Benz (2025): Structure and Interpretation Across Categories #
Three case studies from [Ben25] (PhD dissertation, University of
Pennsylvania) on the syntax–LF interface in German, all running on the
contextual-allosemy substrate of DistributedMorphology.Allosemy. Nominalizations
like Beobachtung carry event, referential, and content readings from a
single syntactic structure, with the variation located in the allosemes of v
and n (Ch. 3). The co-occurrence restrictions among prefixes, particles, and
resultative secondary predicates follow from the conjunction of a
phrase-structural factor and an event-structural one, [Ten94]'s Single
Delimiting Constraint (Ch. 4, Table 3). The three nominalization types
resolve the particle "structure problem" ([Lud01b]) in three
different ways — phrasal inputs, particles-as-heads, outer attachment — from
which the distribution of preverbal elements across them follows (Ch. 5).
The (32), (87)–(89), and (115) stimuli live in Data.Examples.Benz2025.
availableReadings derives the reading inventory from the exponence engine's
licensed allosemes, with adopted_unique characterizing the adopted analysis
as the unique economical derivation of each reading and denoteN grounding
the reading table in typed denotations
(readingFromAllosemes_isSome_iff_denote); blocked_sound and
blocked_complete show the two Ch. 4 principles exactly generate the
co-occurrence paradigm; peAcceptable_from_solutions derives the Ch. 5
distribution from the structure-problem solutions.
Content nominalizations (Ch. 3) #
The three readings of Beobachtung #
The (32) stimulus rows, in margin-label order Event, RN, Content.
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The reading a stimulus row exemplifies, from its reading feature. The
paper's loose "RN" label is rendered as the simple entity reading.
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Beobachtung exhibits all three readings ((32)).
Each (32) example exhibits exactly its characteristic diagnostic — duration modification for the event reading, pluralization for the RN reading, CP complementation for the content reading ([Gri90]-style diagnostics).
Readings from allosemes #
The alloseme pair deriving each reading on the adopted analysis, where v
is semantically vacuous on all readings but the CEN (§3.5, following
[Woo23]). By adopted_roundtrip and adopted_unique, this is the unique
derivation of each reading in which the two heads are not both contentful.
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Each reading is recovered from its adopted alloseme pair.
Among derivations in which the two heads are not both contentful, the adopted pair is the only one deriving the reading — economy of interpretation pins the analysis.
The reading pins the division of labor (the "mirror image" claim of §3.5): an event reading arises only from contentful v with vacuous n, while a result or content reading forces the corresponding contentful n, whatever v contributes.
Alloseme selection in the nominalization structure #
The selection side is DM's own engine, not a further table: allosemes are
Vocabulary Items over neighborhoods, applicability is the Subset Principle,
and canonical defaults are Elsewhere competition (winner?). The readings
available in the (66)/(68) structure [n [v √]] are whatever the licensed
allosemes compose to.
v's context in the nominalization structure [n [v √]] — its complement is the root, event-entailing or not, and it is embedded under n.
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n's context in [n [v √]] — a verbal complement, eventive or not.
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The readings derivable in the nominalization structure: any licensed v alloseme composed with any licensed n alloseme.
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Over an event-entailing root both v allosemes are licensed — the premise of the reading ambiguity — while a non-eventive root licenses only vacuous v.
The canonical v alloseme of the root typology is the engine's Elsewhere
winner: the more specified eventive entry beats vacuous v exactly when the
root entails an event, so Verbalizer.Alloseme.fromRootType is derived, not
stipulated.
Every attested Beobachtung reading is available in the single structure: the engine licenses the allosemes and composition delivers the readings (Ch. 3's chapter claim).
Without an event-entailing root neither the complex event nor the result reading is derivable; the content reading survives, since simple content nouns like Gerücht 'rumor' need no verbal source (Table 2).
Typed alloseme denotations (Ch. 3) #
The denotations of the deverbal allosemes, after [Woo23] as taken over
in Ch. 3: nominalization semantics runs over a domain in which eventualities
are entities, and each n alloseme builds an entity predicate from what v
hands it. The reading typology is then derived, not tabulated: readings exist
exactly where the composition is defined
(readingFromAllosemes_isSome_iff_denote), and the analytical options for
the result and content readings compose to identical entity predicates
(result_options_pred_agree, content_options_agree).
A model for nominalization denotations: eventualities embed into the
entity domain (a nominal can describe an event as an entity), split into
stative and dynamic, with result relating an entity to the eventuality
that produced it and hasContent picking out the entities with
propositional content.
- ev : S → E
Eventualities as entities.
- ev_injective : Function.Injective self.ev
- stative : S → Prop
Stative eventualities.
- result : E → S → Prop
The entity is the result of the eventuality.
- hasContent : E → Prop
The entity has propositional content (rumor, idea, claim).
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A root's contribution to nominalization semantics: what it says of entities and of eventualities, and its Theme relation — which entity an eventuality of the root's kind is predicated of.
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What v hands to n: under the eventive alloseme, verbal event content together with the Theme position v introduces (§2.2); under the zero alloseme, the untouched root — and no argument position, since none is introduced by v (§3.5).
- eventive {E : Type u_3} {S : Type u_4} (p : S → Prop) (theme : E → S → Prop) : VerbalDenotation E S
- zero {E : Type u_3} {S : Type u_4} (ρ : RootMeaning E S) : VerbalDenotation E S
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The v alloseme applied to the root.
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A nominal denotation: the entity predicate, together with the internal-argument relation when the nominal retains one. The relation is present exactly when v introduced the Theme position — no such position is part of the denotation unless v contributes it (§2.2, §3.5).
- pred : E → Prop
What the nominal describes.
- internalArg : Option (E → E → Prop)
The internal-argument relation:
internalArg y xholds whenysaturates the nominalx's Theme position (the observation of the sky).
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The n alloseme applied to v's output, none where the combination
is uninterpretable. The CEN describes the events the verb describes and
retains the Theme position v introduced; the SEN predicates the root's
entity content of an event-entity; the result alloseme picks out what an
event of the root's kind produced ([Woo23]'s denotation); the content
alloseme ignores the verbal layer entirely. The non-deverbal allosemes
have their semantics in Semantics/Possessive/Relational.lean.
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- Benz2025.denoteN m (Benz2025.VerbalDenotation.eventive p theme) (some DistributedMorphology.Allosemy.Nominalizer.Contentful.content) = some { pred := m.hasContent }
- Benz2025.denoteN m (Benz2025.VerbalDenotation.zero ρ) (some DistributedMorphology.Allosemy.Nominalizer.Contentful.entity) = some { pred := ρ.onEntities }
- Benz2025.denoteN m (Benz2025.VerbalDenotation.zero ρ) (some DistributedMorphology.Allosemy.Nominalizer.Contentful.content) = some { pred := m.hasContent }
- Benz2025.denoteN m x✝¹ x✝ = none
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The event and result readings are mirror images at the entity-predicate level: the two analytical options for the result reading — eventive v with n's result alloseme, or vacuous v with the same — agree on what the nominal describes (§3.5, crediting [Woo23]).
...but not on argument structure: on the both-heads-interpreted option the result nominal retains the internal-argument position v introduced, on the v-vacuous option it has none. Since result nominals cannot saturate an internal argument, this is the reason for adopting the vacuous option for the RN reading (§3.5, following [Woo23]).
CENs retain argument structure: the complex event nominal carries
the Theme position v introduced (the observation of the sky), which is
what separates it from every zero-v reading
(zero_v_no_argument_structure).
No zero-v reading has an internal-argument position: none is introduced by v, so none is part of the denotation (§3.5).
The content reading likewise ignores the verbal layer: both v
options compose to hasContent, which is how simple content nouns can
have the reading with no verbal source at all (§3.5).
