Syntax | Terms | Equations | Horn formulas | Universal formulas | First-order formulas | Theories
A list of atomic formulas, quasiequations and universal Horn formulas.
| reflexive: | $xRx$ | ||
| transitive: | $xRy \mbox{ and } yRz\Longrightarrow xRz$ | ||
| 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 R-preserving: | $xRy \Longrightarrow z*x\ R\ z*y$ | right R-preserving: | $xRy \Longrightarrow x*z\ R\ y*z$ |