Anderson (2006): Modern Grammars of Case @cite{anderson-jm-2006}

@cite{anderson-jm-2006} "Modern Grammars of Case: A Retrospective" (OUP) develops localist case grammar (LCG), where all semantic relations decompose into combinations of three first-order case features: absolutive (abs), source/ergative (src), and locative (loc).

Anderson's system (Ch. 6, eq. 11)

The four simple case relations are:

• abs (∅): the semantically empty base — holistic participant
• source/erg ({src}): first-order source — agent, causer
• loc ({loc}): place/location
• abl ({loc, src²}): second-order source subordinated to loc

Arguments bear COMBINATIONS of first-order features to define complex roles (§6.2–6.3):

• Agent = src alone ("Bill read the book", eq. 39a)
• Experiencer = src + loc ("Bill knew the answer", eq. 39h)
• Contactive/patient = abs + loc (eq. 22)
• Self-mover = abs + src ("Bill flew to China", eq. 39c)

Subject selection (eq. 38')

Anderson directly states: erg > abs. The argument with first-order source becomes subject. If no argument has source, the absolutive becomes subject. The hierarchy is NOT derived from feature cardinality.

Subject formation (eq. 40): absolutive ⇒ absolutive{erg}. When an absolutive is selected as subject, it acquires the erg feature.

Improvement over the two-feature model

Our earlier formalization incorrectly used only two features (abs, erg) and collapsed experiencer with agent as {abs, erg}. Anderson's actual system DISTINGUISHES them: agent = {src}, experiencer = {src, loc}. Both have src (so both can be subjects), but they differ in the loc feature. The third feature (loc) is essential to Anderson's theory.

Costs

The three-feature system collapses some Fragment distinctions:

• {src} collapses agent, source, instrument, stimulus
• {abs} collapses patient and theme But it correctly distinguishes experiencer from agent (unlike the two-feature simplification).

def AndersonJM2006.CaseRelation.canonicalTheta (cr : Core.CaseRelation) : Option ThetaRole

Anderson's canonical mapping from case-feature bundles to theta roles.

The three-feature system makes finer distinctions than the old two-feature version: experiencer ({src, loc}) is now SEPARATE from agent ({src}).

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def AndersonJM2006.thetaToCaseRelation : ThetaRole → Core.CaseRelation

Reverse mapping: from the Fragment's 8-role inventory to Anderson's case relations.

Key differences from the old two-feature mapping:

• experiencer → srcLoc (was absErg, same as agent)
• agent → ergative (was absErg, conflated with experiencer)
• goal → locative (spatial goal = loc{goal})

The many-to-one collapses that remain:

• agent, source, instrument, stimulus → ergative {src}
• patient, theme → absolutive {abs}

Equations

• AndersonJM2006.thetaToCaseRelation ThetaRole.agent = Core.CaseRelation.ergative
• AndersonJM2006.thetaToCaseRelation ThetaRole.experiencer = Core.CaseRelation.srcLoc
• AndersonJM2006.thetaToCaseRelation ThetaRole.patient = Core.CaseRelation.absolutive
• AndersonJM2006.thetaToCaseRelation ThetaRole.theme = Core.CaseRelation.absolutive
• AndersonJM2006.thetaToCaseRelation ThetaRole.goal = Core.CaseRelation.locative
• AndersonJM2006.thetaToCaseRelation ThetaRole.source = Core.CaseRelation.ergative
• AndersonJM2006.thetaToCaseRelation ThetaRole.instrument = Core.CaseRelation.ergative
• AndersonJM2006.thetaToCaseRelation ThetaRole.stimulus = Core.CaseRelation.ergative

Anderson's derivations from Chapter 6 (eq. 39) show how the three-feature system assigns case relations to English verb arguments. For each verb, the subject is the argument with the highest subjectRank.

theorem AndersonJM2006.read_derivation : have agent := Core.CaseRelation.ergative; have patient := Core.CaseRelation.absolutive; agent.subjectRank > patient.subjectRank

Eq. 39a: "Bill read the book" — erg + abs. Agent (src, rank 2) + patient (abs, rank 1). Agent is subject.

theorem AndersonJM2006.fell_derivation : have theme := Core.CaseRelation.absolutive; have goal := Core.CaseRelation.locative; theme.subjectRank > goal.subjectRank

Eq. 39b: "Bill fell to the ground" — abs + loc{goal}. Theme (abs, rank 1) + locative goal (loc, rank 0). Theme is subject.

theorem AndersonJM2006.flew_derivation : have selfMover := Core.CaseRelation.srcAbs; have goal := Core.CaseRelation.locative; selfMover.subjectRank > goal.subjectRank

Eq. 39c: "Bill flew to China" — abs,erg + loc{goal}. Self-mover (abs+src, rank 2) + goal (loc, rank 0). Self-mover is subject.

