Let ⊢ be the ordinary deduction relation of classical first-order logic. We provide an "analytic" subrelation ⊢a of ⊢ which for propositional logic is defined by the usual "containment" criterion Γ ⊢a φ iff Γ⊢φ and Atom ⊆ Atom, whereas for predicate logic, ⊢a is defined by the extended criterion Γ⊢aφ iff Γ⊢aφ and Atom ⊆' Atom, where Atom ⊆' Atom means that every atomic formula occurring in φ "essentially occurs" also in Γ. If Γ, φ are quantifier-free, then the (...) notions "occurs" and "essentially occurs" for atoms between Γ and φ coincide. If ⊢ is formalized by Gentzen's calculus of sequents, then we show that ⊢a is axiomatizable by a proper fragment of analytic inference rules. This is mainly due to cut elimination. By "analytic inference rule " we understand here a rule r such that, if the sequent over the line is analytic, then so is the sequent under the line. We also discuss the notion of semantic relevance as contrasted to the previous syntactic one. We show that when introducing semantic sequents as axioms, i.e. when extending the pure logical axioms and rules by mathematical ones, the property of syntactic relevance is lost, since cut elimination no longer holds. We conclude that no purely syntactic notion of analytic deduction can ever replace successfully the complex semantico-syntactic deduction we already possess. (shrink)

This paper develops a semantical model - theoretic account of (logical) content complementing the syntactically specified account of content developed in "A New Theory of Content I", JPL 23: 596-620, 1994. Proofs of Completeness are given for both propositional and quantificational languages (without identity). Means for handling a quantificational language with identity are also explored. Finally, this new notion of content is compared, in respect of both logical properties and philosophical applications, to alternative partitions of the standard consequence class relation (...) proposed by Stelzner, Schurz and Wiengartner. (shrink)