Unit 2 Patent Application Preparation

3.5 Claim sets based on set theory

Much like a fence defines the boundaries of a parcel of land protected as real property, a patent claim specifies the limits of the technical subject matter for which patent protection is sought. Most patent offices follow a “peripheral claiming” doctrine, where claims define the outer boundaries of the protected subject matter.

Example
Claim 1. A cup with a handle.
Claim 2. A cup with a handle, wherein the cup is made of clay.
Claim 3. A cup with a handle, further comprising a spoon detachably attached to the handle.

In the Figure, the region enclosed by the red curve (set A) represents the scope of Claim 1, covering any cup with a handle regardless of material, shape, or additional features. The region enclosed by the purple curve (set B) represents Claim 2. Since Claim 2 is a specific type of the cup in Claim 1 (made of clay), set B lies within set A. Likewise, the green curve (set C) represents the scope of Claim 3.

The blue-striped overlap of sets A, B, and C represents a cup containing all limitations of Claims 1, 2, and 3. In claim language, this can be expressed as:

Claim 4. A cup with a handle, wherein the cup is made of clay and further comprising a spoon detachably attached to the handle.

Embodiments are shown as a1, a2, b1, c1, etc. For example, a1-a4 lie within set A but outside sets B and C, meaning they are cups with handles that are neither limited to clay nor include a detachably attached spoon. Thus, a1 may be a metal cup with a handle and an inner isolation layer, while a2 may be a wooden cup, both without a spoon attached to the handle. Similarly, b1 may be any clay cup with a handle but without a spoon attached, since it lies outside set C.

Illustrating Claim Relationships with Set Theory and Venn Diagrams

Venn diagrams are a key tool in set theory for visually representing logical relationships among sets. These concepts are useful in patent law for illustrating relationships between independent and dependent claims, as well as between claims and their embodiments.

Understanding Sets in Patent Claim Context
A set is a collection of elements sharing a common characteristic. For example, “the people currently in this room” form a set, while the universal set would include all people worldwide. A proposition can be true or false, whereas a defining sentence merely specifies membership criteria for a set.

Patent Claims as Defining Sentences
A patent claim functions as a defining statement that establishes the boundaries of a particular technical subject matter, whether relating to devices, chemicals, biological materials, processes, or industrial methods.

Figure: Scopes of independent Claim 1 and dependent Claims 2 and 3

For clarity, sets are typically shown as closed shapes in Venn diagrams. Likewise, the scope of a patent claim can be represented by a closed boundary. Although not shown explicitly, the universal set is generally defined by the claim preamble.

Understanding Subsets and Dependencies
In set theory, A₂ is a subset of A₁ if every member of A₂ is also a member of A₁ (A₂ ⊆ A₁). If A₂ is entirely contained within A₁ and not identical to it, it is a proper subset (A₂ ⊂ A₁). In patent practice, when the scope of one claim is a subset of another, the former is dependent on the latter. This dependency is transitive: if A₂ ⊆ A₁ and A₃ ⊆ A₂, then A₃ ⊆ A₁. Thus, if Claim 2 depends on Claim 1 and Claim 3 depends on Claim 2, Claim 3 also depends on Claim 1. Figure 4 illustrates this hierarchy.

In Figure 4:

Claim 1 is the only independent claim.
Claim 2 depends on Claim 1.
Claim 3 depends on Claim 2 and therefore also falls within Claim 1’s scope.

These diagrams represent technical scope rather than claim format. A dependent claim may reference one preceding claim (single dependent form) or multiple preceding claims (multiple dependent form). Figure 4 shows the single dependent form.

Figure 5 extends this structure by adding Claims 4-6, whose scopes are mutually exclusive and do not overlap. This arrangement is sometimes called a dependency pyramid, with Claim 3 as its vertex. Claim 1 remains the sole independent claim.

In Figure 5, Claims 4-6 arise from three alternative versions of a component “D” specified in Claim 3. This commonly occurs when “D” is defined as a Markush group, such as “D is selected from D1, D2, and D3.” A specific selection (e.g., D1) can be represented as a subset of the broader component D (D1 ⊂ D).

Figure: Scopes of independent Claim 1 and dependent Claims 2 to 6

Figure 6 presents a claim structure different from the dependency pyramids shown earlier:

Claim 1 remains the only independent claim.
Claims 2, 3, and 4 each depend on Claim 1, forming a dependency cluster.

Further analysis of the scopes reveals:

Claim 4 depends on both Claim 2 and Claim 3, creating the chains Claim 1 → Claim 2 → Claim 4 and Claim 1 → Claim 3 → Claim 4.
Although Claim 3 depends only on Claim 1 and has no direct dependency on Claim 2, their scopes partially overlap because Claim 4 is a subset of both.
From a drafting perspective, Claim 4 could logically depend on either Claim 2 or Claim 3 due to this shared subject matter.