The reading typology tracks denotational definedness: a (v, n) pair has a reading exactly when its composed denotation is defined.
A complex event nominal holds only of event-entities: the ground of its event reading (temporal modification, aspectual behavior).
Prefixes, particles, and resultatives (Ch. 4) #
The three preverbal-element types #
The three types of German preverbal elements (Ch. 4).
- pfx : PreverbalElement
- prt : PreverbalElement
- rsp : PreverbalElement
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- Benz2025.instDecidableEqPreverbalElement x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Benz2025.instReprPreverbalElement = { reprPrec := Benz2025.instReprPreverbalElement.repr }
A morphological element is either a head (X⁰) or a phrase (XP).
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- Benz2025.instDecidableEqSynLevel x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Benz2025.instReprSynLevel.repr Benz2025.SynLevel.head prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Benz2025.SynLevel.head")).group prec✝
- Benz2025.instReprSynLevel.repr Benz2025.SynLevel.phrase prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Benz2025.SynLevel.phrase")).group prec✝
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- Benz2025.instReprSynLevel = { reprPrec := Benz2025.instReprSynLevel.repr }
Whether an element obligatorily introduces a result-state specification. Prefixes and RSPs always specify a result state, while particles can have non-delimiting (directional, completive) readings (§4.4).
- specifies : ResultStateSpec
- neutral : ResultStateSpec
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- Benz2025.instDecidableEqResultStateSpec x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Benz2025.instReprResultStateSpec = { reprPrec := Benz2025.instReprResultStateSpec.repr }
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The two compatibility factors #
Structural combinability of an outer and an inner element, the inner one closer to the root. A phrasal inner element is impossible, since a head outside it cannot form a complex head with the root, and a phrasal outer element competes with it for the verb's single complement position (§4.4).
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- Benz2025.incorporationAllowed Benz2025.SynLevel.head Benz2025.SynLevel.head = true
- Benz2025.incorporationAllowed Benz2025.SynLevel.phrase Benz2025.SynLevel.head = true
- Benz2025.incorporationAllowed Benz2025.SynLevel.head Benz2025.SynLevel.phrase = false
- Benz2025.incorporationAllowed Benz2025.SynLevel.phrase Benz2025.SynLevel.phrase = false
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Structural combinability depends only on the inner element's level — derived, not stipulated.
Two elements that both obligatorily specify a result state cannot co-occur, since the end state of a complex event can only be specified once — [Ten94]'s Single Delimiting Constraint (p. 79, quoted at (159)).
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- Benz2025.structurallyCompatible outer inner = Benz2025.incorporationAllowed outer.synLevel inner.synLevel
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- Benz2025.interpretivelyCompatible outer inner = Benz2025.resultStatesCompatible outer.resultSpec inner.resultSpec
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A combination is predicted possible iff both factors permit it (§4.4).
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- Benz2025.predictedAllowed outer inner = (Benz2025.structurallyCompatible outer inner && Benz2025.interpretivelyCompatible outer inner)
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Prefix and particle inventory (Table 4) #
German inseparable prefixes (Table 4). ge- is the rare non-participial prefix (ge-bären, ge-denken, ge-fallen).
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- Benz2025.inseparablePrefixes = ["be", "ent", "er", "ge", "miss", "ver", "zer"]
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German prepositional separable particles (Table 4, which additionally lists nominal and adjectival particles like klavier-, rad-, leicht-, whose classification is controversial).
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- Benz2025.separableParticles = ["ab", "an", "auf", "aus", "bei", "ein", "los", "nach", "vor", "zu"]
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Elements occurring both as prefix and as particle (Table 4).
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- Benz2025.ambiguousElements = ["durch", "hinter", "über", "um", "unter", "wider"]
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The ambiguous elements appear in neither pure inventory.
