Describes a collection of related deductive systems that intend to capture the position that no proposition should entail its own negation. Frequently, logics described as connexive enjoy theorems such as Aristotle’s thesis:
or Boethius’ thesis:
Formal accounts of these theses have generally been accompanied by severe restrictions. For example, because axiomatic representations of the inference rule of simplification entail that both and , systems containing Boethius’ thesis are inconsistent with axiomatic forms of this rule. Likewise, contraposition is not admissible in many connexive logics.