Relation types

In Nesso, every edge carries a semantic type: a named relation describing how two concepts are connected, with semantic coefficients reserved for graph-analysis algorithms (future work, no algorithm currently consumes them). The vocabulary is fixed at 52 types across 8 categories, drawn from prior work in knowledge representation, lexical semantics, temporal logic, and signed-network theory.

Note

This set and its coefficients are a starting point. Both the types and their coefficient values will evolve as real graphs accumulate, edge cases surface, and the analysis algorithms that consume the coefficients get built out. Treat them as a considered first cut, not a final spec.

Coefficients

Each relation type declares the coefficients below. They define the contract that graph-analysis algorithms will consume; closing the enum guarantees every type comes with them, where a user-defined type would arrive without and stay analytically opaque.

• Transitive (T): Y (strict), N (none), or weak (transitivity with decay; algorithms may discount per step).
• Inverse (I): the canonical inverse type in the set; self for symmetric relations. Asymmetric relations declare it explicitly so traversal is first-class in both directions. The explicit-inverse design follows knowledge-graph embedding work [1], which lists symmetry, antisymmetry, inversion, and composition as the four properties a good relation set should support.
• Strength (S): per-type semantic weight in 0..1. Encodes how “tight” the relation is in general (e.g. defines 0.90 vs similar-to 0.40), not how sure the user is about a specific edge. The idea that different relation types carry different semantic distance comes from lexical-taxonomy weighting schemes [2], [3].
• Polarity (P): +1 positive effect, -1 antagonistic, 0 neutral/structural. From signed-network theory [4]: with polarity, the graph becomes a signed network where balance and cycle-sign analyses can apply.
• Cardinality (C): expected mapping pattern, always declared. One of 1-1, 1-N, N-1, N-N (no a-priori constraint). Setting this consistently lets algorithms flag structural anomalies (e.g. two competing defines edges into the same term).

Categories

Each category answers a specific question about the relation. Grouping the types by question makes the vocabulary easier to navigate when authoring a graph, and lets graph-analysis algorithms compare and aggregate at category level instead of only per individual type.

Taxonomic

What kind of thing is it?

Type	Label	I	T	S	P	C
subtype-of	subtype of	has-subtype	Y	0.90	0	N-1
has-subtype	has subtype	subtype-of	Y	0.90	0	1-N
instance-of	instance of	has-instance	N	0.95	0	N-1
has-instance	has instance	instance-of	N	0.95	0	1-N

Taxonomic relations answer the simplest question you can ask about a concept: what kind of thing is it? Nesso splits the answer into two layers that look alike at a glance but behave very differently under reasoning. The class-vs-instance distinction mirrors OWL/RDFS [5]: subtype-of corresponds to rdfs:subClassOf (one class refines another, as a sparrow refines bird), while instance-of corresponds to rdf:type (an individual belongs to a class, as Tweety belongs to sparrow). Inheritance flows freely through the subtype chain, but instances are leaves: Tweety is a sparrow and through that a bird, yet Tweety is not itself “a kind of” anything.

Structural

What is it made of or composed from?

Type	Label	I	T	S	P	C
part-of	part of	contains	Y	0.85	0	N-1
contains	contains	part-of	Y	0.85	0	1-N
made-of	made of	composes	weak	0.75	0	N-N
composes	composes	made-of	weak	0.75	0	N-N

Structural relations describe how a thing decomposes into its parts. The category covers two patterns. part-of and its inverse contains capture discrete structural decomposition: an engine is part of a car, a paragraph is part of a chapter, and transitivity flows cleanly through the chain. made-of and composes capture material or substantive composition instead: water is made of hydrogen and oxygen, a chair is made of wood. Transitivity there is only weak, because what something is made of doesn’t always propagate in a meaningful way (a chair made of wood, made of cellulose, made of carbon, made of atoms dilutes the relationship as the chain grows).

Causal

What does it do or prevent?

