# A Proof-Theoretic Semantics for Adjectival Modification

## Abstract

The paper introduces a proof-theoretic semantics (PTS) for adjectival modification (adjective–noun combination) as an alternative to the traditional model-theoretic semantics basing meaning on truth-conditions. The paper considers the proof-theoretic meaning of modification by means of the three traditional adjective classes: intersective, subsective and privative. It does so by introducing a meaning-conferring natural-deduction proof system for such modification. The PTS theory of meaning is not polluted by ontological commitments, for example, a scale for beauty and a yardstick for being beautiful. It only uses syntactic artefacts of the proof language. The paper also defines, by suitable rules, iterated modification, shedding light on the relationship between iteration and adjectival classes. Modification via coordinated adjectives is covered too. An appendix delineates briefly the main ingredients of PTS.

## Keywords

Proof-theoretic semantics Adjectival modification Intersective, subsective and privative adjectives Iterated adjectival modification Natural-deduction## Notes

### Acknowledgements

I thank Itamar Francez and Chris Kennedy for various discussions and clarifications about the topics of the paper. I thank Ivo Pezlar for spotting and correcting some errors in an earlier version of the manuscript.

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