README- ::equalBeliefError::equal
- ::not_equalBeliefError::not_equal
- ::to_reprBeliefError::to_repr
- ::equalActionDecision::equal
- ::not_equalActionDecision::not_equal
- ::to_reprActionDecision::to_repr
- ::equalDecisionPolicy::equal
- ::not_equalDecisionPolicy::not_equal
- ::to_reprDecisionPolicy::to_repr
- ::cardinalityFrame::cardinality
- ::coarse_preimageFrame::coarse_preimage
- ::complementFrame::complement
- ::differenceFrame::difference
- ::equalFrame::equal
- ::intersectionFrame::intersection
- ::is_subsetFrame::is_subset
- ::labelsFrame::labels
- ::membersFrame::members
- ::not_equalFrame::not_equal
- ::refinement_inverseFrame::refinement_inverse
- ::sizeFrame::size
- ::subsetFrame::subset
- ::subsetsFrame::subsets
- ::to_reprFrame::to_repr
- ::unionFrame::union
- ::universeFrame::universe
- ::equalFusionStep::equal
- ::not_equalFusionStep::not_equal
- ::to_reprFusionStep::to_repr
- ::equalHypothesisScore::equal
- ::not_equalHypothesisScore::not_equal
- ::to_reprHypothesisScore::to_repr
- ::equalLimits::equal
- ::max_dense_cellsLimits::max_dense_cells
- ::max_focalsLimits::max_focals
- ::max_pairsLimits::max_pairs
- ::not_equalLimits::not_equal
- ::to_reprLimits::to_repr
- ::alignMass::align
- ::beliefMass::belief
- ::belief_tableMass::belief_table
- ::coarsenMass::coarsen
- ::commonalityMass::commonality
- ::commonality_tableMass::commonality_table
- ::conditionMass::condition
- ::condition_openMass::condition_open
- ::conditional_intervalMass::conditional_interval
- ::conflictMass::conflict
- ::decideMass::decide
- ::denseMass::dense
- ::discountMass::discount
- ::entriesMass::entries
- ::equalMass::equal
- ::expected_lossesMass::expected_losses
- ::expected_utilitiesMass::expected_utilities
- ::focal_countMass::focal_count
- ::forget_detailMass::forget_detail
- ::frameMass::frame
- ::ignoranceMass::ignorance
- ::intervalMass::interval
- ::json_textMass::json_text
- ::nonspecific_massMass::nonspecific_mass
- ::normalizeMass::normalize
- ::not_equalMass::not_equal
- ::pignisticMass::pignistic
- ::plausibilityMass::plausibility
- ::rankingMass::ranking
- ::refineMass::refine
- ::relabelMass::relabel
- ::survivalMass::survival
- ::to_jsonMass::to_json
- ::to_reprMass::to_repr
- ::weightMass::weight
- ::equalPipelineResult::equal
- ::massPipelineResult::mass
- ::not_equalPipelineResult::not_equal
- ::pair_workPipelineResult::pair_work
- ::stepsPipelineResult::steps
- ::to_reprPipelineResult::to_repr
- ::equalRule::equal
- ::not_equalRule::not_equal
- ::to_reprRule::to_repr
- ::equalSource::equal
- ::massSource::mass