Type	Label	I	T	S	P	C
causes	causes	caused-by	N	0.85	+1	N-N
caused-by	caused by	causes	N	0.85	+1	N-N
produces	produces	produced-by	N	0.70	+1	N-N
produced-by	produced by	produces	N	0.70	+1	N-N
enables	enables	enabled-by	weak	0.60	+1	N-N
enabled-by	enabled by	enables	weak	0.60	+1	N-N
prevents	prevents	prevented-by	N	0.85	−1	N-N
prevented-by	prevented by	prevents	N	0.85	−1	N-N
triggers	triggers	triggered-by	N	0.70	+1	N-N
triggered-by	triggered by	triggers	N	0.70	+1	N-N
inhibits	inhibits	inhibited-by	N	0.55	−1	N-N
inhibited-by	inhibited by	inhibits	N	0.55	−1	N-N
disables	disables	disabled-by	weak	0.60	−1	N-N
disabled-by	disabled by	disables	weak	0.60	−1	N-N
consumes	consumes	consumed-by	N	0.65	−1	N-N
consumed-by	consumed by	consumes	N	0.65	−1	N-N
delays	delays	delayed-by	weak	0.55	−1	N-N
delayed-by	delayed by	delays	weak	0.55	−1	N-N

Causal is the largest category in Nesso, because causation in the real world doesn’t come in a single flavor. On the positive side, causes describes direct generation of an outcome, triggers describes the initiation of something that then plays out on its own (a spark triggers an explosion), and enables describes making something possible without forcing it. The negative side mirrors this: prevents is total blockage, inhibits is partial reduction, and disables is switching off a capacity or function. Intensity and mechanism live at the type level rather than as per-edge weights, so choosing between inhibits and prevents is a semantic decision about what is actually happening, not about how confident the author is.

consumes and delays round out the category. consumes captures resource destruction, which is causal rather than dependency-flavored: it is distinct from uses, where the resource survives the interaction. delays carries negative polarity because slowing or postponing an outcome hinders it, even though nothing is destroyed.

Dependency

What does it need or serve?

Type	Label	I	T	S	P	C
requires	requires	required-by	Y	0.85	0	N-N
required-by	required by	requires	Y	0.85	0	N-N
uses	uses	used-by	weak	0.50	0	N-N
used-by	used by	uses	weak	0.50	0	N-N
used-for	used for	purpose-of	N	0.55	+1	N-N
purpose-of	purpose of	used-for	N	0.55	+1	N-N

Dependency relations capture what a concept needs rather than what causes it. A car requires an engine to function, but the engine doesn’t cause the car, and that difference shows up in how the graph traverses these edges. requires and required-by are the hard form, where the dependency is essential and transitivity is strict: if A requires B and B requires C, A also requires C. uses and used-by are softer, capturing a working relationship that doesn’t necessarily imply the user can’t survive without it, so transitivity decays through the chain. used-for and purpose-of are teleological: they point at the goal or function a thing serves (a hammer is used for driving nails). Cardinality there stays open at N-N, since one tool can serve many purposes and many tools can share a single purpose.

Temporal

When or where does it happen?

Type	Label	I	T	S	P	C
precedes	precedes	follows	Y	0.50	0	N-N
follows	follows	precedes	Y	0.50	0	N-N
occurs-in	occurs in	has-occurrence	Y	0.40	0	N-1
has-occurrence	has occurrence	occurs-in	Y	0.40	0	1-N
during	during	spans	Y	0.55	0	N-1
spans	spans	during	Y	0.55	0	1-N
overlaps-with	overlaps with	self (symmetric)	N	0.45	0	N-N
derives-from	derives from	gives-rise-to	Y	0.70	0	N-1
gives-rise-to	gives rise to	derives-from	Y	0.70	0	1-N

Temporal relations describe when things happen relative to each other and how an event sits inside a larger period. Allen’s interval algebra [6] inspires the containment pair: during and spans model intervals nested inside other intervals (the medieval period spans roughly a thousand years, and Charlemagne’s reign was during it). occurs-in and its inverse work at a different scale, pinning a quasi-point event to the period it falls inside (the moon landing occurs in 1969). precedes and follows cover plain sequence without nesting, and overlaps-with is the symmetric case for two intervals that share a stretch of time without one containing the other.

