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Hughes, G. & M. Cresswell - A Companion to Modal Logic, Methuen, London, 1984.

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Honesty in Partial Logic - van der Hoek, Jaspars, Thijsse (1993)   (Correct)

....notion of stability. Here, we will provide several syntaxtic, of perhaps rather deductive characterizations for honesty 6. Inspecting the properties of saturated and stable sets, one good candidate for this is the disjunction property, defined below. In fact, this property is already mentioned in [HC84], be it that there it is a property of logical systems, rather than of formulas. In partial logic this property should be slightly reformulated. Definition 3.32 Disjunction Properties Let 6 . The following conditions define when is said to have the disjunction property (Dr) the propo si tional ....

Hughes, G. & M. Cresswell - A Companion to Modal Logic, Methuen, London, 1984


Honesty in Partial Logic - van der Hoek, Jaspars, Thijsse (1994)   (Correct)

....many logically different choices for the ff i;j , fi i;k and i in the semi disjunctive normal form displayed on page 10. Therefore there are only finitely many non equivalent formulas. For Henkin style completeness proofs in classical (modal) logic the notion of maximal consistency is used [HC84]. A maximally consistent set of formulas is a consistent set which cannot be extended consistently. Maximally consistent sets facilitate completeness proofs since they form the syntactic counterparts of possible worlds. These sets enable the construction of a canonical model. The corresponding ....

....notion of stability. Here, we will provide several syntactic, or perhaps rather deductive characterizations for honesty. Inspecting the properties of saturated and stable sets, one good candidate for this is the disjunction property, defined below. In fact, this property is already mentioned in [HC84], be it that there it is a property of logical systems, rather than of formulas. In partial logic the property should be slightly reformulated, and adapted to the different notions of honesty. Definition 3.34 (Disjunction Properties) Let 2 L. The following conditions determine when has the ....

Hughes, G. & M. Cresswell - A Companion to Modal Logic, Methuen, London, 1984.


Honesty in Partial Logic - van der Hoek, Jaspars, Thijsse (1996)   (Correct)

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Hughes, G. & M. Cresswell - A Companion to Modal Logic, Methuen, London, 1984.

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