Deterministic inductive logic: A multi-valued logic for reasoning about categories.

摘要

In logic, induction is used to formulate theories (generalizations) from specifics, while deduction is used to derive theories (specializations) from axioms (generalizations). Induction has traditionally employed probabilistic models to formulate representations (models) analogous to logic's domains of discourse, where the resulting models are inherently non-deterministic. An implementation of classical deductive logic that applies to organizing conceptual spaces is ontology, where the classification of a universe of discourse may contain multiple levels of hierarchy to support successively refined deterministic subsets, which are used to facilitate conceptual differentiation. In this paper deterministic inductive logic is defined and described as the complement of classical (deterministic) deductive logic. The logic described is a multi-valued logic that supports formulating theories (generalizations) by combining “specifics” into categories or classes. Three primitive operators are defined and described that support: (1) COMBINE , (2) COMPARE and (3) CONTRAST. Examples are provided to show that deterministic inductive logic: (1) provides a method for building classifications by generalizing about specifics either by defining a class from its members, or a super-class from its member classes; and (2) facilitates the creation of hierarchical structures compatible with classical deductive logic (hierarchical subsumption). An approach is also described for implementing deterministic inductive logic to build information structures to organize and manage information analogously to the controlled vocabulary approach to organizing information.