Trust: Definitions & Models

• Trust is a relational, context-dependent construct defined by a willingness to accept vulnerability under uncertainty and is modeled using diverse formal mechanisms such as promise theory and matrix factorization.
• Advanced methodologies quantify trust through mathematical representations, bias adjustments, and dynamic updating techniques across domains like IoT systems, human–computer interaction, and secure distributed systems.
• Robust trust frameworks integrate continuous evaluation, behavior tracking, and formal verification to ensure calibrated decision-making even under adversarial conditions.

Trust is a relational, context-dependent, and often explicitly quantified construct that links a trustor to a trustee under uncertainty. In the surveyed literature, trust is variously defined as a “willingness to accept vulnerability based on positive expectations,” a “subjective local belief that a node will behave normally,” an expectation that an autonomous agent will keep a promise, a dynamic metric attached to operating code, a formally verified relation grounded in current abilities and commitments, and a signed parameter that determines whether feedback should be used, ignored, or inverted (Beltrão et al., 7 Apr 2026, Putra et al., 2019, 0912.4637, Creado et al., 2014, Fathabadi et al., 2023, Hosseini et al., 26 Jan 2026). Taken together, these formulations suggest that trust is not a single yes/no attribute, but a family of typed, state-sensitive, and domain-specific mechanisms for deciding when reliance is warranted.

1. Conceptual meanings and domains of trust

Several lines of work treat trust as inseparable from vulnerability, uncertainty, and expectation. In human–computer interaction, trust in technology is defined as a belief that a technological system will help users achieve their goals in situations of uncertainty and vulnerability, and as an attitude that mediates behavior such as reliance, monitoring, override, or bypass (Beltrão et al., 7 Apr 2026). In formal work on AI, trust is contractual: a human trusts a model $M$ to uphold a contract $C$, such as correctness, fairness, privacy, or robustness, and that trust is warranted only if it is caused by the model’s actual capability to maintain $C$ (Jacovi et al., 2020).

Other traditions define trust in terms of expectation over behavior. In promise theory, an agent is trustworthy if it is expected that it will keep a promise; local trust is the expectation $E_A(S \xrightarrow{b} R)$ that promiser $S$ will keep promise body $b$ to $R$, as assessed by observer $A$ (0912.4637). In decentralized IoT access control, trust is “a subjective local belief that a node will behave normally,” whereas reputation is “a global view of a node’s previous behavior from aggregated trust relationships in other nodes” (Putra et al., 2019). In system security, trust is not just authenticated identity and not a single singular entity; it is a combination of characteristics attached to operating code, quantified as a metric that gets stronger or weaker over time (Creado et al., 2014).

Social-scientific work shows that trust can also be treated as an attitude toward categories of people and institutions. “Trust of strangers on the street” is measured on a 5-point Likert scale from “Definitely distrust” to “Definitely trust,” and is shaped most strongly by Social Trust and Institutional Trust, while trust of friends and family has a mild negative effect (Berry, 6 Jan 2025). The claim that trust is “not automatically endowed” is therefore empirical as well as conceptual: in that study, 47.58% of respondents explicitly distrust strangers on the street, and only 16.24% explicitly trust them (Berry, 6 Jan 2025).

2. Formal representations and mathematical structures

The surveyed literature contains several mathematically distinct trust formalisms.

Domain	Representation of trust	Representative source
Promise theory	$E_A(S \xrightarrow{b} R)$	(0912.4637)
Multi-aspect inference	$\hat{T}(u,v)$ from factorization and bias	(Yao et al., 2012)
IoT access control	Local $C$0, global $C$1	(Putra et al., 2019)
Robust advice	Trust region $C$2	(Dworczak et al., 10 Feb 2026)
Conviction-based epistemics	$C$3, $C$4	(Iyengar, 9 Mar 2026)

In multi-aspect trust inference, trust is modeled as a partially observed matrix $C$5, where $C$6 is a directed, subjective, continuous trust rating. MaTrust factorizes trust into trustor and trustee stereotypes and adds specified factors for global bias, trustor bias, and trustee bias. The predicted trust score is

$C$7

with latent factors capturing multi-aspect trust and bias terms capturing systematic tendencies of raters and ratees (Yao et al., 2012). This formulation treats trust inference as a matrix factorization problem rather than a path-propagation problem.

In decentralized IoT systems, direct trust and global reputation are separated mathematically. The direct trust of service provider $C$8 in consumer $C$9 is $C$0, updated from a time-decayed interaction score

$C$1

and mapped through a Gompertz function

$C$2

Global reputation is

$C$3

which rewards credible interaction with more distinct peers and discounts older interactions (Putra et al., 2019).

