Deep Semantic Pollution

The paper compares the multiplicative system LKm for classical propositional logic with its fully additive variant LKa. As is well-known, the latter is obtained from the former by absorbing the structural rules through the joint adoption of the generalized axiom and the context-sharing formulation of the logical rules. We show that the very absorption of the structural rules may have the effect of turning LKa into a merely semantic device. We further argue that this, very simple, case-study may be of some interest when considered in the context of the current debate on semantic pollution. As a matter of fact, LKm and LKa are two proof systems that share not only theorems, but also the very syntactic structures they use, though LKa can be collapsed into an appropriate algebraic setting. The subtext to this observation is twofold: (i) to support and further clarify Avron’s notorious position on the topic, and (ii) to point out a language-independent form of semantic pollution that we call ‘deep’.