theorem AndersonJM2006.knew_derivation : have experiencer := Core.CaseRelation.srcLoc; have stimulus := Core.CaseRelation.absolutive; experiencer.subjectRank > stimulus.subjectRank

Eq. 39h: "Bill knew the answer" — E + abs = erg,loc + abs. Experiencer (src+loc, rank 2) + stimulus (abs, rank 1). Experiencer is subject because it has src.

theorem AndersonJM2006.experiencer_agent_distinct_same_rank : Core.CaseRelation.srcLoc ≠ Core.CaseRelation.ergative ∧ Core.CaseRelation.srcLoc.subjectRank = Core.CaseRelation.ergative.subjectRank

Anderson's key distinction: experiencer ≠ agent in feature content, but BOTH outrank absolutive. Agent = {src}, experiencer = {src, loc}. The loc feature distinguishes them without affecting subject selection.

def AndersonJM2006.toScenario (v : Semantics.Lexical.VerbCore) : Core.Scenario

Derive Anderson's Scenario from a Fragment verb entry's derived roles.

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def AndersonJM2006.andersonLinking : Interfaces.SyntaxSemantics.LinkingTheory Core.Scenario Unit

Anderson's case grammar as a LinkingTheory (@cite{anderson-jm-2006}). The verb type is Scenario, the context is Unit (lexicalist: linking is derived entirely from case-relation rank, no structural input).

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def AndersonJM2006.andersonPredictedSubjectTheta (v : Semantics.Lexical.VerbCore) : Option ThetaRole

Anderson's predicted subject theta role for a verb entry.

Equations

• AndersonJM2006.andersonPredictedSubjectTheta v = AndersonJM2006.andersonLinking.predict (AndersonJM2006.toScenario v) () Interfaces.SyntaxSemantics.ArgPosition.subject

theorem AndersonJM2006.anderson_canonical_linking : andersonLinking.predict Core.Scenario.transitive () Interfaces.SyntaxSemantics.ArgPosition.subject = some ThetaRole.agent ∧ andersonLinking.predict Core.Scenario.transitive () Interfaces.SyntaxSemantics.ArgPosition.directObject = some ThetaRole.patient ∧ andersonLinking.predict Core.Scenario.unergative () Interfaces.SyntaxSemantics.ArgPosition.subject = some ThetaRole.agent ∧ andersonLinking.predict Core.Scenario.unaccusative () Interfaces.SyntaxSemantics.ArgPosition.subject = some ThetaRole.patient ∧ andersonLinking.predict Core.Scenario.experiencer () Interfaces.SyntaxSemantics.ArgPosition.subject = some ThetaRole.experiencer ∧ andersonLinking.predict Core.Scenario.experiencer () Interfaces.SyntaxSemantics.ArgPosition.directObject = some ThetaRole.patient

Anderson correctly predicts argument linking for the canonical verb types, including experiencer (which the old two-feature model collapsed with agent).

theorem AndersonJM2006.experiencer_correctly_predicted : andersonLinking.predict Core.Scenario.experiencer () Interfaces.SyntaxSemantics.ArgPosition.subject = some ThetaRole.experiencer

The three-feature system correctly predicts experiencer as subject, which the old two-feature system collapsed into agent.

theorem AndersonJM2006.anderson_linking_accuracy : (List.filter (fun (v : Fragments.English.Predicates.Verbal.VerbEntry) => (andersonPredictedSubjectTheta v.toVerbCore).isSome == (AndersonJM2006.subjectRole✝ v.toVerbCore).isSome) Fragments.English.Predicates.Verbal.allVerbs).length = Fragments.English.Predicates.Verbal.allVerbs.length

Anderson correctly predicts which argument becomes subject for every verb in the Fragment: the prediction is defined iff the verb has a derived subject role.

The three-feature system collapses fewer roles than the old two-feature model. Experiencer is now correctly distinguished from agent. The remaining collapses are:

• {src} collapses agent with source, instrument, and stimulus
• {abs} collapses patient with theme

theorem AndersonJM2006.patient_theme_collapse : thetaToCaseRelation ThetaRole.patient = thetaToCaseRelation ThetaRole.theme ∧ ThetaRole.patient.canonicalProfile.pPatientScore = 3 ∧ ThetaRole.theme.canonicalProfile.pPatientScore = 1

Patient and theme both map to {abs}, but @cite{dowty-1991} distinguishes them: patient has 3 P-Patient entailments, theme has only 1.

theorem AndersonJM2006.src_collapses : thetaToCaseRelation ThetaRole.agent = thetaToCaseRelation ThetaRole.source ∧ thetaToCaseRelation ThetaRole.agent = thetaToCaseRelation ThetaRole.instrument ∧ thetaToCaseRelation ThetaRole.agent = thetaToCaseRelation ThetaRole.stimulus

Agent, source, instrument, and stimulus all map to {src}.