A different formalization appears in “Robust Trust,” where an agent receives advice from an informed but potentially misaligned adviser. Every optimal rule has a trust region representation in belief space: advice is taken at face value when it induces a posterior within a trust region $C$4, and otherwise the agent acts as if the posterior were on the boundary of $C$5 (Dworczak et al., 10 Feb 2026). In the binary-state case, the trust region is a closed interval $C$6; if $C$7, the optimal solution is trivial, $C$8, meaning the adviser is ignored, while for $C$9 the interval expands as alignment increases (Dworczak et al., 10 Feb 2026).

The conviction framework defines trust in sources through the probability that a source’s stance is vindicated by independent consensus. Conviction on claim $E_A(S \xrightarrow{b} R)$0 is

$E_A(S \xrightarrow{b} R)$1

and reputation over a field $E_A(S \xrightarrow{b} R)$2 is

$E_A(S \xrightarrow{b} R)$3

This formulation explicitly rejects correctness or faithfulness alone as the basis for trust, especially when a source may be augmentative rather than merely assimilative (Iyengar, 9 Mar 2026).

3. Trust as a dynamic metric in distributed and secure systems

In operating-system security, trust is attached to code rather than merely to users or hardware. The explicit trust model defines four characteristics—Invulnerable, Integrity, Verification, and Trustworthy—and maintains for each code block a Functional Trust Level (FTL) and a Transactional Trust Level (TTL) (Creado et al., 2014). Trust is recalculated after every execution: signatures are verified, managed states are monitored, operational history is updated, and a deterministic trust algorithm computes new TTL values from historical executions, correct executions, incorrect executions, owner trust metric, and other key inputs (Creado et al., 2014). Reinforcement moves code toward Operational Trust; incorrect or detrimental executions demote it toward Untrustable Trust or Denied Trust.

In peer-to-peer systems, Absolute Trust replaces relative ranking with a global consensus over absolute values of trust. Local trust is derived from transaction outcomes, and the global trust of peer $E_A(S \xrightarrow{b} R)$4 is computed as

$E_A(S \xrightarrow{b} R)$5

where the first term is a weighted average of local trust and the second is the trust of the evaluator set (Awasthi et al., 2016). The paper argues that normalized eigenvector-style methods yield only relative ranking, whereas absolute trust allows a peer to decide that all responders are malicious if they all fall below a global threshold (Awasthi et al., 2016).

Trustchain moves the locus of trust from opaque certification authorities to “genuine, pre-existing relationships between recognisable institutions.” In this decentralized PKI, users judge for themselves the level of trust they are willing to place in a given chain of attestations, and the root of trust is established through independently-verifiable timestamping on a proof-of-work chain (Hobson et al., 2023). Trust in issuing authorities is treated as inherent to any credential system, but trust in the data infrastructure is minimized by placing raw DID content off-chain, anchoring content hashes through Bitcoin and IPFS, and allowing users to verify root DID timestamps, attestation chains, and revocation completeness themselves (Hobson et al., 2023).

These systems share a design pattern: trust is updated from behavior, provenance, and verifiable state rather than from static credentials alone. A plausible implication is that many security architectures are shifting from one-shot authentication toward continuous or iterative trust maintenance.

4. Trust in AI, human–computer interaction, and formal verification

In AI, trust is explicitly decoupled from trustworthiness. A human trusts a model $E_A(S \xrightarrow{b} R)$6 contractually to $E_A(S \xrightarrow{b} R)$7 if the human perceives that $E_A(S \xrightarrow{b} R)$8 is trustworthy to $E_A(S \xrightarrow{b} R)$9 and accepts vulnerability to $S$0’s actions; $S$1 is trustworthy to $S$2 if it is capable of maintaining the contract (Jacovi et al., 2020). The paper further distinguishes warranted trust from unwarranted trust: trust is warranted if it is caused by trustworthiness in $S$3, in the sense that changing the model’s capability would change the user’s trust (Jacovi et al., 2020). Intrinsic trust arises from the model’s observable reasoning; extrinsic trust arises from evaluation schemes, expert opinion, and observed behavior.

A measurement-oriented HCI line operationalizes trust through the Human-Computer Trust Scale (HCTS), a 9-item instrument with four constructs: Competence, Benevolence, Perceived Risk, and Structural Assurance (Beltrão et al., 7 Apr 2026). The overall trust propensity score is the mean of the nine items after reversing the risk items, and the paper proposes interpretive zones: $S$4 These thresholds are presented as contextual guides rather than absolute clinical cut-offs, and the target is calibrated trust rather than maximal trust (Beltrão et al., 7 Apr 2026).

Formal methods work goes further by treating trust itself as a property to be verified. In Event-B, “actual trust” is defined relative to current abilities, knowledge, and commitments rather than past behavior. The core relation is

$S$5

and refinements add

$S$6

and

$S$7

The resulting model verifies properties such as no self-trust and no deadlock, and trust is permitted only when the trustee set can perform the task, is known to the trustor, and is committed to the task (Fathabadi et al., 2023). This suggests a move from informal reliance to correctness-by-construction trust relations in multiagent systems.

5. Robust and adversarial trust

A large part of recent work studies trust precisely where feedback or advice may be noisy, strategic, or adversarial. In preference-based reinforcement learning, TriTrust-PBRL introduces an expert-specific scalar trust parameter $S$8 into the Bradley–Terry model,

$S$9

so that $b$0 means trust, $b$1 means ignore, and $b$2 means flip adversarial labels (Hosseini et al., 26 Jan 2026). The key claim is that trust regimes emerge naturally during gradient-based optimization: reliable experts are pushed positive, noisy experts remain near zero, and adversarial experts become negative. With bounded and normalized trust, the model is identifiable up to a global sign flip, and empirically it maintains near-oracle performance under adversarial corruption where standard preference-based RL fails catastrophically (Hosseini et al., 26 Jan 2026).

The robust-advice model provides a decision-theoretic analogue. With known alignment probability $b$3, the agent maximizes worst-case expected payoff against arbitrary misaligned messages, and every optimal rule has a trust region in belief space (Dworczak et al., 10 Feb 2026). In binary-state environments, $b$4 yields a trivial trust region $b$5, while $b$6 yields a non-degenerate interval. More generally, the “minimal viable alignment” $b$7 satisfies

$b$8

and if the adviser’s posterior matrix has full rank $b$9, then $R$0 (Dworczak et al., 10 Feb 2026). Trust is therefore characterized as a robust filtering of advice rather than unconditional deference.

The decentralized auditing framework TRUST extends this adversarial perspective to LLM reasoning. It identifies four challenges—Robustness, Scalability, Opacity, and Privacy—and addresses them with a consensus mechanism among diverse auditors, a hierarchical DAG decomposition of reasoning traces, a blockchain ledger, and privacy-preserving segmentation (Huang et al., 23 Oct 2025). The framework provides correctness guarantees under up to $R$1 malicious participants and proves a Safety–Profitability Guarantee: by choosing voting parameters and economic parameters appropriately, the probability that a trace fails in $R$2 can be bounded by a target $R$3, honest auditors are profitable in expectation, and malicious auditors are lossmaking in expectation (Huang et al., 23 Oct 2025).

Across these papers, trust is neither naive reliance nor simple filtering. It is an adaptive response to partially adversarial information, often implemented as thresholding, clipping, weighting, inversion, or consensus.

6. Measurement, calibration, and recurring controversies

Trust is frequently measured, but the literature repeatedly warns against treating it as a single scalar detached from context. In the SEM model of trust of strangers, Social Trust has coefficient $R$4, Institutional Trust $R$5, Demographics $R$6, Person Trust $R$7, and Information Trust $R$8 with $R$9, showing that generalized trust in strangers is strongly linked to socially visible others and institutional representatives, but not meaningfully to information-source trust in that model (Berry, 6 Jan 2025). In HCI, the preferred target is “adequate trust,” not complete trust, precisely because both undertrust and overtrust can be forms of miscalibration (Beltrão et al., 7 Apr 2026).

One persistent controversy concerns whether trust should be reduced to correctness, faithfulness, or successful authentication. The conviction framework argues that correctness is assimilative and penalizes innovation, while faithfulness can be “faithfully wrong”; trust should instead be grounded in conviction and continuously accrued reputation (Iyengar, 9 Mar 2026). Promise theory makes a different criticism: trust is fundamentally heuristic and provides insufficient information for agents to make a rational judgement, because promises are scoped, typed, incomplete, and non-transitive (0912.4637). The explicit code-trust model similarly criticizes binary outcomes based on superficial constructs such as username/password or code signing alone, insisting on behavior, state, provenance, and evolving trust levels (Creado et al., 2014).

Another recurring dispute concerns transparency versus privacy. Trustchain minimizes trust in infrastructure through independently-verifiable timestamping while still requiring trust in institutions (Hobson et al., 2023). TRUST for LLM auditing records verification decisions publicly on-chain while sharing only partial reasoning steps to protect proprietary logic (Huang et al., 23 Oct 2025). Formalizing Trust in AI makes the related point that explanations are useful for trust only when they illuminate a stated contract; otherwise they risk increasing unwarranted trust (Jacovi et al., 2020).

The common thread is that trust is most defensible when it is typed, explicit, revisable, and tied either to verifiable structure or to empirically grounded calibration. This suggests that the modern technical treatment of trust is moving away from generic confidence and toward domain-specific mechanisms for deciding when vulnerability, delegation, or reliance is justified.