Logic Colloquium 2009, Sofia

– p.1/20Derivable and admissible rules Consider a propositional logic L, defined by a finitary consequence relation ⊢L closed under substitution. A rule ̺ = ϕ1,.,ϕk ψ is derivable in L, if ϕ1,.,ϕk ⊢L ψ, admissible in L, if the set of theorems of L is closed under ̺: for every substitution σ, if L proves all σϕi, then it proves σψ. (We write ϕ1,.,ϕk| ∼ L ψ.) Typical non-classical logics admit some nonderivable rules. Logic Colloquium 2009, Sofia – p.2/20Properties of admissible rules Questions about admissibility: decidability semantic characterization description of a basis Well-understood for some superintuitionistic and modal