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Linglib.Syntax.ConstructionGrammar.Basic

Constructions and the constructicon #

A construction is a learned pairing of a form and a meaning ([Gol06]), the basic unit of grammatical knowledge in CxG. The form side is a TypedForm: a sequence of Slots, each fixing a lexeme, opening a category, or admitting any phrase, with a construction's Specificity derived from its slot structure rather than stipulated.

Main definitions #

How specified a construction's form side is: [Gol03]'s degree-of-abstraction continuum, discretized as in [GS25]'s Table 8.

  • lexicallySpecified : Specificity

    Every slot lexically filled: veggie-wrap, must-read.

  • partiallyOpen : Specificity

    Fixed and open slots mixed: N-wrap, a simple ⟨PAL⟩.

  • fullyAbstract : Specificity

    Every slot open: [N⁰ N⁰ N⁰], [N′ PAL⁰ N].

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      Mode of information transfer in an inheritance link, orthogonal to the link's semantic relation ([Gol95] §3.3.1, p. 73–74).

      • normal : InheritanceMode

        The child inherits defaults from its parents but may override them — the only mode [Gol95] uses.

      • complete : InheritanceMode

        All information is inherited strictly, with no conflicts allowed — the mode "normally assumed in unification-based grammars" (p. 74).

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          The semantic relation an inheritance link records: [Gol95]'s four major link types (§3.3.2, p. 75).

          • polysemy : LinkType

            I_P: relates a construction's central sense to an extension, which inherits the syntax but differs in meaning (the six senses of the ditransitive, pp. 75–77).

          • metaphorical : LinkType

            I_M: source and target related by a systematic metaphor (caused-motion → resultative via motion→change, p. 81).

          • subpart : LinkType

            I_S: the child is a proper subpart of the parent (intransitive motion inside caused-motion, p. 78).

          • instance : LinkType

            I_I: the child is a more fully specified version of the parent (drive-crazy as an instance of the resultative, p. 79).

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              X-bar level of a syntactic position or constructional output.

              • zero : BarLevel

                X⁰, a word-level position.

              • bar : BarLevel

                X′, an intermediate projection.

              • phrase : BarLevel

                XP, a full phrase.

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                  Typed slots #

                  Slot content comes at [Dun25]'s three representation levels — LEX (a fixed lexeme), SYN (any word of a category), SEM (a semantic constraint) — plus [KF99]'s headed phrases, grammatical functions, coreference indices, and slot constraints.

                  inductive ConstructionGrammar.SlotFiller (Lex : Type u_1) :
                  Type u_1

                  A slot's filler: the representation level of slot content.

                  Parameterized over Lex (the lexeme type) so the same representation works for strings, morphemes, or phonological forms.

                  • fixed {Lex : Type u_1} : LexSlotFiller Lex

                    A specific word form (LEX level): fixed "must"

                  • open_ {Lex : Type u_1} : UD.UPOSSlotFiller Lex

                    Any word of a given POS category (SYN level): open_ .VERB

                  • headed {Lex : Type u_1} : LexUD.UPOSSlotFiller Lex

                    A phrase headed by a specific lexeme ([KF99]): headed "doing" .VERB is a VP headed by doing. LEX-level — the head lexeme is fixed even though the phrase is open.

                  • semantic {Lex : Type u_1} : StringSlotFiller Lex

                    A semantically constrained slot ([Dun25], SEM level): semantic "animate" is any expression denoting an animate.

                  • phrasal {Lex : Type u_1} : SlotFiller Lex

                    Any phrase, with no fixed head and no category restriction on its internal structure — the filler of a phrasal-compound or PAL slot (the ⟨phrase⟩ node of [GS25]'s Figure 5).

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                    def ConstructionGrammar.instDecidableEqSlotFiller.decEq {Lex✝ : Type u_1} [DecidableEq Lex✝] (x✝ x✝¹ : SlotFiller Lex✝) :
                    Decidable (x✝ = x✝¹)
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                      def ConstructionGrammar.instReprSlotFiller.repr {Lex✝ : Type u_1} [Repr Lex✝] :
                      SlotFiller Lex✝Std.Format
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                        instance ConstructionGrammar.instReprSlotFiller {Lex✝ : Type u_1} [Repr Lex✝] :
                        Repr (SlotFiller Lex✝)
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                        Whether a slot is open — not lexically anchored: open_, semantic, and phrasal fillers count as open; fixed and headed do not, the latter fixing its head lexeme even though the phrase is open.

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                          Grammatical function of a valence member ([KF99], Figure 12), distinct from semantic role: a subject can be an agent, a theme, or an experiencer.

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                              Referential index for cross-slot coreference constraints. Slots sharing a RefIndex have unified semantic values ([KF99]'s #1, #2).

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                                Syntactic constraint on a slot ([KF99], Figure 12).

                                • locMinus : SlotConstraint

                                  [loc -]: must occur left-isolated, not VP-internal.

                                • negMinus : SlotConstraint

                                  [neg -]: cannot be negated.

                                • refEmpty : SlotConstraint

                                  [ref ∅]: nonreferential — no variable-binding function.

