# Differences

This shows you the differences between two versions of the page.

horn_formulas [2010/08/18 12:35]
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horn_formulas [2017/10/01 20:07] (current)
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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: | $xRy \Longrightarrow x*z\ R\ y*z$ |