Arc Relationship Labels
An arc connects two propositions and names their relationship. The label is the answer to a single question: how does proposition B relate to proposition A? The arcing label set used in Disputation.app distinguishes eighteen relations. Most passages use only a handful. Learning to recognize each one is the practical skill that arcing trains.
Each entry below gives a one-sentence definition, the direction the relationship runs (which proposition supports or modifies which), a short diagnostic for spotting the relationship in the text, and a New Testament example. Examples cite the English Luther Bible.
1. Action / Emotion
Definition: The main verb of a proposition. Marks what the subject does or experiences.
Direction: Internal to a single proposition. Action / Emotion is the anchor that other arc labels relate to.
When to use
Every proposition has one. Action / Emotion is not a connection between two propositions but the basic act each proposition performs. Identify it before deciding how that proposition relates to the next.
Example
Romans 5:1 (English Luther Bible): "we have peace with God." The verb have is the action; peace with God is what is had. Identifying the action lets you ask the next question: what supports it? (See Inference.)
2. Grounds
Definition: B is the reason A is true or commanded. A rests on B.
Direction: A ← B. The arc points from B (the supporting reason) up to A (the claim it supports).
When to use
The surface text uses for, because, or since. The connection answers the question: why is A so? Grounds is the most common arc label in epistolary prose because Paul argues by giving reasons.
Example
Philippians 4:4–5 (English Luther Bible): "Rejoice in the Lord always, and again I say, rejoice. Let your gentleness be known to all men! The LORD is near!"
The final clause grounds the imperative: rejoice (A) because the LORD is near (B).
3. Inference
Definition: A leads to B as a logical or practical conclusion. B follows from A.
Direction: A → B. The arc points from A (the premise) down to B (the conclusion drawn from it).
When to use
The surface text uses therefore, so, thus, or then. Inference is the mirror image of Grounds: where Grounds asks why is A true?, Inference asks what follows from A?
Example
Romans 5:1 (English Luther Bible): "Now that we have been justified through faith, we have peace with God through our Lord Jesus Christ."
Justified through faith (A) yields the inference we have peace with God (B).
4. Purpose
Definition: A is done in order that B might result. B is the intended (not yet realized) goal.
Direction: A → B. The arc runs from the action to its intended end.
When to use
The surface text uses in order that, so that, or that with subjunctive or volitional force. The intended outcome is named, but the text does not (within the proposition) declare that the outcome has actually occurred. Purpose is intended; Result is actual.
Example
Ephesians 1:4 (English Luther Bible): "Just as he chose us through him before the foundation of the world was laid, that we should be holy and blameless before him in love."
The election (A) is done with the purpose of holiness and blamelessness (B). The goal is named as the reason for the action.
5. Result
Definition: B actually results from A. The outcome is stated as accomplished fact.
Direction: A → B. The arc runs from the cause to the realized effect.
When to use
The surface text uses so that with indicative force, or marks the outcome as something that has happened or always happens. Test by asking: did this actually occur, or is it only the goal? If the text reports it as fact, the label is Result. If only intended, the label is Purpose.
Example
John 3:16 (English Luther Bible): "So God loved the world, that he gave his only begotten Son, so that all who believe in him may not be lost, but have eternal life."
God's giving (A) results in believers having eternal life (B). The clause names the actual effect, not merely the aim.
6. Means
Definition: B is the instrument by which A is accomplished.
Direction: A ← B. B is subordinate to A: A is the action, B is how the action is performed.
When to use
The surface text uses by, through, or by means of. The diagnostic is instrumental: B answers the question by what? Means differs from Manner: Means names an instrument (something used), while Manner names a quality of the action (how it is carried out).
Example
Ephesians 2:8 (English Luther Bible): "For by grace you are saved, through faith."
The action is salvation (A); the means is faith (B). Faith is the instrument, not the cause; the cause is grace.
7. Manner
Definition: A is carried out in the way B describes. Manner names the mode or character of the action.
