Trust transitivity and conditional belief reasoning

Abstract. Trust transitivity is a common phenomenon embedded in human reasoning about trust. Given a specific context or purpose, trust transitivity is often manifested through the humans' intuition to rely on the recommendations of a trustworthy advisor about another entity that the advisor recommends. Although this simple principle has been formalised in various ways for many trust and reputation systems, there is no real or physical basis for trust transitivity to be directly translated into a mathematical model. In that sense, all mathematical operators for trust transitivity proposed in the literature must be considered ad hoc; they represent attempts to model a very complex human phenomenon as if it were lendable to analysis by the laws of physics. Considering this nature of human trust transitivity in reality, any simple mathematical model will essentially have rather poor predictive power. In this paper, we propose a new interpretation of trust transitivity that is radically different from those described in the literature so far. More specifically, we consider recommendations from an advisor as evidence that the relying party will use as input arguments in conditional reasoning models for assessing hypotheses about the trust target. The proposed model of conditional trust transitivity is based on the framework of subjective logic

The logic of epistemic justification

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic

"If Oswald had not killed Kennedy" – Spohn on Counterfactuals

Wolfgang Spohn's theory of ranking functions is an elegant and powerful theory of the structure and dynamics of doxastic states. In two recent papers, Spohn has applied it to the analysis of conditionals, claiming to have presented a unified account of indicative and subjunctive (counterfactual) conditionals. I argue that his analysis fails to account for counterfactuals that refer to indirect causes. The strategy of taking the transitive closure that Spohn employs in the theory of causation is not available for counterfactuals. I have a close look at Spohn's treatment of the famous Oswald-Kennedy case in order to illustrate my points. I sketch an alternative view that seems to avoid the problems

Factors and processes in children's transitive deductions

Transitive tasks are important for understanding how children develop socio-cognitively. However, developmental research has been restricted largely to questions surrounding maturation. We asked 6-, 7- and 8-year-olds (N = 117) to solve a composite of five different transitive tasks. Tasks included conditions asking about item-C (associated with the marked relation) in addition to the usual case of asking only about item-A (associated with the unmarked relation). Here, children found resolving item-C much easier than resolving item-A, a finding running counter to long-standing assumptions about transitive reasoning. Considering gender perhaps for the first time, boys exhibited higher transitive scores than girls overall. Finally, analysing in the context of one recent and well-specified theory of spatial transitive reasoning, we generated the prediction that reporting the full series should be easier than deducing any one item from that series. This prediction was not upheld. We discuss amendments necessary to accommodate all our earlier findings

Evidence: A Guide for the Uncertain

Assume that it is your evidence that determines what opinions you should have. I argue that since you should take peer disagreement seriously, evidence must have two features. (1) It must sometimes warrant being modest: uncertain what your evidence warrants, and (thus) uncertain whether you’re rational. (2) But it must always warrant being guided: disposed to treat your evidence as a guide. Surprisingly, it is very difficult to vindicate both (1) and (2). But diagnosing why this is so leads to a proposal—Trust—that is weak enough to allow modesty but strong enough to yield many guiding features. In fact, I claim that Trust is the Goldilocks principle—for it is necessary and sufficient to vindicate the claim that you should always prefer to use free evidence. Upshot: Trust lays the foundations for a theory of disagreement and, more generally, an epistemology that permits self-doubt—a modest epistemology

Local and Global Trust Based on the Concept of Promises

We use the notion of a promise to define local trust between agents possessing autonomous decision-making. An agent is trustworthy if it is expected that it will keep a promise. This definition satisfies most commonplace meanings of trust. Reputation is then an estimation of this expectation value that is passed on from agent to agent. Our definition distinguishes types of trust, for different behaviours, and decouples the concept of agent reliability from the behaviour on which the judgement is based. We show, however, that trust is fundamentally heuristic, as it provides insufficient information for agents to make a rational judgement. A global trustworthiness, or community trust can be defined by a proportional, self-consistent voting process, as a weighted eigenvector-centrality function of the promise theoretical graph

Defeaters and Disqualifiers

Justification depends on context: even if E on its own justifies H, still it might fail to justify in the context of D. This sort of effect, epistemologists think, is due to defeaters, which undermine or rebut a would-be justifier. I argue that there is another fundamental sort of contextual feature, disqualification, which doesn't involve rebuttal or undercutting, and which cannot be reduced to any notion of screening-off. A disqualifier makes some would-be justifier otiose, as direct testimony sometimes does to distal testimony, and as manifestly decisive evidence might do to gratuitous evidence on the same team. Basing a belief on disqualified evidence, moreover, is distinctively irrational. One is not necessarily irresponsible. Instead one is turning down a free upgrade to a sleeker, stabler basis for one's beliefs. Such an upgrade would prevent wastes of epistemic effort, since someone who bases her belief on a disqualified proposition E will need to remember E and rethink her belief should E ever be defeated. The upgrade might also reduce reliance on unwieldy evidence, if E is relevant only thanks to some labyrinthine argument; and if even ideal agents should doubt their ability to follow such arguments, even they should care about disqualifiers

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