Mathematical Structures: History of Linear logic algebras

# History of Linear logic algebras

 Revision 2 . . July 26, 2004 9:37 pm by Jipsen Revision 1 . . July 9, 2004 9:03 am by Jipsen

Difference (from prior major revision) (no other diffs)

Changed: 28,30c28,29
 \Large Name of class \quad\href{http://math.chapman.edu/cgi-bin/structures?action=edit;id=Template}{edit} % Note: replace "Template" with Name_of_class in previous line

Changed: 32c31
 \abbreviation{Abbr}
 \abbreviation{LLA}

Changed: 35,36c34,38
 A ... is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle ...\rangle$ such that
 A linear logic algebra is a structure $\mathbf{A}=\langle A,\vee,\bot,\wedge,\top,\cdot,1,+,0,\neg\rangle$ of type $\langle 2,0,2,0,2,0,2,0,1\rangle$ such that $\langle A,\vee,\wedge,\cdot,1,\neg\rangle$ is an \href{Involutive residuated lattices.pdf}{involutive residuated lattice} $\bot$ is the least element: $\bot\le x$

Changed: 38c40
 $\langle A,...\rangle$ is a \href{Name_of_class.pdf}{name of class}
 $\top$ is the greatest element: $x\le \top$

Changed: 40c42
 $op_1$ is (name of property): $axiom_1$
 $+$ is the dual of $\cdot$: $x+y=\neg(\neg x\cdot\neg y)$

Changed: 42c44
 $op_2$ is ...: $...$
 $0$ is the dual of $1$: $0=\neg 1$