- ::nameSource::name
- ::not_equalSource::not_equal
- ::to_reprSource::to_repr
- ::equalSourceSensitivity::equal
- ::not_equalSourceSensitivity::not_equal
- ::to_reprSourceSensitivity::to_repr
- Vbayesian
- Vconjunctive
- Vdecision_policy
- Vdefault_limits
- Vdempster
- Vdisjunctive
- Vdubois_prade
- Vexecute_json
- Vexecute_request
- Vfocal_total_variation
- Vframe
- Vfrom_commonality
- Vfuse
- Vjousselme
- Vleave_one_out
- Vlimits
- Vmass
- Vmass_from_json
- Vmaximum_belief_difference
- Vmixture
- Vparse_mass
- Vpcr5
- Vpipeline
- Vrule_from_string
- Vsimple_support
- Vsource
- Vsubset_mobius
- Vsubset_zeta
- Vsuperset_mobius
- Vsuperset_zeta
- Vvacuous
- Vyager
moonbelief
Bounded finite-frame belief-function calculus, explicit conflict fusion and explainable decisions in pure MoonBit
belief-functions
dempster-shafer
evidence-fusion
uncertainty
Author
Version
0.1.0
License
MIT
Repository
Last updated
8 hours ago
Downloads
4
#MoonBelief
有限分类框架上的证据质量函数、显式冲突融合与可拒绝决策。纯 MoonBit 实现，无运行时网络、训练或第三方算法依赖；模块 TWISTY2Ynb/moonbelief@0.1.0，MIT。
它解决的是“若干来源只支持一组候选，但不足以选定一个候选”时的计算问题。集合质量不是普通分类概率：{a,b} 上的质量表示没有继续分配的支持；空集质量表示冲突。使用者必须先保证类别互斥、穷尽，并说明来源依赖性与可靠度。融合规则不是从观测自动推导的真理。
#安装与最小集成
moon add TWISTY2Ynb/moonbelief@0.1.0在消费者的 moon.pkg 中加入：
import {
"TWISTY2Ynb/moonbelief" @belief,
}在可抛出 @belief.BeliefError 的函数中使用：
let f = @belief.frame(["clear", "blocked"])
let optical = @belief.simple_support(f, 1, 0.8)
let sonar = @belief.simple_support(f, 2, 0.6)
let result = @belief.yager(optical, sonar)
let (lower, upper) = result.interval(1)
assert_true(lower <= upper)位掩码中第 i 位对应第 i 个标签；0 是空集，f.universe() 是全集。框架标签顺序属于语义：即使标签相同，顺序不同也不可直接融合；显式使用 align。完整接口见 pkg.generated.mbti。
#六种融合规则
| API / 协议值 | 交集为空时的处理 | 重要边界 |
|---|---|---|
| conjunctive | 留在空集 | 支持开放世界质量；不隐去冲突 |
| dempster | 以非空存活质量归一化 | 存活量默认不得小于等于 1e-12 |
| disjunctive | 所有质量按并集累计 | 表示至少一个来源有效的不同假设 |
| yager | 冲突移到全集 | 不等价于概率归一化；多源顺序可能影响结果 |
| dubois_prade / dubois-prade | 不相容对移到该对的并集 | 确定的二元规则 |
| pcr5 / pairwise-pcr5 | 按每对质量比例重新分配 | 仅闭世界输入；不是广义多源 PCR5 |
pipeline 对 1–32 个命名来源先用调用者提供的可靠度折扣，再按调用顺序左折叠。它保留每步冲突、无知与焦元数；诊断计算和融合计算均计入总 pair budget。单来源只折扣，不额外归一化。不要将顺序敏感规则的左折叠称为多源闭式规则。
#可复用能力
- 有界框架与质量构造：重复焦元合并、有限数校验、补偿求和、向外复制数组，不暴露可变内部状态。
- belief、plausibility、commonality、区间、全集无知、非单点质量、直接计算的存活质量。
- 稠密 zeta/Möbius 变换与 commonality 反演；不一致的逆向输入报错。
- 开放/归一化条件化、可靠度折扣、细化/粗化、显式同标签重排与位置重命名。
- Pignistic 投影、稳定排序、效用/损失、冲突/非特异性/效用间隔拒绝策略。
- Jousselme 距离、焦元总变差、最大 belief 差、留一来源敏感性；不据此自动学习来源可信度。
- 无 I/O 的 execute_request / execute_json，以及同一协议的单次 CLI。
#三个实际工作流
moon run examples/sensors --target wasm-gc
moon run examples/diagnostics --target wasm-gc