Figure: Scopes of independent Claim 1 and dependent Claims 2, 3 and 4

Analyzing claim dependencies is important in two key areas:

Validity Assessment (Examination & Litigation): Patent examiners and courts use dependency analysis to evaluate novelty and inventive step.
Infringement Assessment (Litigation): Understanding claim dependencies helps determine whether an accused product or process falls within the patent’s scope.

Figure 7: (a) Claims 1-5 are novel; (b) Claims 1-3 lack novelty, but Claims 4 and 5 are novel

Consider a dependency group of Claims 1-5:

Claim 1 is the independent claim.
Claims 1-4 form a dependency chain, with Claim 4 having the narrowest scope.
Claim 5 does not overlap with Claim 2 and therefore does not overlap with Claims 3 or 4.

Figure 7a shows a case where all claims are novel.

Figure 7b shows Claims 1-3 lacking novelty while Claims 4 and 5 remain novel, illustrating how narrower claims can preserve patentability even when broader claims fail.

Novelty is assessed by comparing claim scope with prior art:

Figure 7a: Prior art reference P1 lies completely outside Claim 1. Therefore, Claim 1 is novel, and all dependent Claims 2-5 are also novel with respect to P1.
Figure 7b: Prior art reference P2 lies within Claim 3. Since Claim 3 is within the scopes of Claims 1 and 2, P2 destroys the novelty of Claims 1-3. However, P2 falls outside Claims 4 and 5, so those claims remain novel.
A common misconception is that invalidating an independent claim automatically invalidates all dependent claims. This is incorrect. Moreover, novelty alone does not establish validity; other requirements, such as inventive step, must also be satisfied.

Next, consider literal infringement analysis using Figures 8a and 8b, assuming all claims are valid. Infringement requires:

A prohibited act (e.g., making, using, or selling the invention without authorization).
An accused embodiment falling within the scope of at least one valid claim.

Figure 8a: The accused embodiment Q1 lies outside the scope of Claim 1. Therefore, Claim 1 is not infringed, and none of its dependent claims are infringed.
Figure 8b: The accused embodiment Q2 falls within the scope of Claim 3, meaning all elements of Claim 3 are present. Because Claim 3 depends on Claims 1 and 2, the elements of those claims are also present. Accordingly, Claims 1, 2, and 3 are infringed by Q2.
However, Q2 falls outside the scope of Claim 4, so Claim 4 is not infringed. The same applies to Claim 5 in this example.

A common misconception is that infringement of an independent claim automatically results in infringement of all dependent claims. Figure 8b demonstrates that this is not always true.

Schematic Example of Drafting a Set of Claims

Drafting patent claims is a complex process influenced by:

Information and inventive concepts provided by the inventors.
Relevant prior art.
The applicant’s business objectives.
The patent drafter’s expertise, experience, and available time.

Figure 8: (a) No infringement of Claims 1-5; (b) Claims 1-3 are infringed, but not Claims 4 and 5

The drafting process usually begins with a brainstorming session between the patent drafter and inventor(s) to identify and define the invention’s key features and scope.

The evaluation of novelty involves comparing a claim’s scope with prior art references, illustrated in Figures 7a and 7b as P1 and P2.

Figure 7a: Prior art reference P1 lies completely outside the scope of independent Claim 1. Therefore, Claim 1 is novel, and all dependent Claims 2-5 are also novel with respect to P1. If this holds for all prior art references, all claims may be considered novel.
Figure 7b: Prior art reference P2 falls within the scope of Claim 3. Because Claim 3 is within the scopes of Claims 1 and 2, P2 destroys the novelty of Claims 1-3. However, P2 lies outside the scopes of Claims 4 and 5, so those claims remain novel.

A common misconception is that invalidation of an independent claim automatically invalidates all dependent claims. This is incorrect. In addition, novelty alone does not establish validity; other requirements, such as inventive step, must also be met.

Literal infringement analysis, assuming all claims are valid, requires two determinations:

Prohibited Act: An infringing act (e.g., making, using, or selling the invention without authorization) has occurred.
Scope Comparison: The accused product or process falls within the scope of at least one valid claim.

Figure 8a: The accused embodiment Q1 lies outside the scope of independent Claim 1. Therefore, Claim 1 is not infringed, and none of its dependent claims are infringed.
Figure 8b: The accused embodiment Q2 falls within the scope of Claim 3, meaning all elements of Claim 3 are present. Since Claim 3 depends on Claims 1 and 2, those claims are also infringed. However, Q2 lies outside the scope of Claim 4, so Claim 4 is not infringed. Claim 5 is likewise not infringed.

