Abstract : Logic systems can be defined using a trichotomized rather than the dichotomized universe used in classical logic. We partition these designated logic systems using the negation (or complement) function into the designated, antidesignated and neutral logic classes. The complement function alone is not sufficient to uniquely determine an assignment of logic elements to partition classes. Using a modified definition of conjunction within the designated logic system framework we can uniquely determine an assignment up to equivalence for any designated logic system. We build a hierarchy of mathematical systems to describe properties found in some common designated computer logic systems. Starting with a simple algebra and imposing constraints we end up with an order defined for some of the designated logic systems. Using this hierarchy we find the number of conjunction functions homomorphic to classical logic when only designated and antidesignated values are conjoined. The logic systems described by these twelve homomorphisms are designated logic systems closest in behavior to classical logic.
[1]
Susanne K. Langer,et al.
An Introduction to Symbolic Logic
,
1939,
Mathematical Gazette.
[2]
Paul C. Rosenbloom,et al.
The Elements of Mathematical Logic
,
1951
.
[3]
Patrick Suppes,et al.
Introduction To Logic
,
1958
.
[4]
Martha Kneale,et al.
The development of logic
,
1963
.
[5]
Nicholas Rescher,et al.
Topics in philosophical logic
,
1968
.
[6]
C. L. Liu,et al.
Introduction to Combinatorial Mathematics.
,
1971
.
[7]
C. L. Liu.
Elements of Discrete Mathematics
,
1985
.