Lambda the Ultimate

Given the recent posts on computation and logic, those of you who will be in Silicon Valley on Thursday Jan. 7 might be interested in the following event at 4PM at SRI:

Direct Inference in Direct Logic(TM)
Carl Hewitt

Direct inference is reasoning that requires a more direct inferential connection between premises and conclusions than classical logic.

For example, in classical logic, (not WeekdayAt5PM) can be inferred from the premises (not TrafficJam) and (WeekdayAt5PM infers TrafficJam). However, direct inference does not sanction concluding (not WeekdayAt5PM) because it might be that there is no traffic jam but it undesirable to infer (not WeekdayAt5PM). The same issue affects probabilistic (fuzzy logic) systems. Suppose (as above) the probability of TrafficJam is 0 and the probability of (TrafficJam given WeekdayAt5PM) is 1. Then the probability of WeekdayAt5PM is 0. Varying the probability of TrafficJam doesn’t change the principle involved because the probability of WeekdayAt5PM will always be less than or equal to the probability of TrafficJam.

Direct inference is the foundation of reasoning in the logical system Direct Logic. Direct Logic has an important advantage over classical logic in that it provides greater safety in reasoning using inconsistent information. This advantage is important because information about the data, code, specifications, and test cases of cloud computing systems is invariable inconsistent and there is no effective way to find the inconsistencies.

Direct Logic has important advantages over previous proposals (e.g. Relevance Logic) to more directly connect antecedents to consequences in reasoning. These advantages include using natural deduction reasoning, preserving the standard Boolean equivalences (double negation, De Morgan, etc.), and having an intuitive deduction theorem that connects logical implication with inference. Direct Logic preserves as much of classical logic as possible given that it is based on direct inference. The recursive decidability of inference for Boolean Direct Logic will be proved where a Boolean proposition uses only the connectives for conjunction, disjunction, implication, and negation. In this way Direct Logic differs from Relevance Logic because Boolean Relevance Logic is recursively undecidable