Autore: Minari, Pierluigi
Titolo: Infinitary Modal Logic and Generalized Kripke Semantics
Periodico: Annali del dipartimento di filosofia
Anno: 2011 - Volume: 17 - Pagina iniziale: 135 - Pagina finale: 166

This paper deals with the infinitary modal propositional logic K?1, featuring countable disjunctions and conjunc- tions. It is known that the natural infinitary extension LK???1 (here presented as a Tait-style calculus, TK??1 ) of the standard sequent calculus LK??p for the propositional modal logic K is incomplete w.r. to Kripke semantics. It is also known that in order to axiomatize K?1 one has to add to LK???1 new initial sequents corresponding to the infinitary propositional counterpart BF?1 of the Barcan- formula. We introduce a generalization of Kripke seman- tics, and prove that TK??1 is sound and complete w.r. to this generalized semantics. By the same proof strategy, we show that the stronger system TK?1 , allowing countably infinite sequents, axiomatizes K?1, although it provably doesn’t admit cut-elimination.


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SICI: 1824-3770(2011)17<135:IMLAGK>2.0.ZU;2-3
Testo completo: http://www.fupress.net/index.php/adf/article/download/11278/10791

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