The co-occurrence paradigm (Table 3) #
A cell of Table 3's factor columns, recording whether the factor predicts
the combination to be possible. particleDependent renders the table's
parenthesized check mark, a prediction that depends on the specific particles
involved (§4.1).
- predicts : FactorVerdict
- particleDependent : FactorVerdict
- excludes : FactorVerdict
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- Benz2025.instDecidableEqFactorVerdict x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Benz2025.instReprFactorVerdict = { reprPrec := Benz2025.instReprFactorVerdict.repr }
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Boolean reading of a factor cell, on which particleDependent counts as
possible since the generic classification treats particles as
result-neutral.
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A row of Table 3 (repeated as Table 5). The printed table's final row
merges pfx-RSP and PRT-RSP into one row "pfx/PRT-RSP", rendered here by a
two-element outers list.
- outers : List PreverbalElement
The outer element(s) of the printed row.
- inner : PreverbalElement
The inner element, closer to the root.
- allowed : Bool
The Allowed column.
- structureVerdict : FactorVerdict
The Structure Predicts column.
- interpretationVerdict : FactorVerdict
The Interpretation Predicts column.
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- Benz2025.instReprCooccurrenceRow = { reprPrec := Benz2025.instReprCooccurrenceRow.repr }
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- Benz2025.instBEqCooccurrenceRow.beq x✝¹ x✝ = false
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Table 3, cell for cell.
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The conjunction of the two factors reproduces the Allowed column at every cell of Table 3.
The structural factor reproduces the Structure column at every cell.
The interpretive factor reproduces the Interpretation column at every cell
except the merged row's particle half (see
prt_rsp_interpretation_particle_dependent).
The printed table marks the merged pfx/PRT-RSP row's interpretation cell ✗, but on the account's own classification only the prefix half is interpretively excluded. For PRT-RSP the structural factor does the work, while only "some RSP-particle verbs are additionally also ruled out semantically" (§4.4).
PRT-pfx is the unique allowed combination ((84) aus-er-wählen, an-ver-trauen, vor-ent-halten, um-ent-scheiden, ab-er-kennen).
Neither factor alone predicts the paradigm — structure alone misses the double-delimitation rows (pfx-pfx, RSP-pfx) and interpretation alone misses the phrase-structure rows (pfx-PRT, PRT-PRT, RSP-PRT).
Blocking derivations #
A proof that a preverbal-element combination violates one of the two
principles. Soundness and completeness against predictedAllowed show the
two principles exactly generate the paradigm.
- byPhrasalInner
{o i : PreverbalElement}
: i.synLevel = SynLevel.phrase → Blocked o i
A phrasal element cannot occupy the inner position, since a head outside it cannot form a complex head with the root and a phrasal outer competes for the verb's single complement position (§4.4).
- bySingleDelimiting
{o i : PreverbalElement}
: o.resultSpec = ResultStateSpec.specifies → i.resultSpec = ResultStateSpec.specifies → Blocked o i
Two obligatory result-state specifiers conflict, since the end state of a complex event can only be specified once ([Ten94]'s Single Delimiting Constraint, (159)).
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Every blocking derivation corresponds to a predicted-blocked combination — the theory does not over-generate.
Every blocked combination has a derivation — the two principles account for all restrictions.
The allowed combination has no derivation, since the prefix is a head and the particle is result-neutral.
pfx-pfx is blocked only by the Single Delimiting Constraint (both are heads), so the interpretive rule is not redundant.
pfx-PRT is blocked only structurally (particles are result-neutral), so the structural rule is not redundant.
Cross-framework contrast: the phrase-in-word-slot cell #
ConstructionGrammar.Slot.IsPhraseInWordSlot — a phrasal filler in a
zero-level position — is the configuration of phrasal compounds and the PAL
construction ([GS25]; contemporaneous with this dissertation,
neither cites the other). In this file's terms that configuration is exactly
the banned phrasal-inner cell: the structural principle rejects what the
constructionist analysis licenses (cf. GoldbergShirtz2025.pal_load_bearing).