A frequent misconception is that infringement of an independent claim automatically results in infringement of all dependent claims. Figure 8b shows that this is not necessarily true.

Schematic example of drafting a set of claims

Drafting a coherent and strategically robust set of patent claims depends on several factors:

Inventor Input: The technical information and inventive concepts provided by the inventor(s).
Prior Art Landscape: Knowledge of relevant existing patents and publications.
Business Objectives: The applicant’s commercial and strategic goals.
Drafter’s Expertise: The patent drafter’s knowledge, experience, and available time.

Figure 8: (a) No infringement of Claims 1-5; (b) Claims 1-3 are infringed, but not Claims 4 and 5

The drafting process usually begins with a brainstorming session between the patent drafter and inventor(s). The primary objectives are to:

Identify the invention(s) and core inventive concept(s).
Select the most appropriate type of first independent claim, recognizing that additional independent claims may be added later.
Choose a suitable preamble that reflects the desired level of generality for the claim group.

This preparation should consider:

Specific embodiments, drawings, and examples.
The closest prior art.

The independent claim is the foundation of patent protection. It should define the essential elements required to achieve the technical effect that solves the problem addressed by the invention.

To maximize protection:

The independent claim should include all elements necessary for the invention’s core functionality.
These elements should be defined as broadly as possible while remaining consistent with the invention and prior art.

For both independent and dependent claims, a sound inventive-step strategy is required to show that the invention is non-obvious or provides an unexpected technical advantage.

Product Claims: Focus on the technical features that create the advantage, not the advantage itself.
Avoiding Mere Desideratum: Claims should specify the technical means of achieving a result rather than merely stating a desired outcome.

While independent claims provide the broadest protection, dependent claims define more specific embodiments.

Structure of Dependent Claims

One Element Per Claim (Generally): A dependent claim typically introduces or further specifies a single additional element.
Exceptions (e.g., Markush Formulas): Multiple alternatives may sometimes be included in a single claim.
Antecedent Basis: A dependent claim that limits or modifies an existing element should depend on a claim that provides a clear antecedent for that element. A claim introducing a separate new element may depend on any appropriate preceding claim, including multiple claims.
Successive Addition: Additional elements are usually introduced step by step, often in order of their importance to the invention.

The discussion then proceeds to a schematic example of drafting a single dependency group of claims for an initial patent application intended to serve as the basis for a future PCT filing across multiple jurisdictions.

Example
Following a brainstorming session, the inventor and patent drafter conclude that:

A writing device is an appropriate designation for the claimed subject matter.
The prototype consists of a writing device having A11, B11, C1, D, E, and F, which will be described in the embodiments section.
Only A11, B11, and C1 (or broader versions thereof) are considered essential elements.
The remaining elements are ranked in importance as D > E > F. Element G, although not part of the prototype, is also of interest but is less important than F.
Two mutually exclusive alternatives, H1 and H2, are considered useful for addressing different market segments.
The closest prior art discloses a writing device having A11 and B11.
There is strong support for broadening A11 → A1 → A and B11 → B1 → B.
A skilled person would likely regard C1 as equivalent to C2, C3, and C4, justifying a Markush group containing these alternatives.

Based on these assumptions, the following independent claim can be drafted:

[Standard Format]

Claim 1. A writing device comprising:

element A;
element B; and
element C selected from the group consisting of C1, C2, C3 and C4.

Depending on the circumstances, an EPO examiner may require a two-part format. Considering that “a writing device having A11 and B11” belongs to the prior art, Claim 1 could be written as:

[Two-Part Format]

Claim 1. A writing device comprising: element A; and element B; characterized by further comprising element C selected from the group consisting of C1, C2, C3 and C4.

Regardless of the format used, before introducing dependent claims with additional elements, the drafter recommends adding fallback positions through dependent claims that progressively narrow the broader elements of Claim 1.

In this example, selected values are introduced in the order A > B > C, reflecting the relative importance of these elements and the available support for broadening them. The first dependent claims are therefore:

Claim 2. The writing device according to Claim 1, wherein element A is A1.

Claim 3. The writing device according to Claim 2, wherein element A1 is A11.

Up to this point, Claims 1-3 form a dependency chain with only singular dependency, which is recommended when introducing successive selected elements.

When later dependent claims introduce additional elements, particularly for EPO practice, it is recommended to use multiple dependent claims. Thus:

Claim 4. The writing device according to any one of Claims 1-3, wherein element B is B1.
Claim 5. The writing device according to Claim 4, wherein element B1 is B11.
Claim 6. The writing device according to any one of Claims 1-5, wherein element C is C1.

