Formula & Theorem Quick Reference Handbook | 法律公式定理速查手册

📚 Formula & Theorem Quick Reference Handbook | 法律公式定理速查手册

Law might not look like a subject full of mathematical formulas, but it has its own structured ‘formulas’ — legal tests, principles and essential elements that must be proved or satisfied to establish liability, create a contract or decide a case. This handbook distils key CIE IGCSE Law concepts into clear, repeatable frameworks, helping you to analyse scenarios, structure answers and apply the law with precision. Treat each section as a ready-made reasoning template for your examinations.

法律也许不像一门充满数学公式的学科，但它有自己结构化的“公式”——法律检验标准、原则和必要构成要素，必须被证明或满足才能确立法律责任、成立合同或判决案件。本手册将 CIE IGCSE 法律的核心概念提炼成清晰、可重复使用的框架，帮助你分析情景、组织答案并准确适用法律。把每一节都当作考试中现成的推理模板来使用。

1. Actus Reus & Mens Rea | 犯罪行为与犯罪意图

In criminal law, almost every offence can be broken down into a two‑part ‘formula’: Actus Reus (guilty act) + Mens Rea (guilty mind). The prosecution must prove both elements beyond reasonable doubt for a conviction. The actus reus includes the physical conduct, circumstances and, often, the consequences of the defendant’s actions, while mens rea refers to the mental state, such as intention, recklessness or negligence, as specified by the offence. Without one of these ingredients, the crime is incomplete.

在刑法中，几乎每项犯罪都可以分解为一个两部分“公式”：犯罪行为 + 犯罪意图。控方必须在排除合理疑问后同时证明这两个要素，才能定罪。犯罪行为包括被告的身体行为、所处情境以及通常是其行为造成的后果，而犯罪意图是指法律规定的心理状态，例如蓄意、轻率或疏忽。缺少其中任何一个要素，犯罪便不完整。

Actus reus must be voluntary and can be an act, omission (in limited situations) or a state of affairs.
犯罪行为必须是自愿的，可以是一种作为、不作为（在有限情形下）或状态。
Mens rea types: intention (direct or oblique), recklessness (Cunningham: defendant foresaw the risk and went ahead anyway), negligence (falling below the standard of a reasonable person).
犯罪意图类型：蓄意（直接或间接）、轻率（Cunningham 标准：被告预见到风险仍执意为之）、疏忽（低于合理人的标准）。
Coincidence of actus reus and mens rea: they must occur at the same time; a continuing act can link them.
犯罪行为与犯罪意图同时发生：必须同时出现；持续行为可以将两者联系起来。

2. The Neighbour Principle for Duty of Care | 注意义务的邻人原则

The foundation of negligence is the duty of care, and its classic ‘formula’ comes from Donoghue v Stevenson. Lord Atkin stated you must take reasonable care to avoid acts or omissions which you can reasonably foresee would be likely to injure your ‘neighbour’. In law, your neighbour is anyone who is so closely and directly affected by your actions that you ought reasonably to have them in contemplation. This test transformed tort law by creating a general principle for when a duty arises.

过失侵权的基础是注意义务，其经典“公式”来自 Donoghue v Stevenson 案。Atkin 勋爵指出，你必须采取合理谨慎，避免你可以合理预见到可能伤害你“邻人”的作为或不作为。在法律上，你的邻人是指任何受你行为如此密切和直接影响，你理应将其放在心上的人。这一检验标准通过确立注意义务何时产生的一般原则，重塑了侵权法。

Foreseeability of harm: would a reasonable person have foreseen damage to this claimant?
损害的可预见性：一个合理人能否预见到会对该索赔人造成损害？
Proximity: there must be a sufficiently close relationship between the parties (time, space, relationship).
接近性：当事人之间必须有足够密切的关系（时间、空间或关系）。
Fair, just and reasonable: the court must also be convinced that imposing a duty is fair, just and reasonable (this third limb is part of the Caparo refinement).
公平、公正和合理：法院还必须确信，施加一项注意义务是公平、公正和合理的（这第三个要件属于 Caparo 案的完善）。

