A Constructive Type-Theoretical Formalism for the Interpretation of Subatomically Sensitive Natural Language Constructions
Studia Logica 100 (4):815-853 (2012)
AbstractThe 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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Citations of this work
Subatomic Natural Deduction for a Naturalistic First-Order Language with Non-Primitive Identity.Bartosz Więckowski - 2016 - Journal of Logic, Language and Information 25 (2):215-268.
Compositionality and the Prospect of a Pluralistic Semantic Theory.Adam C. Podlaskowski - 2019 - Australasian Journal of Philosophy 97 (2):325-339.
References found in this work
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Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.
Proof-Theoretic Semantics for a Natural Language Fragment.Nissim Francez & Roy Dyckhoff - 2010 - Linguistics and Philosophy 33 (6):447-477.
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