Common sense for inconsistency robust information integration using Direct Logic(TM) Reasoning and the Actor Model
Carl E. Hewitt · 2008
Direct Logic is a minimal fix to classical mathematical logic and statistical probability (fuzzy) inference that meets the requirements of modern computer science by addressing the following issues: inconsistency robustness, contrapositive inference bug, and direct argumentation.. For example, in classical logic, the contrapositve holds for inference. The same issue affects probabilistic (fuzzy) inference. Also, in the Tarskian framework of classical mathematical logic, a theory cannot directly express argumentation. Goedel first formalized and proved that nontrivial mathematical theories are incomplete. However, the incompleteness theorem (as generalized by Rosser) relies on the assumption of consistency. This paper proves a generalization of the Goedel/Rosser incompleteness theorem: theories in Direct Logic are self-provably incomplete using inconsistency robust reasoning. However, there is a further consequence: Since the Goedelian paradoxical proposition is self-provable, theories in Direct Logic are self-provably inconsistent. This paper also proves that Logic Programming is not computationally universal in that there are concurrent programs for which there is no equivalent in Direct Logic. Consequently the Logic Programming paradigm is strictly less general than the Procedural Embedding of Knowledge paradigm. Thus the paper makes use of a concurrent programming language ActorScript(TM) (suitable for expressing massive concurrency in large software systems) that is defined meta-circularly in terms of itself. Direct Logic makes the following contributions over previous work: * Direct Inference (no contrapositive bug for inference) * Direct Argumentation (inference directly expressed) * Inconsistency Robustness * Practical natural deduction without artifices such as indices * Boolean Equivalences hold * Incompleteness self-proved using Self-annihilation