Probability Logics by Zoran Ognjanović Miodrag Rašković & Zoran Marković

Author:Zoran Ognjanović, Miodrag Rašković & Zoran Marković
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

3.4.2 Completeness

In the proof of the completeness theorem we adapt the Henkin style procedure and the strategy developed for proving completeness for modal logics. So, the proof consists of the following main steps:We start with a form of Deduction theorem (Theorem 3.3) and some other auxiliary statements (the Lemmas 3.1, 3.2 and 3.3).

Then, we prove Lindenbaum’s theorem, i.e., we show how to extend a consistent set T of formulas to a maximal consistent set (Theorem 3.4).

Finally, the canonical model is constructed using the set (Theorem 3.5) such that iff (Theorem 3.6).

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