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Taxonomy of Modal Logics

Taxonomy of Modal Logics. Logical Omiscience Problem. One should know all valid formulae and Knowledge/belief being closed under logical consequence; Collectively they contribute to two issues:-

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Taxonomy of Modal Logics

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  1. Taxonomy of Modal Logics

  2. Logical Omiscience Problem • One should know all valid formulae and • Knowledge/belief being closed under logical consequence; • Collectively they contribute to two issues:- • (1) Consistency: Ideal reasoners assumed within possible world semantics cannot have inconsistent beliefs……..the consequence of such would be that necessarily they would have to believe every formula in the language as the consequential closure of an inconsistent set of formula is the set of all formula. • Konolidge argues that the demand for logical consistency is too strong and argues rather for non contradictory beliefs ie can not believe a and not a at the same instance.

  3. Logical Omiscience Problem (2) Equivalent propositions are not equivalent as beliefs; Consider: Bob’s favouritecolour is black Bob’s favouritecolour is black AND every book can be made up of four colours The second conjunct of the second formula is valid and will thus be believed The first sentence and the second are thus logically equivalent as the second can only be true when the first is true. The reasoners will believe that the two propositions are true.

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