Strong completeness and limited canonicity for PDL and similar modal logics
نویسندگان
چکیده
Propositional dynamic logic (PDL) is complete but not compact. As a consequence, strong completeness (the property Γ |= φ ⇒ Γ ` φ) requires an infinitary proof system. In this paper, we present a short proof for strong completeness of PDL relative an infinitary proof system containing the rule from [α;βn]φ for all n ∈ N, conclude [α;β∗]φ. The proof uses a universal canonical model, and it is generalized to other modal logics with infinitary proof rules, such as epistemic knowledge with common knowledge. Also, we show that the universal canonical model of PDL lacks the property of modal harmony, the analogue of the Truth lemma for modal operators.
منابع مشابه
Strong Completeness and Limited Canonicity for PDL
1. First of all, Lemma 1 on the equivalence of saturated and maximal consistent sets forPDLω is not original, contrary to what we stated in the paper. In fact, it has been proved before as Corollary 9.3.6 on p. 222 of Goldblatt (1993) and as Corollary 3.10 in Segerberg (1994). 2. Theorem 1 of Renardel de Lavalette et al. (2008) on strong completeness of PDLω is not really new. InGoldblatt (1982...
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