moon run examples/ensemble --target wasm-gc
python scripts/check_examples.py --target wasm-gc- 分类传感器：光学与声纳分别提供“通行/受阻”的集合支持，指定可靠度后 Yager 融合。原始交集冲突为 0.3456，输出无知为 0.4912，通行 plausibility 为 0.8656，避免把冲突悄悄变成置信结论。
- 设备诊断：对电源/机械/软件的集合质量折扣、按硬件事件条件化并粗化，得到电源区间 [0.16, 0.76]，硬件 belief 为 1；这是设备演示，不是临床诊断。
- 分类器集成：三个分类器输出集合支持，通过 Yager 与业务效用矩阵产生 accept，期望效用 0.31；示例策略接受该建议，逐个去除来源时三个获胜标签均不变。这个玩具结果不证明真实模型校准或安全性。
#JSON 与 CLI
moon run cmd/moonbelief --target wasm-gc -- '{"schema":"moonbelief.request.v1","frame":["a","b"],"rule":"yager","sources":[{"name":"sensor","masses":[{"subset":["a"],"mass":0.7},{"subset":["a","b"],"mass":0.3}]}],"queries":[["a"]]}'Windows PowerShell 推荐先把 JSON 放入字符串变量，再作为一个参数传入。完整请求示例在 examples/request.json；也可直接调用纯函数 execute_json。
- moonbelief.mass.v1：schema、有序 frame、masses（subset 标签数组和 mass 数值）。
- moonbelief.request.v1：schema、frame、rule、1–32 个 sources；来源字段为 name、可选 reliability、masses。可选 queries 与 decision。
- decision：actions、逐行动作×逐列类别的 utilities，以及可选 policy（max_conflict、max_nonspecific、min_margin）。默认 0.5、0.8、0.05。效用间隔的单位由调用者定义，单动作间隔定义为 0。
- moonbelief.report.v1：规范质量、冲突、非单点质量、排序、融合步骤、pair_work，以及请求的查询/决策。
- moonbelief.error.v1：结构化错误。CLI 的领域错误仍以进程状态 0 返回，消费者必须检查 schema/kind，不能只看退出码。 全冲突无法生成排序，因此报告服务报错；底层 conjunctive API 可保留全冲突质量。
输入拒绝未知字段；JSON 重复对象键遵循 core 解析器的最后一个值覆盖行为，不保证检测重复键。需防止重复键歧义的接入方必须在上游单独拒绝它们。
#资源与数值契约
- 1–16 个唯一非空标签，每个最多 256 字符；输入质量须有限且在 [0,1]，总和允许误差 1e-10；内部计算结果重新归一化。正的极小质量不人为截断。
- 默认/硬上限：4096 焦元、1,000,000 次 pair 工作、65536 稠密单元；limits 只能收紧。稠密变换是 O(n·2^n)，不是大规模连续状态算法。
- JSON 文本最多 262144 UTF-16 代码单元、容器嵌套最多 12；查询最多 256。决策最多 64 动作×16 类别，效用/损失绝对值不超过 1e12。
- 错误为 Invalid、Budget、FrameMismatch、TotalConflict。归一化与 pignistic 直接求和非空质量，避免用 1-conflict 丢失微小存活量；默认阈值仍主动拒绝数值不稳定区域。
- 反演只对不超过 1e-12 的负舍入残差截零；不是任意修复不合法质量。
#验证
moon info && moon fmt
moon fmt --check
moon check --deny-warn --target wasm-gc
moon test --deny-warn --target wasm-gc
moon build --deny-warn --target wasm-gc
python scripts/differential.py
python scripts/audit.py验证工具链为 Moon 0.1.20261012 / moonc v0.10.15+943464bfa（2026-10-12）；源码与 CI 使用同一版本的规范格式。CI 在 Linux 上分别检查/测试/构建 wasm-gc、wasm、js、native，并对三个例子断言输出。工具链下载带 ETag 与 SHA-256 校验，见 CI 安装脚本。本地 Windows 已运行 wasm-gc/wasm/js；native 本地只有严格 check，缺少 C 编译器，不声称本地 native 执行成功。
测试不是覆盖率数字：35 个 test 声明中包含 13,475 个双源规则枚举结果，以及边界、可变别名、变换与顺序测试；另有 72 个经实际 CLI 的有理数差分案例。具体口径见 验证说明。
#范围与参考
不做贝叶斯网络训练、连续状态 Kalman 滤波、密码学取证、自动可靠度学习或安全认证。来源相关性、框架是否穷尽及规则是否适用须由调用者论证；存在冲突并不说明哪一个来源错了。
BeliefError
ActionDecision
ActionDecision::not_equal
DecisionPolicy
DecisionPolicy::not_equal
Frame
Ordered, exhaustive, mutually exclusive hypotheses. Order is semantic.
Frame::coarse_preimage
fn Frame::coarse_preimage(self : Frame, target : Frame, mapping : Array[Int], event : Int) -> Int raise BeliefErrorPreimage event on the source frame for a category-level query.
Frame::difference
Frame::intersection
Frame::is_subset
Frame::refinement_inverse
Derive the inverse category map from a valid refinement partition.
Frame::subsets
Enumerate subsets of a query, not of an implicitly unbounded universe.
FusionStep
HypothesisScore
HypothesisScore::not_equal
Limits
Limits can tighten, never increase, the engine's hard resource ceilings.
Mass
Sparse canonical mass assignment; empty-set mass is retained explicitly.
Mass::align
Reorder to an exactly matching set of labels. Fusion never aligns silently.
Mass::belief
Sum of nonempty focal masses included in the event (unnormalized TBM).
Mass::belief_table
Mass::coarsen
mapping[i] is the target hypothesis index for source hypothesis i.
Surjectivity forbids introducing unsupported target categories.
Mass::commonality
Commonality includes empty-set mass only when event is empty.
Mass::commonality_table
Mass::condition
fn Mass::condition(self : Mass, event : Int, min_survival? : Double, budget? : Limits) -> Mass raise BeliefErrorClosed-world conditioning uses the same near-total-conflict gate as Dempster.
Mass::condition_open
Conditioning by certain event evidence. Incompatible mass stays empty.
An impossible/empty observation is rejected rather than fabricated.
Mass::conditional_interval
fn Mass::conditional_interval(self : Mass, query : Int, given : Int, min_survival? : Double, budget? : Limits) -> (Double, Double) raise BeliefErrorConditional belief/plausibility bounds, not a posterior probability vector.
Mass::decide
fn Mass::decide(self : Mass, actions : Array[String], utilities : Array[Array[Double]], policy : DecisionPolicy) -> ActionDecision raise BeliefErrorExplicit supplied policy; equal scores keep the first action.
If only one action exists its margin is defined as zero, not infinity.
Margins have utility units, so caller must calibrate the policy accordingly.
Mass::dense
A copy of mass values in integer-mask order, including empty set at index 0.
Mass::discount
Shafer reliability discounting: alpha scales every focal, including empty,
then 1-alpha is transferred to the full frame. Reliability is supplied,
never inferred from agreement. This is not a source-dependence correction.
Mass::expected_losses
Loss rows have the same layout, but must be nonnegative.
Mass::expected_utilities
Rows are actions; columns are hypotheses in frame order. Limited to 64
actions and finite magnitudes <=1e12. Returned expectations use BetP.
Mass::forget_detail
Explicitly move all nonsingleton nonempty masses to the full frame.
Conflict and singleton commitments are retained; no hidden pruning occurs.
Mass::interval
Mass::nonspecific_mass
Nonspecificity: total nonempty mass assigned to nonsingleton subsets.
This is not Shannon entropy and is distinct from mass on the full frame.
Mass::normalize
Removes explicit conflict by conditioning on nonempty mass.
Summing surviving focals directly avoids catastrophic 1-conflict cancellation.
Mass::pignistic
Singleton decision projection. This is pignistic probability, not belief.
Conflict is removed by conditioning on directly summed nonempty mass.
Mass::plausibility
Sum of masses intersecting the event; empty-set conflict contributes zero.
Mass::ranking
Stable descending pignistic ranking: ties retain original frame order.
Belief and plausibility columns remain unnormalized open-world bounds.
Mass::refine
Each source hypothesis maps to a nonempty disjoint block of the target.
Blocks must partition the target. No probabilities are invented within a
block: every focal is extended to the union of its corresponding blocks.
Mass::relabel
Rename positionally; caller asserts that the new labels mean the same
hypotheses. This is not semantic matching or automatic label inference.
Mass::survival
Surviving mass is summed directly to avoid cancellation of 1-conflict.
