Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
There is at least one more requirement for “plausible” reasoning. Classical logic is “monotonic”: assertions cannot be retracted without compromising the entire system of beliefs. Once something has been proven to be true, it will be true forever. Classical Logic was not designed to deal with "news". But our daily lives are full of events that force us to reexamine our beliefs all the time: our daily system of logic is “non-monotonic”. Therefore, a crucial tool for plausible reasoning is non-monotonic logic, which allows inferences to be made provisionally and, if necessary, withdrawn at any time. A handful of such logics became popular during the 1980s.
Drew McDermott's formulation of Modal Logic is based on a coherence operator: "P is coherent with what is known" if P cannot be proven false by what is known (“Nonmonotonic Logic”, 1980).
Robert Moore's "Autoepistemic Logic" (“Semantic Considerations On Nonmonotonic Logic”, 1983) is based on the notion of belief (related to McDermott's coherence) and models the beliefs of an agent reflecting upon his own beliefs.
And so forth.
Matthew Ginsberg classified formal approaches to nonmonotonic inference into: proof-based approaches (Reiter's logic), modal approaches (McDermott's logic, Moore's logic) and minimization approaches (circumscription). Ginsberg argued that a variety of approaches to nonmonotonic reasoning can be unified by resorting to multi-valued logics (logics that deal with more than just true and false statements).
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