Analogic: Inference beyond logic

Abstract

Analogic is the unique class of many-valued, non-monotonic logics which preserves the richness of inferences in (Boolean) logic and the manipulability of (Boolean) algebra underlying logic, and, in addition, contains a number of unexpected, emergent properties which extend inferentiability in non-trivial ways beyond the limits of logic. For example, one such inference is rada (reductio ad absurdum, reasoning by contradiction, but now in the absence of excluded middle). This is important to retain since direct proofs of many theorems are not known. Another example is chaining. Transitivity is uncommon in many-valued logics; however, in analogic we can carry out inferences in either direction even through weak links in the chain. The latter, impossible in logic, simulate intuitive leaps in reasoning. Protologic effects inferences using only (n+1) implications which require 2n implications in logic. Indeed protologic has no counterpart in logic, or any other form of reasoning. Analogic is useful in formulating problems which are largely inferential including document and pattern classification and retrieval. These inference properties, long sought after in alternative logics by adding appropriate axioms or other indicative implicit or explicit restrictions, are now available in analogic, in turn the result of removing an axiom and letting inferences become many-valued.