PipelineResult
PipelineResult::not_equal
Rule
Source
SourceSensitivity
SourceSensitivity::equal
SourceSensitivity::not_equal
bayesian
Bayesian mass: one explicit probability for each hypothesis in frame order.
conjunctive
Unnormalized conjunctive fusion: each pair transfers mass to intersection.
Empty intersections are preserved as conflict, never renormalized here.
decision_policy
fn decision_policy(max_conflict? : Double, max_nonspecific? : Double, min_margin? : Double) -> DecisionPolicy raise BeliefErrordempster
Dempster's normalized conjunctive rule, with an explicit instability gate.
disjunctive
Disjunctive fusion transfers each focal pair to its union.
This is an alternative source model, not interchangeable with conjunction.
dubois_prade
Dubois-Prade transfers each incompatible pair to its union.
Both-empty pairs stay empty; open-world inputs are not silently normalized.
execute_request
Pure request/report facade: no I/O, credentials, training or network.
Total conflict produces a domain error instead of invalid ranking numbers.
focal_total_variation
Total variation of focal-mass vectors (not a belief metric).
frame
A finite powerset is deliberately bounded to at most sixteen hypotheses.
from_commonality
Invert a normalized commonality vector; negative rounding noise <=1e-12
may be clamped, but inconsistent vectors are rejected, never renormalized.
jousselme
Jousselme distance with D(empty,empty)=1. Different frames are rejected.
Work is quadratic in the union of nonzero difference focals, not powerset.
leave_one_out
fn leave_one_out(sources : Array[Source], rule : Rule, budget? : Limits) -> Array[SourceSensitivity] raise BeliefErrorLeave-one-out is a sensitivity diagnostic, not source-reliability learning.
Limited to 2..16 sources. The pair budget is shared across baseline and
all reruns; no per-source failures are hidden. Total conflict raises an error.
limits
mass
Duplicate subsets are merged; totals must be one within 1e-10.
Tiny positive focals are preserved, not pruned by a hidden threshold.
maximum_belief_difference
fn maximum_belief_difference(a : Mass, b : Mass, budget? : Limits) -> (Int, Double) raise BeliefErrorLargest difference over all belief queries, using bounded zeta transforms.
mixture
Convex pooling is an alternative to independent-evidence fusion.
alpha is the weight of the first source, not a reliability estimate.
pcr5
Two-source PCR5 only. Incompatible pair products are redistributed to
those same two focals in proportion to their original masses.
Inputs must have zero empty-set mass; sequential use is order-sensitive.
pipeline
fn pipeline(sources : Array[Source], rule : Rule, budget? : Limits) -> PipelineResult raise BeliefErrorDeterministic left fold in caller order. Not a generalized multisource
PCR5 or associativity guarantee. One source yields its discounted mass.
Pair budget covers BOTH diagnostic and fusion cross products globally.
simple_support
fn simple_support(f : Frame, event : Int, support : Double, budget? : Limits) -> Mass raise BeliefErrorSimple support does not silently create empty-set conflict.
source
subset_mobius
fn subset_mobius(f : Frame, values : Array[Double], budget? : Limits) -> Array[Double] raise BeliefErrorsubset_zeta
fn subset_zeta(f : Frame, values : Array[Double], budget? : Limits) -> Array[Double] raise BeliefErrorsuperset_mobius
fn superset_mobius(f : Frame, values : Array[Double], budget? : Limits) -> Array[Double] raise BeliefErrorsuperset_zeta
fn superset_zeta(f : Frame, values : Array[Double], budget? : Limits) -> Array[Double] raise BeliefErrorSource Files
- alignment.mbt
- alternative_rules.mbt
- coarsen.mbt
- conditioning.mbt
- conjunctive.mbt
- constructors.mbt
- decision.mbt
- discount.mbt
- distance.mbt
- error.mbt
- frame.mbt
- json_codec.mbt
- json_service.mbt
- limits.mbt
- mass.mbt
- normalization.mbt
- pcr5.mbt
- pignistic.mbt
- pipeline.mbt
- queries.mbt
- refine.mbt
- sensitivity.mbt
- subsets.mbt
- transforms.mbt
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belief-functionsdempster-shaferevidence-fusionuncertainty
MIT
Updated 8 hours ago
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