A Constructive Type-Theoretical Formalism for the Interpretation of Subatomically Sensitive Natural Language Constructions
- Bartosz Więckowski
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The analysis of atomic sentences and their subatomic components poses a special problem for proof-theoretic approaches to natural language semantics, as it is far from clear how their semantics could be explained by means of proofs rather than denotations. The paper develops a proof-theoretic semantics for a fragment of English within a type-theoretical formalism that combines subatomic systems for natural deduction  with constructive (or Martin-Löf) type theory [8, 9] by stating rules for the formation, introduction, elimination and equality of atomic propositions understood as types (or sets) of subatomic proof-objects. The formalism is extended with dependent types to admit an interpretation of non-atomic sentences. The paper concludes with applications to natural language including internally nested proper names, anaphoric pronouns, simple identity sentences, and intensional transitive verbs.
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- A Constructive Type-Theoretical Formalism for the Interpretation of Subatomically Sensitive Natural Language Constructions
Volume 100, Issue 4 , pp 815-853
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- Springer Netherlands
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- Constructive type theory
- Proof-theoretic semantics of natural language
- Subatomic semantics
- Type-theoretical grammar
- Author Affiliations
- 1. Institut für Philosophie, Universität Greifswald, Baderstraße 6–7, 17489, Greifswald, Germany