Using a graph representation of classical logic, the paper shows that the liar or Yablo pattern occurs in every semantic paradox. The core graph theoretic result generalizes theorem of Richardson, showing solvability of finite graphs without odd cycles, to arbitrary graphs which are proven solvable when no odd cycles nor patterns generalizing Yablo's occur. This follows from an earlier result by a new compactness-like theorem, holding for infinitary logic and utilizing the graph representation.

翻译：本文通过经典逻辑的图表示法，论证了说谎者悖论或亚布罗模式存在于每一个语义悖论中。核心图论结果将理查森定理——有限无奇环图具有可解性——推广至任意图，证明当图中既无奇环也无亚布罗悖论的推广模式时，该图具有可解性。这一结论源自此前一项通过新型紧致性类定理得到的结果，该定理适用于无穷逻辑并利用了图表示法。