Direction: A ← B. B modifies A by giving its quality.
When to use
The surface text uses just as, in the same way, or an adverbial phrase describing how the action is performed. The diagnostic is qualitative: B answers the question in what manner? rather than by what instrument?
Example
1 Corinthians 16:14 (English Luther Bible): "Let all your things be done in love!"
The action is everything you do (A); the manner is in love (B). Love is not the instrument of the action but the character that ought to mark every action.
8. Condition
Definition: B is the prerequisite for A. A holds or obtains only when B is true.
Direction: A ← B. B is the conditional clause; A is the apodosis (the consequent).
When to use
The surface text uses if or unless. Condition is hypothetical: B is offered as a possibility, and A follows only when B holds. Distinguish from Grounds, which gives a reason that is true in fact.
Example
Romans 10:9 (English Luther Bible): "For if you confess Jesus with your mouth, that he is the Lord, and believe in your heart that God has raised him from the dead, you will be saved."
The condition is the confession-and-belief clause (B); the consequent is salvation (A). A is contingent on B.
9. Concession
Definition: A is true despite B. B would seem to prevent A but does not.
Direction: A ← B. B is acknowledged as an objection or counter-pressure that A overcomes.
When to use
The surface text uses although, even though, even if, or though. The diagnostic is concessive: B is the obstacle the author admits, then sets aside. Concession is the most rhetorically muscular label: the author concedes ground in order to claim the more.
Example
2 Corinthians 4:16 (English Luther Bible): "Therefore we do not grow weary; but though our outward man decays, yet the inward is renewed from day to day."
The decaying clause (B) is the concession; the renewal clause (A) is the claim that holds in spite of it.
10. Comparison
Definition: A is like B. The two propositions illuminate each other through similarity.
Direction: A ↔ B (illuminative). Neither dominates; the comparison runs both ways.
When to use
The surface text uses just as... so also, like, or any explicit simile or analogy. Used for analogies, parables, and structural parallels. Comparison differs from Manner: Comparison sets two distinct subjects in parallel; Manner describes one action's quality.
Example
Romans 5:18 (English Luther Bible): "So then, as through the sin of one condemnation came upon all men, so also through the righteousness of one the justification of life came upon all men."
The first clause (B, Adam's sin) is set in parallel with the second (A, Christ's righteousness). Each illuminates the other.
11. Contrast
Definition: A is set against B. The two propositions are in tension or opposition.
Direction: A ↔ B (oppositional). Both propositions stand; the relationship is the opposition itself.
When to use
The surface text uses but, however, yet, or whereas. Contrast is the workhorse of Pauline argument: the antithesis between flesh and Spirit, law and gospel, old and new. Distinguish from Concession: Contrast simply opposes; Concession admits B and overcomes it.
Example
Ephesians 5:8 (English Luther Bible): "For you were formerly darkness, but now you are a light in the Lord."
The first clause (B, the past condition) is set against the second (A, the present condition). The contrast structures the entire exhortation that follows.
12. Series (equal)
Definition: A and B are parallel items of equal weight. The items could be listed in any order without changing meaning.
Direction: A = B. Each item is a peer of the others; none dominates.
When to use
The surface text uses and, also, or simple comma-separated lists. Items are coordinate. Test by asking: would the meaning change if the order were reversed? If not, the series is equal. If reordering would lose escalation or climax, see Series (progressive).
Example
Galatians 5:22–23 (English Luther Bible): "But the fruit of the Spirit is love, joy, peace, patience, friendliness, kindness, faith, gentleness, chastity. Against such there is no law."
Each fruit is parallel to the others. Reordering the list does not change Paul's claim. The series is equal.
13. Series (progressive)
Definition: A and B are parallel items with escalation or climactic movement. Order matters.
Direction: A < B < C... Each item builds on the one before.
When to use
The surface text uses and with increasing intensity, or a chain of producing-clauses (X produces Y, Y produces Z). Distinguish from equal series by the movement: a progressive series cannot be reordered without losing the climb.