A CxG bar level in SynLevel terms, where zero-level positions are head
sites and bar- and phrase-level positions are phrasal.
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The SynLevel of a CxG slot filler. Word fillers are heads, phrasal
fillers (with or without a fixed head) are phrases, and SEM+ fillers are
level-unspecified.
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- (ConstructionGrammar.SlotFiller.fixed a).synLevel = some Benz2025.SynLevel.head
- (ConstructionGrammar.SlotFiller.open_ a).synLevel = some Benz2025.SynLevel.head
- (ConstructionGrammar.SlotFiller.headed a a_1).synLevel = some Benz2025.SynLevel.phrase
- ConstructionGrammar.SlotFiller.phrasal.synLevel = some Benz2025.SynLevel.phrase
- (ConstructionGrammar.SlotFiller.semantic a).synLevel = none
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A phrase in a word-level slot occupies the banned cell — its site is a
head and its filler a phrase, so incorporationAllowed rejects the pair. The
standing counterexample class is the PAL construction, which licenses exactly
this configuration.
German resultative data (§4.2) #
Complex predicate semantics after [Wil15], adopted at (158):
⟦v⟧ = λx λe₁ ∃e₂ ∃s. Means(e₁,e₂) & Pred₁(e₂) & Theme(e₁,x) & End(e₁,s) &
Pred₂(s), where the M(eans) predicate is the verb, the R(esult) predicate the
RSP, and the End Theme Postulate (108) links the complex event's Theme to the
end state. See Causation.Resultatives for the complementary causal-dynamics
analysis.
The resultative stimulus rows ((89), (115); the (115) rows are due to [Cre20]).
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German allows non-unergative M predicates in resultatives ((115)), against weak-resultative reanalyses of the whole class.
RSP co-occurrence contrasts (§4.1) #
RSPs are incompatible with prefixed verbs, while the same RSP with the simplex verb is fine ((87), from [Cre20]). Each row's grammatical baseline carries its ungrammatical prefixed alternative, and the ge- of the baselines is participial, not a prefix in the relevant sense.
RSPs are likewise incompatible with particle verbs ((88)), including particles not characterizable as resultative, like an- in (88d).
Interpretive transparency #
Whether the element can receive a non-transparent interpretation with the verb ((161) an-fangen 'start' vs. (162) platt klopfen 'pound flat'). RSPs are always interpreted transparently since they sit outside the locality domain for allosemy, while particles are bare phrasal complements local enough for it.
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Particles pattern with RSPs structurally (both phrasal) but with prefixes interpretively (both can be non-transparent) — the evidence that particles are phrasal yet local enough for allosemy (§4.3).
Prefixes in nominalizations (Ch. 5) #
Nominalization types and the structure problem #
The three German nominalization types discussed in Ch. 5.
- ung : NominalizationType
- ge_e : NominalizationType
- nomInfinitive : NominalizationType
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- Benz2025.instDecidableEqNominalizationType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Benz2025.instReprNominalizationType = { reprPrec := Benz2025.instReprNominalizationType.repr }
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A solution to the particle "structure problem" ([Lud01b]) — how a phrasal particle can end up inside a derived nominal. Ch. 5 argues the three nominalization types favor different solutions, reinforcing "the strange status of particles in the grammar".
- phrasalInput : StructureSolution
- particleAsHead : StructureSolution
- outerAttachment : StructureSolution
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- Benz2025.instDecidableEqStructureSolution x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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- Benz2025.instReprStructureSolution = { reprPrec := Benz2025.instReprStructureSolution.repr }
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The solution each nominalization type favors (§5.2–5.4). Nominalized infinitives take phrasal inputs (even das Durch-den-Wald-Reiten), -ung favors particles-as-heads, and Ge-...-e favors outer attachment ((223)), since its no-internal-argument eventive semantics conflicts with prefix verbs' argument-structural demands.
