Differences

horn_formulas [2010/08/18 12:35] jipsen		horn_formulas [2017/10/01 20:07] (current) jipsen
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	[[Syntax]] | [[Terms]] | [[Equations]] | [[Horn formulas]] | [[Universal formulas]] | [[First-order formulas]] | [[Theories]]		[[Syntax]] | [[Terms]] | [[Equations]] | [[Horn formulas]] | [[Universal formulas]] | [[First-order formulas]] | [[Theories]]
-	A list of quasiequations and universal Horn formulas.	+	A list of atomic formulas, quasiequations and universal Horn formulas.
		+	|reflexive: | $xRx$ |||
	|transitive: | $xRy \mbox{ and } yRz\Longrightarrow xRz$  |||		|transitive: | $xRy \mbox{ and } yRz\Longrightarrow xRz$  |||
	|antisymmetric: | $xRy \mbox{ and } yRx\Longrightarrow x=y$  |||		|antisymmetric: | $xRy \mbox{ and } yRx\Longrightarrow x=y$  |||
	|left cancellation: | $x*y=x*z\Longrightarrow y=z$ | right cancellation: | $x*z=y*z\Longrightarrow x=y$  |		|left cancellation: | $x*y=x*z\Longrightarrow y=z$ | right cancellation: | $x*z=y*z\Longrightarrow x=y$  |
		+	|left R-preserving: | $xRy \Longrightarrow z*x\ R\ z*y$ | right R-preserving: | $xRy \Longrightarrow x*z\ R\ y*z$ |