Example
Romans 5:3–4 (English Luther Bible): "We also boast in tribulations, since we know that tribulation brings patience, and patience brings experience, and experience brings hope."
The chain runs tribulation → patience → experience → hope. Reversing the order would destroy the argument.
14. Bilateral
Definition: A and B are mutually conditioning; neither makes full sense without the other. The relationship runs both directions.
Direction: A ↔ B (mutual). Each side requires the other.
When to use
The surface text uses both... and, or pairs the two propositions in such a way that removing either would collapse the meaning. Bilateral is rarer than the other coordinating labels and identifies a deliberate paired structure.
Example
Galatians 6:2 (English Luther Bible): "Bear one another's burden, and so you will fulfill the law of Christ."
The burden-bearing and the law-fulfilling are mutually conditioning: bearing one another's burden is the way the law is fulfilled, and the law of Christ is what bearing burdens means in practice.
15. Temporal
Definition: A and B are related by time sequence or simultaneity.
Direction: A ↔ B (temporal). One precedes, follows, or coincides with the other.
When to use
The surface text uses when, after, while, before, or as. The relationship is purely temporal: B says when A happens, not why or how. Especially common in narrative prose.
Example
Acts 2:1 (English Luther Bible): "And when the day of Pentecost was fulfilled, they were all of one mind together."
The first clause (B) gives the time at which the second clause (A) holds. The relationship is temporal, not causal.
16. Substantive
Definition: B is the content of what A says, believes, knows, commands, or hopes.
Direction: A ← B. B is what is being said, believed, or commanded; A is the act of saying, believing, or commanding it.
When to use
The surface text uses that introducing a content clause: I want you to know that..., he commanded that..., we believe that... Substantive is one of the most common connectives in epistolary prose. Distinguish from Purpose: Substantive supplies the content of speech, belief, or thought; Purpose names the goal of an action.
Example
1 Thessalonians 4:13 (English Luther Bible): "But we do not want to keep from you, dear brothers, concerning those who sleep, so that you are not sorrowful like the others who have no hope."
The act of teaching (A) carries the substantive content (B): how the Thessalonians should think about the dead. B is what A says.
17. Elaboration / Restatement
Definition: B restates, clarifies, or unpacks A. B adds no new proposition; it illuminates A by saying the same thing differently.
Direction: A ← B. B is subordinate to A: it does not advance the argument but explicates the previous claim.
When to use
The surface text uses that is, namely, in other words, or a colon followed by an explication. Distinguish from Grounds (B gives a reason for A) and from Inference (B follows from A). Elaboration neither grounds nor follows; it restates.
Example
Romans 7:18 (English Luther Bible): "For I know that in me, that is, in my flesh, dwells nothing good."
The clause that is, in my flesh (B) restates and clarifies in me (A). Paul is not introducing a new claim; he is qualifying what he meant.
18. Locative
Definition: B specifies the place or domain in which A holds.
Direction: A ← B. B is subordinate to A: it locates the action.
When to use
The surface text uses where, in which, among whom, or a prepositional phrase identifying the locus. The relationship is spatial or domain-specifying. Especially common in Pauline phrases like in Christ and in the heavenly places.
Example
Ephesians 1:3 (English Luther Bible): "Praised be God and the Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in heavenly goods, through Christ."
The blessing (A) is located in heavenly goods, through Christ (B). B does not modify the blessing's manner; it specifies the domain in which the blessing obtains.
How to use these labels in the app
Open the Charting tab and choose Arcing & Diagramming to draw arcs between propositions of any passage. The Arcing pane lets you label each connection from the full set above. The colors and shorthand match the labels listed here.
For a guided practice run on a specific passage, use the Teaching the Arc action in AI Studio. It splits the passage into propositions, presents the arc connections as a fill-in-the-blank worksheet, then reveals the answer diagram so you can check your work. The labels and definitions on this page are the answer key.