3. Negligence – Caparo Three‑Stage Test | 过失 – Caparo 三阶段测试

Modern courts often use the three‑stage Caparo Industries v Dickman test as the definitive formula for establishing a duty of care. First, was the damage to the claimant reasonably foreseeable? Second, was there a relationship of proximity between the claimant and defendant? Third, even if both are satisfied, is it fair, just and reasonable for the court to impose a duty? This test works alongside the neighbour principle and is particularly useful when the situation does not fall neatly within an existing duty category.

现代法院经常使用 Caparo Industries v Dickman 案 的三阶段检验作为确立注意义务的权威公式。第一，对索赔人造成的损害是否是可合理预见的？第二，索赔人和被告之间是否存在接近关系？第三，即使前两项都满足，法院施加注意义务是否公平、公正和合理？这一检验与邻人原则配合使用，当情况无法完全归入现有义务类别时尤其有用。

Duty of Care = Foreseeability + Proximity + Fair, Just and Reasonable

注意义务 = 可预见性 + 接近性 + 公平、公正和合理

Once a duty is established, the claimant must also prove that the defendant breached that duty (fell below the standard of the reasonable person) and that the breach caused the damage, both in fact (the ‘but for’ test) and in law (the damage must not be too remote). The complete negligence formula therefore reads: Duty + Breach + Causation (factual & legal) + Damage.

一旦确立注意义务，索赔人还必须证明被告违反了该义务（未达到合理人的标准）且该违反行为导致了损害，包括事实上的因果关系（“若非”检验）和法律上的因果关系（损害不能过于遥远）。因此，完整的过失公式为：注意义务 + 违反义务 + 因果关系（事实与法律） + 损害。

4. Contract Formation Formula | 合同成立公式

A valid contract in English law requires four essential ingredients. Think of it as a mandatory checklist: Offer + Acceptance + Consideration + Intention to Create Legal Relations. In addition, the parties must have the capacity to contract, and the agreement must not be vitiated by factors like misrepresentation or duress. If any core element is missing, there is no enforceable contract.

在英国法中，一项有效的合同需要四个基本要素。可以把它想象成一个强制性清单：要约 + 承诺 + 对价 + 设立法律关系的意图。此外，当事人必须具备缔约能力，而且协议不得因不实陈述或胁迫等因素而无效。如果缺少任何一个核心要素，就不存在可强制执行的合同。

Valid Contract = Offer + Acceptance + Consideration + Intention to Create Legal Relations (+ Capacity + Legality)

有效合同 = 要约 + 承诺 + 对价 + 设立法律关系的意图（+ 能力 + 合法性）

Offer: a clear statement of terms on which the offeror is prepared to be bound.
要约：关于要约人愿意受约束的条款的明确陈述。
Acceptance: unconditional agreement to all terms of the offer, communicated to the offeror.
承诺：对要约全部条款的无条件同意，并传达给要约人。
Consideration: something of value exchanged between the parties (e.g. money for goods).
对价：双方之间交换的有价值之物（如以金钱换取货物）。
Intention: presumptions operate — commercial agreements intend legal relations; social/domestic agreements do not, unless rebutted.
意图：推定规则适用——商事协议推定有设立法律关系的意图；社交或家庭协议则推定没有，除非被推翻。

5. Offer & Acceptance | 要约与承诺

Within the contract formation formula, the mechanism of offer and acceptance is itself governed by precise rules. An offer must be distinguished from an invitation to treat, which is merely an invitation to make an offer (e.g. goods on a shelf). An offer can be terminated by revocation, rejection, lapse of time, death or a counter‑offer. An acceptance must mirror the offer exactly — this is known as the mirror image rule; any variation becomes a counter‑offer, which destroys the original offer. Acceptance is generally effective when communicated, but the postal rule creates an exception: acceptance by post takes effect when the letter is posted, not when it is received.

