an algorithm for the generation of inconsistency models. We evaluate running-time of the algorithm by generating models for 15 published evidence structures

Implementation with evidence

We generalize the canonical problem of Nash implementation by allowing agents to voluntarily provide discriminatory signals, i.e. evidence. Evidence can either take the form of hard information or, more generally, have differential but non-prohibitive costs in different states. In such environments, social choice functions that are not Maskin-monotonic can be implemented. We formulate a more general property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation in economic environments. In some settings, such as when agents have small preferences for honesty, any social choice function is evidence-monotonic. Additional characterizations are obtained for hard evidence. We discuss the relationship between the implementation problem where evidence provision is voluntary and a hypothetical problem where evidence can be chosen by the planner as part of an extended outcome space.Mechanism design, costly signaling, verifiable information, Nash implementation

Hypotheses, evidence and relationships: The HypER approach for representing scientific knowledge claims

Biological knowledge is increasingly represented as a collection of (entity-relationship-entity) triplets. These are queried, mined, appended to papers, and published. However, this representation ignores the argumentation contained within a paper and the relationships between hypotheses, claims and evidence put forth in the article. In this paper, we propose an alternate view of the research article as a network of 'hypotheses and evidence'. Our knowledge representation focuses on scientific discourse as a rhetorical activity, which leads to a different direction in the development of tools and processes for modeling this discourse. We propose to extract knowledge from the article to allow the construction of a system where a specific scientific claim is connected, through trails of meaningful relationships, to experimental evidence. We discuss some current efforts and future plans in this area