Chains on linearized syntactic objects

A chain is the set of positions of one object. On a copy object, where Internal Merge leaves the mover in place, two positions are in one chain when they hold one term (chainRel, the kernel of termAt), so a chain has a position per occurrence of its term (card_chainRel), and Form Copy's copies are the pairs of its positions in c-command (self_mem_copyRel_iff).

On an object with traces, a lower copy is a trace leaf Vertex.traceOf tok remembering the head of the mover, and the chain of a token lists its pronounced and deleted copies, each standing for the maximal projection of its token under a head function. A token moves when it has a deleted copy, and one bound in situ, as for Pesetsky, has a single copy; a deleted copy above the pronounced one is Huang's covert movement, a pronounced copy between deleted ones Sato and Ngui's partial movement, and a token with two pronounced copies is shared, Citko's Parallel Merge. A copy is linked to the nearest copy whose projection c-commands it, c-command being Reinhart's (RoseTree.CCommands); the locality of links is in Locality/Chain.lean.

Main definitions

• Minimalist.LinearizedSyntacticObject.chainRel: the chains of a copy object.
• Minimalist.tokenList, Minimalist.traceList: the pronounced and the deleted copies.
• occurrences, traces, chain, Moves, IsShared: the copies of a token.
• occurrencesWith: the pronounced copies of the tokens a predicate holds of.
• HasAntecedent, orphanTraces: whether a pronounced copy c-commands a deleted one.
• IsLink, links, chainTop: the links of a chain and its scope position.

Implementation notes

• On an object with traces, positions, not terms, individuate copies: two deleted copies of one token are the same term. Remnant movement carries a deleted copy away from its antecedent, so an externalized object can have orphan traces.

TODO

• The chains of tokens as the contraction of the chains of the copy object of Derivation.replayWithCopies? (Copy/Replay.lean), where no remnant moves.

References

• Marcolli et al. 2025, Mathematical Structure of Syntactic Merge: An Algebraic Model for Generative Linguistics formalized
• Citko 2005, On the nature of Merge: External Merge, Internal Merge, and Parallel Merge
• Pesetsky 1987, Wh-in-situ: Movement and unselective binding
• Huang 1982, Logical Relations in Chinese and the Theory of Grammar
• Sato & Ngui 2017, Wh-questions in Singapore English tell us what about questions with declarative syntax?
• Barker & Pullum 1990, A Theory of Command Relations formalized