theorem AndersonJM2006.experiencer_distinguished : thetaToCaseRelation ThetaRole.agent ≠ thetaToCaseRelation ThetaRole.experiencer

The three-feature system correctly separates experiencer from agent. This is the key improvement over the old two-feature formalization.

theorem AndersonJM2006.experiencer_verbs_correct : (List.filter (fun (v : Fragments.English.Predicates.Verbal.VerbEntry) => decide ((AndersonJM2006.subjectRole✝ v.toVerbCore == some ThetaRole.experiencer) = true ∧ (andersonPredictedSubjectTheta v.toVerbCore == some ThetaRole.experiencer) = true)) Fragments.English.Predicates.Verbal.allVerbs).length = (List.filter (fun (v : Fragments.English.Predicates.Verbal.VerbEntry) => AndersonJM2006.subjectRole✝ v.toVerbCore == some ThetaRole.experiencer) Fragments.English.Predicates.Verbal.allVerbs).length

Experiencer subject verbs are now correctly predicted as experiencer, not collapsed into agent (for verbs with entailment profiles).

theorem AndersonJM2006.anderson_blake_concordant : Core.Case.hierarchyRank UD.Case.nom ≥ Core.Case.hierarchyRank UD.Case.acc ∧ Core.CaseRelation.srcAbs.subjectRank > Core.CaseRelation.absolutive.subjectRank ∧ Core.Case.hierarchyRank UD.Case.nom = Core.Case.hierarchyRank UD.Case.acc ∧ Core.CaseRelation.srcAbs.subjectRank ≠ Core.CaseRelation.absolutive.subjectRank

Anderson and Blake are concordant on the core case ordering. Blake: NOM(6) ≥ ACC(6). Anderson: NOM/src+abs outranks ACC/abs (subjectRank 2 > 1). Both are inverse to Caha's containment hierarchy.

def AndersonJM2006.HasSpatialLoc : Core.Case → Prop

Does a morphological case carry the spatial locative feature? ABL, LOC both map to {loc} — they share the locative feature because they involve spatial location.

Equations

• AndersonJM2006.HasSpatialLoc UD.Case.Abl = True
• AndersonJM2006.HasSpatialLoc UD.Case.Loc = True
• AndersonJM2006.HasSpatialLoc x✝ = False

@[implicit_reducible]

instance AndersonJM2006.instDecidablePredCaseHasSpatialLoc : DecidablePred HasSpatialLoc

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theorem AndersonJM2006.spatial_cases_are_locative : Core.Case.toCaseRelation UD.Case.abl = some Core.CaseRelation.locative ∧ Core.Case.toCaseRelation UD.Case.loc = some Core.CaseRelation.locative

ABL and LOC both map to Anderson's locative case relation.

theorem AndersonJM2006.inst_is_ergative : Core.Case.toCaseRelation UD.Case.inst = some Core.CaseRelation.ergative

INST maps to {src} (source of force), not {loc}. Anderson argues that instrumental is the same semantic relation as agent: both are sources of action.

theorem AndersonJM2006.abl_loc_share_feature : Core.Case.toCaseRelation UD.Case.abl = Core.Case.toCaseRelation UD.Case.loc

ABL and LOC share a case relation AND have an extension path between them. Anderson's explanation: a case marker conditioned on {loc} is polysemous across spatial functions.

theorem AndersonJM2006.alignment_is_labeling : Core.Case.toCaseRelation UD.Case.nom = Core.Case.toCaseRelation UD.Case.erg ∧ Core.Case.toCaseRelation UD.Case.acc = Core.Case.toCaseRelation UD.Case.abs ∧ Core.Case.toCaseRelation UD.Case.nom ≠ Core.Case.toCaseRelation UD.Case.acc

Accusative and ergative alignment are different morphological labels for the same two case relations: NOM = ERG = src+abs, ACC = ABS = abs. The case relations are identical; alignment is labeling.

theorem AndersonJM2006.anderson_dowty_transitive_agree : CaseRelation.canonicalTheta Core.CaseRelation.ergative = some ThetaRole.agent ∧ CaseRelation.canonicalTheta Core.CaseRelation.absolutive = some ThetaRole.patient ∧ Semantics.ArgumentStructure.EntailmentProfile.OutranksForSubject ThetaRole.agent.canonicalProfile ThetaRole.patient.canonicalProfile

Anderson and Dowty agree on transitive linking despite completely different primitives (features vs entailment profiles).

theorem AndersonJM2006.anderson_dowty_experiencer_agree : thetaToCaseRelation ThetaRole.agent ≠ thetaToCaseRelation ThetaRole.experiencer ∧ ThetaRole.agent.canonicalProfile.pAgentScore > ThetaRole.experiencer.canonicalProfile.pAgentScore

The three-feature system improves on the old two-feature version for the experiencer case: Anderson distinguishes experiencer from agent (via loc), as does Dowty (different P-Agent entailment count).