---
tag: NQFYY76BSM
kind: concept
name: Connexive logic
aliases: [aristotles-thesis, boethiuss-thesis, connexive-implication]
sources:
  - wikipedia: en:12859904@r1339752880
    locator: Connexive logic
    note: adopted
    mention: wikipedia://en/12859904
    sections: [Summary]
same_as:
  wikidata: Q5161806
  wikipedia: Connexive logic
inventory: [Z4XTBHMCSS]
---

## Summary

**Connexive logic** is a class of non-classical logics designed to exclude the paradoxes of material implication. The characteristic that separates connexive logic from other non-classical logics is its acceptance of **Aristotle's thesis**, i.e. the formula,

$$\lnot ( \lnot p \rightarrow p )$$

as a logical truth. Aristotle's thesis asserts that no statement follows from its own denial. Stronger connexive logics also accept **Boethius' thesis**,

$$(p \rightarrow q) \rightarrow \lnot(p \rightarrow \lnot q)$$

which states that if a statement implies one thing, it does not imply its opposite.