Czech Determiners

@cite{giannakidou-1998} @cite{stankova-2025} @cite{zeijlstra-2004}

Polarity-sensitive determiners central to Staňková's (2026) three-way negation diagnostic. Czech lacks articles (ArticleType.none_), so the NCI/PPI contrast on determiners is the primary scope diagnostic for negation position.

Key items

• žádný 'no/any' — Negative Concord Item (NCI), licensed only by inner negation
• nějaký 'some' — Positive Polarity Item (PPI), must outscope negation
• každý 'every' — universal, not polarity-sensitive

Cross-linguistic connections

• The žádný/nějaký contrast mirrors English any (NPI) vs some (PPI), but Czech žádný is an NCI requiring Agree with ¬, not just DE licensing.
• Bridges to Phenomena.Negation.CzechThreeWayNeg.Diagnostic for per-position compatibility.

inductive Fragments.Czech.Determiners.PolarityType : Type

Polarity sensitivity type for Czech determiners.

• nci : PolarityType

  Negative Concord Item: requires Agree with ¬. Stricter than NPI — needs structural relation, not just DE.

• ppi : PolarityType

  Positive Polarity Item: must outscope negation. Blocked in the immediate scope of ¬.

• neutral : PolarityType

  Not polarity-sensitive.

instance Fragments.Czech.Determiners.instDecidableEqPolarityType : DecidableEq PolarityType

Equations

• Fragments.Czech.Determiners.instDecidableEqPolarityType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Fragments.Czech.Determiners.instBEqPolarityType.beq : PolarityType → PolarityType → Bool

Equations

• Fragments.Czech.Determiners.instBEqPolarityType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Fragments.Czech.Determiners.instBEqPolarityType : BEq PolarityType

Equations

• Fragments.Czech.Determiners.instBEqPolarityType = { beq := Fragments.Czech.Determiners.instBEqPolarityType.beq }

instance Fragments.Czech.Determiners.instReprPolarityType : Repr PolarityType

Equations

• Fragments.Czech.Determiners.instReprPolarityType = { reprPrec := Fragments.Czech.Determiners.instReprPolarityType.repr }

def Fragments.Czech.Determiners.instReprPolarityType.repr : PolarityType → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

structure Fragments.Czech.Determiners.DetEntry : Type

A Czech determiner entry with polarity and morphological properties.

• form : String

  Surface form

• gloss : String

  Gloss

• polarityType : PolarityType

  Polarity sensitivity

• diagnostic : Option Semantics.Negation.CzechNegation.Diagnostic

  Which diagnostic from Staňková Table 1 this item tests

• requiresNegLicensing : Bool

  Requires licensing by ¬ (NCIs only)

• mustOutscopeNeg : Bool

  Must outscope ¬ (PPIs only)

• allowsMass : Bool

  Can be used with mass nouns

instance Fragments.Czech.Determiners.instReprDetEntry : Repr DetEntry

Equations

• Fragments.Czech.Determiners.instReprDetEntry = { reprPrec := Fragments.Czech.Determiners.instReprDetEntry.repr }

def Fragments.Czech.Determiners.instReprDetEntry.repr : DetEntry → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Fragments.Czech.Determiners.instBEqDetEntry : BEq DetEntry

Equations

• Fragments.Czech.Determiners.instBEqDetEntry = { beq := Fragments.Czech.Determiners.instBEqDetEntry.beq }

def Fragments.Czech.Determiners.instBEqDetEntry.beq : DetEntry → DetEntry → Bool

Equations

• One or more equations did not get rendered due to their size.
• Fragments.Czech.Determiners.instBEqDetEntry.beq x✝¹ x✝ = false

def Fragments.Czech.Determiners.zadny : DetEntry

žádný 'no, any (NCI)' — the prototypical Czech NCI.

Paradigm: žádný/žádná/žádné (masc/fem/neut), declined for case/number. Requires licensing by ¬ via Agree at LF. Only licensed under inner negation (TP-level ¬), where the Agree relation holds between ne- and žádný. Medial and outer negation are too high.

Equations

• One or more equations did not get rendered due to their size.

def Fragments.Czech.Determiners.nejaky : DetEntry

nějaký 'some (PPI)' — the prototypical Czech PPI determiner.

Paradigm: nějaký/nějaká/nějaké (masc/fem/neut), declined for case/number. Must outscope negation — compatible with medial and outer negation (where ne- doesn't have narrow scope over the DP), but incompatible with inner negation (where ne- c-commands and outscopes the PPI).

Equations

• One or more equations did not get rendered due to their size.

def Fragments.Czech.Determiners.kazdy : DetEntry

každý 'every, each' — universal, not polarity-sensitive.

Compatible with all negation positions. Not a diagnostic for Staňková's three-way distinction.

Equations

• Fragments.Czech.Determiners.kazdy = { form := "každý", gloss := "every", polarityType := Fragments.Czech.Determiners.PolarityType.neutral }

def Fragments.Czech.Determiners.nektery : DetEntry

některý 'some (partitive), certain' — existential, weakly PPI.

Similar to stressed English "some". Not as restricted as nějaký in the scope of negation.

Equations

• Fragments.Czech.Determiners.nektery = { form := "některý", gloss := "some.PART", polarityType := Fragments.Czech.Determiners.PolarityType.ppi, mustOutscopeNeg := true }

def Fragments.Czech.Determiners.allDeterminers : List DetEntry

Equations

• Fragments.Czech.Determiners.allDeterminers = [Fragments.Czech.Determiners.zadny, Fragments.Czech.Determiners.nejaky, Fragments.Czech.Determiners.kazdy, Fragments.Czech.Determiners.nektery]

def Fragments.Czech.Determiners.lookup (form : String) : Option DetEntry

Equations

• Fragments.Czech.Determiners.lookup form = List.find? (fun (d : Fragments.Czech.Determiners.DetEntry) => d.form == form) Fragments.Czech.Determiners.allDeterminers

def Fragments.Czech.Determiners.DetEntry.isNCI (d : DetEntry) : Bool

Is the determiner a Negative Concord Item?

Equations

• d.isNCI = (d.polarityType == Fragments.Czech.Determiners.PolarityType.nci)

def Fragments.Czech.Determiners.DetEntry.isPPI (d : DetEntry) : Bool

Is the determiner a Positive Polarity Item?

Equations

• d.isPPI = (d.polarityType == Fragments.Czech.Determiners.PolarityType.ppi)

def Fragments.Czech.Determiners.compatibleWith (d : DetEntry) (pos : Semantics.Negation.CzechNegation.NegPosition) : Bool

Whether a determiner is compatible with a given negation position, derived from the licenses function in CzechThreeWayNeg.

Equations

• Fragments.Czech.Determiners.compatibleWith d pos = match d.diagnostic with | some diag => Semantics.Negation.CzechNegation.licenses pos diag | none => true

theorem Fragments.Czech.Determiners.zadny_inner : compatibleWith zadny Semantics.Negation.CzechNegation.NegPosition.inner = true

theorem Fragments.Czech.Determiners.zadny_medial : compatibleWith zadny Semantics.Negation.CzechNegation.NegPosition.medial = false

theorem Fragments.Czech.Determiners.zadny_outer : compatibleWith zadny Semantics.Negation.CzechNegation.NegPosition.outer = false

theorem Fragments.Czech.Determiners.nejaky_inner : compatibleWith nejaky Semantics.Negation.CzechNegation.NegPosition.inner = false

theorem Fragments.Czech.Determiners.nejaky_medial : compatibleWith nejaky Semantics.Negation.CzechNegation.NegPosition.medial = true

theorem Fragments.Czech.Determiners.nejaky_outer : compatibleWith nejaky Semantics.Negation.CzechNegation.NegPosition.outer = true

theorem Fragments.Czech.Determiners.zadny_nejaky_complementary (pos : Semantics.Negation.CzechNegation.NegPosition) : compatibleWith zadny pos = !compatibleWith nejaky pos

žádný and nějaký have complementary distributions in negated PQs: exactly the positions where žádný is licensed, nějaký is blocked, and vice versa. This is the core diagnostic for distinguishing inner from non-inner negation.

theorem Fragments.Czech.Determiners.nci_ppi_identifies_inner (pos : Semantics.Negation.CzechNegation.NegPosition) : compatibleWith zadny pos = true ∧ compatibleWith nejaky pos = false → pos = Semantics.Negation.CzechNegation.NegPosition.inner

The NCI/PPI contrast uniquely identifies inner negation: inner is the only position where žádný is OK and nějaký is blocked.