Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Type-theoretical grammar
LACL '96 Selected papers from the First International Conference on Logical Aspects of Computational Linguistics
Electronic Notes in Theoretical Computer Science (ENTCS)
Two kinds of procedural semantics for privative modification
JSAI-isAI'09 Proceedings of the 2009 international conference on New frontiers in artificial intelligence
Proof-theoretic semantics for a natural language fragment
MOL'07/09 Proceedings of the 10th and 11th Biennial conference on The mathematics of language
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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 [20] 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.