We define a notion of formula schema handling arithmetic parameters, indexed propositional variables (e.g. Pi) and iterated conjunctions/disjunctions (e.g. Vn i=1 Pi, where n is a...
Vincent Aravantinos, Ricardo Caferra, Nicolas Pelt...
Abstract. By introducing a parallel extension rule that is aware of independence of the introduced extension variables, a calculus for quantified propositional logic is obtained w...
We consider a classical (propositional) version, CBI, of O'Hearn and Pym's logic of bunched implications (BI) from a model- and prooftheoretic perspective. We present a c...
In 1973, Parikh proved a speed-up theorem conjectured by G¨odel 37 years before: there exist arithmetical formulæ that are provable in first order arithmetic, but whose shorter ...