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                                    structure ConstructionGrammar.Slot (Lex : Type u_1) :
                                    Type u_1

                                    A slot in a construction's form: filler content, headedness, and the bar level of the position itself. level := none leaves the position's bar level unspecified; slots sharing a refIdx are co-indexed, the hook by which a typed meaning pole refers to slots.

                                    • filler : SlotFiller Lex

                                      What fills this slot

                                    • isHead : Bool

                                      Whether this slot is the head of the construction

                                    • level : Option BarLevel

                                      Bar level of the position (some .zero = a word-level slot)

                                    • gf : Option GramFunction

                                      Grammatical function (subj, comp, obj, pred) — [KF99]

                                    • refIdx : Option RefIndex

                                      Coreference index: slots sharing an index have unified semantics

                                    • constraints : List SlotConstraint

                                      Syntactic constraints on this slot ([loc -], [neg -], [ref ∅])

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                                      def ConstructionGrammar.instDecidableEqSlot.decEq {Lex✝ : Type u_1} [DecidableEq Lex✝] (x✝ x✝¹ : Slot Lex✝) :
                                      Decidable (x✝ = x✝¹)
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                                        instance ConstructionGrammar.instDecidableEqSlot {Lex✝ : Type u_1} [DecidableEq Lex✝] :
                                        DecidableEq (Slot Lex✝)
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                                        def ConstructionGrammar.instReprSlot.repr {Lex✝ : Type u_1} [Repr Lex✝] :
                                        Slot Lex✝Std.Format
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                                          instance ConstructionGrammar.instReprSlot {Lex✝ : Type u_1} [Repr Lex✝] :
                                          Repr (Slot Lex✝)
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                                          abbrev ConstructionGrammar.TypedForm (Lex : Type u_1) :
                                          Type u_1

                                          A typed form: the form side of a construction as a sequence of slots.

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                                            A phrase in a word-level slot: phrasal filler, zero-level position — the defining configuration of phrasal compounds and the PAL construction ([GS25]), and the cell that lexical-integrity hypotheses rule out.

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                                              Derived specificity #

                                              The specificity of a form: fullyAbstract when every slot is open (vacuously so for the empty form), lexicallySpecified when none is, and partiallyOpen otherwise.

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                                                Some slot in the form bears the constraint c.

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                                                  def ConstructionGrammar.refGroupCount {Lex : Type u_1} (form : TypedForm Lex) :

                                                  Count of distinct coreference groups in a form.

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                                                    Characterization lemmas #

                                                    A form is fully abstract exactly when every slot is open (vacuously so for the empty form).

                                                    theorem ConstructionGrammar.derivedSpecificity_eq_lexicallySpecified_iff {Lex : Type u_1} (form : TypedForm Lex) :
                                                    derivedSpecificity form = Specificity.lexicallySpecified form [] sform, s.filler.isOpen = false

                                                    A form is lexically specified exactly when it is nonempty and no slot is open.

                                                    Constructions and the network #

                                                    structure ConstructionGrammar.Construction (Sem : Type u_1) :
                                                    Type u_1

                                                    A construction: a learned pairing of form and meaning. The meaning pole is typed by the domain that owns the construction — a composition rule, a MeaningComponents contribution, a presupposition — with Unit for a purely formal record or a defective, form-only construction.

                                                    • name : String
                                                    • form : TypedForm String
                                                    • meaning : Sem

                                                      The meaning pole.

                                                    • pragmaticPoint : Bool

                                                      Whether the construction carries a conventional pragmatic point ([FKOC88] §1.1.4).

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                                                      def ConstructionGrammar.instDecidableEqConstruction.decEq {Sem✝ : Type u_1} [DecidableEq Sem✝] (x✝ x✝¹ : Construction Sem✝) :
                                                      Decidable (x✝ = x✝¹)
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                                                        def ConstructionGrammar.instReprConstruction.repr {Sem✝ : Type u_1} [Repr Sem✝] :
                                                        Construction Sem✝Std.Format
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                                                          instance ConstructionGrammar.instReprConstruction {Sem✝ : Type u_1} [Repr Sem✝] :
                                                          Repr (Construction Sem✝)
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                                                          A construction's specificity, derived from its slot structure.

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                                                            def ConstructionGrammar.Construction.map {Sem : Type u_1} {Sem' : Type u_2} (f : SemSem') (c : Construction Sem) :

                                                            Reinterpret the meaning pole along f, keeping the form.

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                                                                def ConstructionGrammar.instDecidableEqInheritanceLink.decEq (x✝ x✝¹ : InheritanceLink) :
                                                                Decidable (x✝ = x✝¹)
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                                                                  structure ConstructionGrammar.Constructicon (Sem : Type u_2) :
                                                                  Type u_2

                                                                  A constructicon: a network of constructions connected by inheritance links.

                                                                  • constructions : List (Construction Sem)

                                                                    The inventory of constructions.

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                                                                    def ConstructionGrammar.instReprConstructicon.repr {Sem✝ : Type u_2} [Repr Sem✝] :
                                                                    Constructicon Sem✝Std.Format
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                                                                      instance ConstructionGrammar.instReprConstructicon {Sem✝ : Type u_2} [Repr Sem✝] :
                                                                      Repr (Constructicon Sem✝)
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