Reasoning with Ambiguity

Abstract We treat the problem of reasoning with ambiguous propositions. Even though ambiguity is obviously problematic for reasoning, it no less obvious that propositions entail other (both and unambiguous), are entailed by This article gives a formal analysis underlying mechanisms, both from an algebraic logical point view. The main result can be summarized as follows: sound (and complete) requires distinction between equivalence on one congruence side: fact $$\alpha $$ α entails $$\beta β does not imply substituted in all contexts preserving truth. Without this distinction, we will always run into paradoxical results. present (cut-free) sequent calculus $$\mathsf {AL}^{\textit{cf}}$$ AL cf , which conjecture implements complete propositional ambiguity, provide language-theoretic semantics, where letters represent unambiguous meanings concatenation represents ambiguity.