derives-from and gives-rise-to are not just about chronology, they capture genealogical descent: a transformative continuity where something becomes something else over time. Languages, species, and ideas all have lineages of this kind. The relation is close to caused-by but distinct, because causation is direct influence without requiring the cause to become the effect. It is also distinct from taxonomic subtype-of, which is a snapshot of class membership rather than a historical claim. Italian derives from Latin, but Italian is not a subtype of Latin in the modern sense.

Opposition

What does it contrast with?

Type	Label	I	T	S	P	C
contrasts-with	contrasts with	self (symmetric)	N	0.50	−1	N-N
opposite-of	opposite of	self (symmetric)	N	0.80	−1	1-1

Opposition is the category for concepts that stand against each other. The two types differ in strength. contrasts-with is the weaker form, where two concepts highlight each other by sitting at different points on some dimension (warm contrasts with cool, North contrasts with South). opposite-of is the canonical, often binary opposite (alive is the opposite of dead, true is the opposite of false), and its cardinality is 1-1 because a canonical opposite is unique. Both are symmetric: if A is the opposite of B, then B is the opposite of A by definition.

Similarity

What is it like?

Type	Label	I	T	S	P	C
similar-to	similar to	self (symmetric)	weak	0.40	+1	N-N
analogous-to	analogous to	self (symmetric)	N	0.30	+1	N-N

The similarity category includes two related but distinct relations. similar-to is the looser one, where two concepts share enough properties to be grouped together (lions are similar to tigers). analogous-to is more structural: the two concepts aren’t necessarily alike in their properties, but their roles or relationships mirror each other (an electron orbiting an atom is analogous to a planet orbiting the sun). Both are symmetric, and both carry positive polarity because finding similarity or analogy is usually a constructive move in reasoning.

Epistemic

How do we know?

Type	Label	I	T	S	P	C
supports	supports	supported-by	weak	0.70	+1	N-N
supported-by	supported by	supports	weak	0.70	+1	N-N
contradicts	contradicts	self (symmetric)	N	0.75	−1	N-N
explains	explains	explained-by	weak	0.80	0	N-N
explained-by	explained by	explains	weak	0.80	0	N-N
defines	defines	defined-by	N	0.90	0	1-1
defined-by	defined by	defines	N	0.90	0	1-1

The epistemic category is where Nesso models reasoning about claims rather than facts about the world. supports and supported-by connect a piece of evidence to the claim it bolsters; explains and explained-by connect an explanans (the explanatory account) to its explanandum (what is being explained). Both pairs are asymmetric, because evidence points to a claim and an explanation is not equivalent to what it explains.

defines is the most rigid relation in this category. It goes from the defining expression (the definiens) to the term being defined (the definiendum): in “F = ma defines force”, the equation is the definiens and force is the definiendum. Cardinality 1-1 enforces a single canonical definition per term, so two competing defines edges into the same concept signal a real ambiguity worth resolving.

contradicts is the only symmetric relation in the category, because logical incompatibility goes both ways: if A contradicts B, then B equally contradicts A. This distinguishes it from supports and explains, which always point in a particular direction.

References

1. Sun, Z., Deng, Z.-H., Nie, J.-Y., and Tang, J. RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space. ICLR, 2019. ↑
2. Sussna, M. Word sense disambiguation for free-text indexing using a massive semantic network. CIKM ‘93, 1993. ↑
3. Jiang, J. J. and Conrath, D. W. Semantic similarity based on corpus statistics and lexical taxonomy. ROCLING X, 1997. ↑
4. Cartwright, D. and Harary, F. Structural balance: A generalization of Heider’s theory. Psychological Review, 63(5):277–293, 1956. ↑
5. W3C. OWL 2 Web Ontology Language Primer (Second Edition). 2012. ↑
6. Allen, J. F. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832–843, 1983. ↑