# Definitions of Two-Placed Connectives in Lesniewski's Protothetic

Definitions of Two-Placed Connectives in Lesniewski's Protothetic

To describe his extended propositional calculus (protothetic), which is a logical system based on a single axiom, Leśniewski invented a special notation for a propositional function of two arguments . He used a circle and up to four lines around the circle, which point to those values of arguments of for which the function is true, according to the diagram:

f(p,q)

f

False,False | ||

True,False | False,True | |

True,True |

The combinations of the four lines generate a Boolean algebra of 16 elements. As a consequence, let be the negation of ; then the sign for consists of the circle and the four lines that do not belong to the sign of .

g

f

g

f