Formalizing common sense for scalable inconsistency-robust information integration using Direct Logic(TM) reasoning and the Actor Model

People use common sense in their interactions with large information systems. This common sense needs to be formalized so that it can be used by computer systems. Unfortunately, previous formalizations have been inadequate. For example, classical logic is not safe for use with pervasively inconsistent information. The goal is to develop a standard foundation for reasoning in large-scale Internet applications (including sense making for natural language). Inconsistency Robust Direct Logic is a minimal fix to Classical Logic without the rule of Classical Proof by Contradiction (Ψ├ (¬))├ ¬Ψ Addition of the above transforms Inconsistency Robust Direct Logic into Classical Logic. Inconsistency Robust Direct Logic makes the following contributions over previous work:  Direct Inference  Direct Argumentation (argumentation directly expressed)  Inconsistency-robust Natural Deduction that doesn’t require artifices such as indices (labels) on propositions or restrictions on reiteration  Intuitive inferences hold including the following:  Propositional Equivalences (except absorption) including Double Negation and De Morgan  -Elimination (Disjunctive Syllogism), i.e., ¬Φ, (ΦΨ)├ T Ψ  Reasoning by disjunctive cases, i.e., (), (├ T ), (├ T Ω)├ T Ω  Contrapositive for implication i.e., Ψ⇒ if and only if ¬⇒¬Ψ  Soundness, i.e., ├ T ((├ T ) ⇒ )  Inconsistency Robust Proof by Contradiction, i.e., ├ T (Ψ⇒ (¬))⇒¬Ψ