W. J. Blok and P. Kohler. Algebraic semantics for quasi-classical modal logics. Journal of Symbolic Logic, 48:941-964, 1983. Home/Search Document Not in Database Summary Related Articles Check |
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On Logics With Coimplication - Wolter (Correct)
....ML Phi p 3p and ML 3 : ML Phi p 2p, respectively. Also, we shall mostly formulate our results for modal HB logics and not for super HB logics since we can identify HB with ML 23 : ML 2 Phi p 2p. 3 Matrix semantics Recall some basic definitions from matrix theory (cf. e.g. 37] [5], or [9] Consider a propositional language L with connectives f 1 ; f k . A L matrix is a structure M = hA; F i such that A = hA; f A 1 ; f A k i is an L algebra and F A. A valuation V in M is a homomorphism from the algebra of formulas L into A. A formula is valid in a ....
....of matrices in M which are in V , by PM the class of products of families of matrices in M , by R V M the class of relatives of matrices in M which are in V , and by P U M the class of ultrapowers of matrices in M . The following proposition is easy to check (cf. similar results in e.g. 37] and [5]) Proposition 1 For all logics , Mat is closed under the operations H V ; R V ; P; P U ; for all V . Now call an algebra A = hA; 2; 3; i a modal HB algebra (a MLalgebra, for short) if the reduct without 2 and 3 is a HB algebra and 2 = 3 = 2(a b) 2a 2b; and 3(a b) ....
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W. Blok & P. Kohler. Algebraic Semantics for quasi-classical modal logics, Journal of Symbolic Logic 48: 941 - 964, 1983
Monotonic Modal Logics - Hansen (2003) (Correct)
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W. J. Blok and P. Kohler. Algebraic semantics for quasi-classical modal logics. Journal of Symbolic Logic, 48:941-964, 1983.
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