在合同成立公式中，要约与承诺的机制本身也受精确规则的约束。要约必须与要约邀请区分开来，后者仅仅是邀请他人发出要约（如货架上的商品）。要约可因撤回、拒绝、逾期、死亡或反要约而终止。承诺必须与要约完全一致——这被称为镜像规则；任何变动都会构成反要约，从而消灭原要约。承诺通常在传达时生效，但邮寄规则创设了一个例外：以信件作出的承诺在投邮时即生效，而非在收到时。

Invitation to treat (e.g. advertisement, display)	Offer (e.g. customer takes item to till)	Acceptance (shopkeeper takes money)
要约邀请（例如广告、陈列）	要约（顾客将商品拿到收银台）	承诺（店主收下钱款）

6. Consideration | 对价

Consideration is the ‘price’ for which the promise is bought, and it must satisfy a clear formula: it must be sufficient but need not be adequate. This means the courts do not inquire into whether the value is fair, as long as something of value in the eyes of the law is provided. Consideration must not be past (it must be executory or executed, not past), and performance of an existing duty is generally not valid consideration unless it provides a practical benefit (Williams v Roffey Bros). Also, part payment of a debt is not consideration for the whole debt under the rule in Pinnel’s Case.

对价是换取承诺的“代价”，它必须满足一个明确公式：必须有价值但无需对等。这意味着法院不审查价值是否公平，只要在法律看来提供了某种有价值之物即可。对价不能是过去的对价（它必须是待履行的或已履行的，而不是过去的对价），而履行现有义务通常不构成有效的对价，除非它带来了实际利益（Williams v Roffey Bros 案）。此外，根据 Pinnel’s Case 规则，部分支付借款不能作为免除全部债务的对价。

Consideration must move from the promisee: the person wishing to enforce the contract must have given consideration.
对价必须来自受诺人：希望强制执行合同的人必须提供了对价。
Existing public duty or contractual duty: generally not good consideration unless exceeding the duty.
现有公共义务或合同义务：一般不构成有效对价，除非超过了该义务的要求。

7. Legal Interpretation Rules | 法律解释规则

When judges interpret statutes, they apply a series of well‑established ‘formulas’ known as the rules of construction. The literal rule says courts must give words their ordinary, plain meaning even if it leads to an absurd result. The golden rule is a modification: if the literal meaning creates an absurdity, the court can choose an alternative meaning that avoids it. The mischief rule looks at the gap in the old law that the statute was designed to remedy and interprets the words to suppress that mischief. Finally, the purposive approach goes further by asking what Parliament intended to achieve, looking at the whole Act and context. Mastering these rules helps you predict how a judge will apply the law to a given set of facts.

法官在解释制定法时，会适用一系列被称为解释规则的既定“公式”。字面规则要求法院必须按语句通常、平白的含义来理解，即使这会导致荒谬的结果。黄金规则是修正条款：若字面含义产生荒谬，法院可选择一个避免荒谬的替代含义。除弊规则则考察旧法中的漏洞——该立法旨在弥补什么弊端，并据此解释语句以消除该弊端。最后，目的方法更进一步，通过审视整部法律和上下文来追问议会意图实现的目标。掌握这些规则有助于你预测法官如何将法律适用于既定事实。

Literal → Golden → Mischief → Purposive (spectrum of interpretation)

字面 → 黄金 → 除弊 → 目的（解释光谱）

8. Judicial Precedent Formula | 司法先例公式

The doctrine of stare decisis (let the decision stand) is the engine of the common law system. Its working formula is: Ratio decidendi (binding reason) + Court hierarchy = precedent that must be followed. The ratio is the legal principle necessary for the decision in the case; everything else is obiter dicta (things said by the way), which can be persuasive but not binding. Lower courts are bound by the ratios of higher courts within the same hierarchy. This mechanism guarantees consistency and predictability. The Supreme Court (formerly House of Lords) can depart from its own previous decisions using the 1966 Practice Statement, but this is rare.