The remaining elements are then added according to their importance (D > E > F > G), with mutually exclusive alternatives H1 and H2 introduced last:

Claim 7. The writing device according to any one of Claims 1-6, further comprising element D.
Claim 8. The writing device according to any one of Claims 1-7, further comprising element E.
Claim 9. The writing device according to any one of Claims 1-8, further comprising element F.
Claim 10. The writing device according to any one of Claims 1-9, further comprising element G.
Claim 11. The writing device according to any one of Claims 1-10, further comprising element H1.
Claim 12. The writing device according to any one of Claims 1-10, further comprising element H2.

Although the claim set contains only 12 numbered claims below the EPO threshold of 15 claims that can be filed without an additional claim fee it effectively covers 844 actual claim combinations.

When drafting patent claims, the procedural requirements of different patent offices must also be considered. The example above is tailored for the EPO and other jurisdictions that permit multiple dependencies from multiple dependent claims.

USPTO Restriction: The USPTO does not permit multiple dependencies from multiple dependent claims.

Before entering the U.S. national phase from a PCT application drafted in EPO style, the claims must therefore be amended to comply with USPTO rules.

PCT Amendment Opportunity: The PCT system allows claims to be amended to meet national requirements.
Risk of Losing Fallback Positions: If the adaptation is performed by someone other than the original drafter, the carefully designed dependency structure may be simplified. For example, claims originally depending on “any one of Claims 1-x” may be rewritten to depend only on Claim 1.
The Claim 1 Pyramid Problem: Such simplification can create a dependency pyramid with Claim 1 at the top. This is generally undesirable because it weakens fallback positions. If Claim 1 is later found invalid for lack of novelty or inventive step, the entire claim structure may become vulnerable.

The next step is to examine a systematic method for converting claims drafted in the EPO two-part format into a dependency structure compliant with USPTO requirements while preserving the strategic benefits of the original claim set.

Example
Original Claims 1-3 are already suitable for USPTO practice because they contain only singular dependencies. However, original Claims 4 and 6-12 use multiple dependent claim format and must be adapted.

To convert these claims into USPTO-compliant singular dependencies, the practitioner typically prepares:

Dependency chains based on the broadest interpretation of the elements.
Dependency chains based on the most restrictive interpretation of the elements.
Intermediate claim variations, provided the overall claim count remains reasonable (ideally not exceeding 20 claims to avoid additional fees).

In this example, the first two approaches are sufficient to create a 20-claim USPTO-compliant set.

Step 1: Broad Dependency Chain

US-Claims 1-3: Correspond to EPO Claims 1-3 in standard format.
US-Claim 4: According to Claim 1, wherein element B is B1.
US-Claim 5: According to Claim 4, wherein element B is B11.
US-Claim 6: According to Claim 1, wherein element C is C1.
US-Claim 7: According to Claim 1, further comprising element D.
US-Claim 8: According to Claim 7, further comprising element E.
US-Claim 9: According to Claim 8, further comprising element F.
US-Claim 10: According to Claim 9, further comprising element G.
US-Claim 11: According to Claim 10, further comprising element H1.
US-Claim 12: According to Claim 10, further comprising element H2.

Step 2: Narrow Dependency Chain

US-Claim 13: According to Claim 3, wherein element B is B11.
US-Claim 14: According to Claim 13, wherein element C is C1.
US-Claim 15: According to Claim 14, further comprising element D.
US-Claim 16: According to Claim 15, further comprising element E.
US-Claim 17: According to Claim 16, further comprising element F.
US-Claim 18: According to Claim 17, further comprising element G.
US-Claim 19: According to Claim 18, further comprising element H1.
US-Claim 20: According to Claim 18, further comprising element H2.

The logic behind this structure is:

US-Claim 4 depends on the broadest claim (Claim 1) and introduces the broad selection B1, while US-Claim 13 depends on the narrowest of the initial claims (Claim 3) and introduces the most specific selection B11.
US-Claim 6 introduces C1 from the broadest claim, whereas US-Claim 14 introduces the same limitation from the narrower dependency path.
US-Claim 7 adds element D to the broadest claim, creating a broad branch from which US-Claims 8-12 extend.
US-Claim 15 also introduces D, but through the narrower path beginning with Claim 3 and continuing through Claims 13 and 14. Consequently, US-Claims 15-20 form a narrow branch.

As a result, the 20-claim USPTO set preserves both broad and narrow fallback positions while complying with USPTO restrictions on multiple dependencies. Considering U.S. amendment practice and the prohibition against adding new matter, the USPTO will generally allow amendments to claim scopes lying between the broadest claim (US-Claim 1) and the narrowest claims (US-Claims 19-20).

The Secretariat of WIPO assumes no liability or responsibility with regard to the transformation or translation of the original content. World Intellectual Property Organization (WIPO) (2023). WIPO Patent Drafting Manual, Second edition. Geneva: WIPO. DOI: 10.34667/tind.44657