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A relation algebra is a structure $\mathbf{A}=\langle A,\vee,0, \wedge,1,\neg,\circ,^{\smile},e\rangle$ such that |
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A relation algebra is a structure $\mathbf{A}=\langle A,\vee,0,\wedge,1,\neg,\circ,^{\smile},e\rangle$ such that |
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$\langle A,\vee,0,\wedge,1,\neg\rangle$ is a \href{Boolean_algebras.pdf}{Boolean algebra} |
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$\langle A,\vee,0, \wedge,1,\neg\rangle$ is a \href{Boolean_algebras.pdf}{Boolean algebras} |
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$\langle A,\circ,e\rangle $ is a \href{Monoids.pdf}{monoid} |
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$\circ$ is join-preserving: $(x\vee y)\circ z=(x\circ z)\vee (y\circ z)$ |
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$\langle A,\circ,e\rangle $ is a \href{Monoids.pdf}{monoids} |
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$^{\smile}$ is an involution: $x^{\smile\smile}=x$, $(x\circ y)^{\smile}=y^{\smile}\circ x^{\smile}$ |
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$^{\smile}$ is join-preserving: $(x\vee y)^{\smile}=x^{\smile}\vee y^{\smile}$ |
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$\circ$ is join-preserving: $(x\vee y)\circ z=(x\circ z)\vee (y\circ z)$ $^{\smile}$ is an involution: $x^{\smile\smile}=x$, $(x\circ y)^{\smile}=y^{\smile}\circ x^{\smile}$ $^{\smile}$ is join-preserving: $(x\vee y)^{\smile}=x^{\smile}\vee y^{\smile}$ $\circ$ is residuated: $x^{\smile}\circ(\neg (x\circ y))\le\neg y$ |
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$\circ$ is residuated: $x^{\smile}\circ(\neg (x\circ y))\le\neg y$ |
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