遵循先例原则是普通法制度的引擎。其运作公式为：判决理由（有约束力的理由） + 法院等级 = 必须遵循的先例。判决理由是案件判决所必需的法律原则；其余部分均为附带意见（裁判过程中的附随论述），虽有说服力但不具约束力。下级法院受同一等级体系中上级法院判决理由的约束。这一机制保障了法律的一致性和可预测性。最高法院（原上议院）可以依据 1966 年实践声明偏离其既往判决，但这并非常态。

Binding precedent: ratio of a higher court in the same jurisdiction.
有约束力的先例：同一法域内上级法院的判决理由。
Persuasive precedent: obiter dicta, ratios of lower courts, decisions from other jurisdictions.
有说服力的先例：附带意见、下级法院的判决理由、其他法域的判决。
Distinguishing: a judge may avoid following a precedent if the material facts of the current case are different.
区别：若当前案件的关键事实不同，法官可避免遵循一项先例。

9. Assault & Battery | 攻击与殴打

In criminal law, assault and battery are distinct offences, each with its own formula. Assault is committed when the defendant intentionally or recklessly causes the victim to apprehend immediate and unlawful personal violence. No physical contact is necessary — a threat or gesture that creates fear of imminent force is sufficient. Battery, on the other hand, involves the actual infliction of unlawful personal force upon the victim, intentionally or recklessly. The least unwanted touching can amount to battery. Together they form the building blocks of non‑fatal offences against the person.

在刑法中，攻击与殴打是相互独立的犯罪，各有其公式。攻击的构成是：被告蓄意或轻率地使受害人立即担心遭受非法的个人暴力。无需实际身体接触——造成对即时暴力恐惧的威胁或姿势即已足够。殴打则涉及实际对受害人施加非法的个人暴力，主观上为蓄意或轻率。最轻微的不受欢迎触碰也可能构成殴打。两者共同构成针对人身的非致命犯罪的基础。

Assault = Apprehending Immediate Unlawful Force + Intention/Recklessness

攻击 = 担心即时的非法暴力 + 蓄意/轻率

Battery = Unlawful Physical Contact + Intention/Recklessness

殴打 = 非法身体接触 + 蓄意/轻率

10. ABH & GBH | 实际身体伤害与严重身体伤害

Sections 47, 20 and 18 of the Offences Against the Person Act 1861 create a hierarchy of more serious non‑fatal offences, each with a fixed formula. Actual bodily harm (ABH, s.47) requires an assault or battery that causes ‘actual bodily harm’, defined as any hurt or injury calculated to interfere with the health or comfort of the victim. The mens rea for s.47 is the same as for assault or battery — there is no need to prove intention or recklessness as to the harm itself. Grievous bodily harm (GBH, s.20) involves either wounding (a break in the continuity of the skin) or inflicting grievous (really serious) bodily harm, with mens rea of recklessness as to some harm. GBH with intent (s.18) is the most serious, requiring proof of a specific intent to cause GBH or to resist/prevent lawful arrest.

《1861 年人身犯罪法》第 47 条、第 20 条和第 18 条规定了更严重的非致命犯罪层级，各有其固定公式。实际身体伤害（ABH，第 47 条）要求构成攻击或殴打，并造成“实际身体伤害”，定义为任何旨在影响受害人健康或舒适度的伤害。第 47 条的犯罪意图与攻击或殴打相同——无需证明对伤害本身具有蓄意或轻率。严重身体伤害（GBH，第 20 条）涉及造成创伤（皮肤连续性的破裂）或导致严重（真正严重的）身体伤害，犯罪意图为对某些伤害的轻率。蓄意 GBH（第 18 条）最为严重，要求证明具有造成 GBH 或抗拒/阻止合法逮捕的特定蓄意。