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Whether the element can attach as a non-phrasal head. Prefixes always do, particles can attach low as heads (§5.3), and RSPs cannot be attached non-phrasally ((205)–(206)).
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The preverbal elements a structure-problem solution accommodates. Phrasal inputs admit everything, particles-as-heads admits the head-attachers, and outer attachment admits the phrasal elements, since prefixes are verbal heads and cannot attach outside a noun.
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The observed Ch. 5 distribution. -ung takes prefixes and particles but not RSPs ((197), (204) *Platt-hämmer-ung). Ge-...-e takes particles ((212)) and a subset of RSPs ((216) das Wach-ge-küss-e, restricted to non-obligatorily-transitive bases) but not prefixes ((218) *Ge-be-such-e, in either affix order). Nominalized infinitives take all three ((193)).
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- Benz2025.peAcceptable Benz2025.NominalizationType.ung Benz2025.PreverbalElement.pfx = true
- Benz2025.peAcceptable Benz2025.NominalizationType.ung Benz2025.PreverbalElement.prt = true
- Benz2025.peAcceptable Benz2025.NominalizationType.ung Benz2025.PreverbalElement.rsp = false
- Benz2025.peAcceptable Benz2025.NominalizationType.ge_e Benz2025.PreverbalElement.pfx = false
- Benz2025.peAcceptable Benz2025.NominalizationType.ge_e Benz2025.PreverbalElement.prt = true
- Benz2025.peAcceptable Benz2025.NominalizationType.ge_e Benz2025.PreverbalElement.rsp = true
- Benz2025.peAcceptable Benz2025.NominalizationType.nomInfinitive x✝ = true
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Each nominalization type admits exactly the elements its structure-problem solution accommodates — the Ch. 5 distribution projects the same head/phrase classification that drives the Ch. 4 paradigm.
Prefixes and RSPs are in complementary distribution across -ung and Ge-...-e, since head attachment and outer attachment make opposite demands.
Particles occur in both -ung and Ge-...-e — the dual attachment options (head or phrase) that constitute the structure problem.
Nominalized infinitives accept all three element types ((193)).
-ung and event structure #
Whether a verb can undergo -ung nominalization, which requires complex ("bi-eventive") change-of-state event structure ([RK10], endorsed at §5.3.1). Over this fragment's entries the bi-eventive verbs are the accomplishments (the simplex deadjectival cases of (199) are not represented).
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- Benz2025.canUngNominalize (some Features.VendlerClass.accomplishment) = true
- Benz2025.canUngNominalize x✝ = false
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In the (198c) minimal pair *Mal-ung vs Be-mal-ung, the prefix supplies the complex change-of-state structure -ung needs, derived here from the fragment entries' Vendler classes.
Simplex activity verbs cannot form -ung nominalizations ((198) *Mal-ung, *Arbeit-ung, *Schieß-ung; the other fragment activities pattern identically).
Prefix and particle verbs with complex event structure form -ung nominalizations ((197) Ein-führ-ung, Ver-bind-ung; Ch. 3 Beobacht-ung).
Fragment grounding #
Transitivity derived from the fragment entry's typed fields.
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- Benz2025.isTransitiveVerb v = (v.complementType == ComplementType.np && !v.unaccusative)
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The stimulus rows' verb_class labels are derivable from the fragment
entries their m_predicate features name, so changing frieren's
unaccusative field or hämmern's complementType would break this theorem
without touching the rows.
brechen (result root) and frieren (property-concept root) yield
opposite canonical v allosemes, connecting the fragment's rootType to
Verbalizer.Alloseme.fromRootType and Verbalizer.Alloseme.introducesEvent.
A result root selects eventive v, which with vacuous n yields brechen's complex event reading.
A property-concept root selects vacuous v, which with entity n yields frieren's simple entity reading. Allosemy leaves the eventive v available too, since the canonical alloseme is a default rather than a constraint.