Predication in the logic of terms

Abstract

The paper contrasts modern predicate logic (MPL) and term/functor logic (TFL) on predication. A predication in TFL consists of two terms and a “logical copula” that has formal properties such as symmetry or transitivity. The I-functor in ‘PiS’ (the old form of ‘(some) Sis P’) is symmetrical, behaving like the plus sign of high school algebra; TFL transcribes ‘PiS’ as ‘P + S’. The transitive A-functor in ‘PaS’ (every S is P) is minuslike: ‘P — S = — ((—P) + S) ’ represents the equivalence of ‘PaS’ to ‘not ((— P)iS) ’. In propositional logic ‘q + p’ transcribes ‘p & q’ and ‘q — p’ transcribes ‘q if p’; thus ‘q — p = —((—q) + p) ’ is the algebraic form of ‘p -> q = - (p & (-q)) \ TFL applies to relational statements of any complexity. E.g., to show the inconsistency of ‘every A is B and something R to an A is not R to a B’ we add ‘- (R + B) + (R + A) ’ to ‘P – A’ to get the contradiction ‘— (R + B) + (R + B) \ The predicative functors are shown to give TFL a slight advantage over MPL in expressive and inference power when dealing with singular statements. © 1990 by the University of Notre Dame. All rights reserved.