Offence	Actus Reus	Mens Rea
s.47 ABH	Assault or battery causing ABH	Intention or recklessness as to assault/battery
s.20 GBH	Wounding or inflicting GBH	Recklessness as to some harm
s.18 GBH with intent	Wounding or causing GBH	Specific intent to cause GBH or resist arrest

中文对照表：第 47 条 ABH：犯罪行为为攻击或殴打导致 ABH，犯罪意图为对攻击/殴打的蓄意或轻率；第 20 条 GBH：犯罪行为为创伤或导致 GBH，犯罪意图为对某些伤害的轻率；第 18 条蓄意 GBH：犯罪行为为创伤或造成 GBH，犯罪意图为造成 GBH 或抗拒逮捕的特定蓄意。

11. Defences in Tort Law | 侵权法抗辩

Even when a claimant proves the elements of a tort, defendants can rely on established defences, each with its own formula. Volenti non fit injuria (voluntary assumption of risk) applies where the claimant freely and fully consented to the risk of harm, knowing its nature and extent. Contributory negligence reduces damages if the claimant failed to take reasonable care for their own safety, which contributed to the damage. Illegality (ex turpi causa) may bar a claim entirely if the claimant was involved in a criminal act connected to the harm. Self‑defence and necessity can also justify otherwise tortious acts, provided the force or action was reasonable and proportionate.

即使索赔人证明了侵权行为的各项要素，被告仍可依赖既定的抗辩理由，每种抗辩都有各自的公式。自愿者不构成伤害（volenti non fit injuria）适用于索赔人自由且完全同意承担伤害风险，并知晓风险的性质和程度。共同过失会在索赔人未能对自己的安全采取合理谨慎、并对损害有所促进时按比例减少损害赔偿。违法性（ex turpi causa）可在索赔人卷入与损害相关的犯罪行为时完全阻止其索赔。自卫和紧急避险也可以使本属侵权的行为正当化，前提是使用的武力或采取的行动合理且相称。

Defences to negligence = Volenti + Contributory negligence + Illegality + Necessity/Self‑defence (reasonableness tested)

过失侵权抗辩 = 自愿承受风险 + 共同过失 + 违法性 + 紧急避险/自卫（均须检验合理性）

12. Strict Liability | 严格责任

Strict liability is a special type of criminal or tort liability where the prosecution (or claimant) does not need to prove mens rea for at least one element of the actus reus. The formula becomes: Actus reus alone (or actus reus + only partial mens rea) = liability. In criminal law, offences of strict liability are often regulatory or quasi‑criminal, designed to protect public safety, and the statute makes no mention of a mental element. In tort, the rule in Rylands v Fletcher imposes strict liability for a non‑natural use of land that brings onto the land something likely to do mischief if it escapes, and it does escape causing damage. The defendant need not be at fault.

严格责任是一种特殊的刑事或侵权责任类型，控方（或索赔人）无需就犯罪行为的至少一个要素证明犯罪意图。公式由此变为：仅犯罪行为（或犯罪行为 + 仅部分犯罪意图） = 责任。在刑法中，严格责任犯罪通常是监管性或准刑事犯罪，旨在保护公共安全，且法律条文中未提及犯意要素。在侵权法中，Rylands v Fletcher 案的规则对土地的非自然使用课以严格责任：若将一旦逸出就可能造成损害之物带至土地上，且该物确实逸出并造成损害，即须承担责任，被告无需存在过错。

Common strict liability offences: selling alcohol to minors, speeding, food safety regulations.
常见严格责任犯罪：向未成年人出售酒精、超速行驶、食品安全法规。
Exceptions in criminal law: defence of due diligence or third‑party act may be available if statute allows.
刑法中的例外：若法律允许，可提出适当注意抗辩或第三人行为抗辩。
Rylands v Fletcher requirements: accumulation, non‑natural use, escape, damage.
Rylands v Fletcher 要件：积聚、非自然使用、逸出、损害。

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Formula & Theorem Quick Reference Handbook | 法律公式定理速查手册