Map of Some Logical Systems Peter Suber, Philosophy Department, Earlham College
D. Higher order logics
not (generally) consistent
C. First order polyadic predicate logic
with or without identity
consistent, semantically complete
not decidable, syntactically complete, negation complete
B. First order monadic predicate logic
consistent, semantically complete, decidable
not syntactically complete, negation complete
A. Truth-functional propositional logic
consistent, semantically complete, syntactically complete, decidable
not negation complete
The purpose of this map is to show that these important systems of logic are related by subsumption, and that to "climb" to the next higher, more encompassing system, one must sacrifice some important metalogical properties.
In climbing from A to B, one gives up syntactic completeness and truth-functionality. In climbing from B to C, one gives up decidability; note that one must climb at least this high to have a "respectable" system of arithmetic. In climbing from C to D, one (generally) gives up consistency.
This file is an electronic hand-out for the course, Logical Systems.
Department of Philosophy,
Earlham College, Richmond, Indiana, 47374, U.S.A.
firstname.lastname@example.org. Copyright © 1997, Peter Suber.