The paper introduces a proof-theoretic semantics for adjectival modification 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. (shrink)

In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has undesirable (...) results and that it is ill-supported by the arguments brought in its favour. (shrink)

A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint.