AIC Seminar Series
Direct Inference in Direct Logic(TM)
Carl Hewitt  Electrical Engineering and Computer Science, MIT  [Home Page] 
Notice: Hosted by Richard Waldinger. Note that venue is not the usual one.
Date: 20100107 at 16:00
Location: EK255 (SRI E building) (Directions)

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 doesnt 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. Also, 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.
 

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