Speaking about transitive frames in propositional languages

Authors: 
Suzuki, Yasuhito
Wolter, Frank
Zakharyaschev, Michael
Year: 
1997
Language: 
English
Abstract: 
This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions which also reveals some unexpected phenomena. The balance between the intuitionistic and modal languages is restored by adding to the former one more implication.
Appeared / Erschienen in: 
Vortrag (Workshop New Aspects in Non-Classical Logics, Kyoto, Februar 1997) (wird erscheinen in Journal of Logic, Language and Information)
Pubdate / Erscheinungsdatum: 
1997
Pages / Seitenanzahl: 
23
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