Probability Logic of Finitely Additive Beliefs
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In this article, we provide a complete deductive system Σ+ for probability logic that is different from the systems by Fagin and Halpern and by Heifetz and Mongin in the literature. The most important principle of the axiomatization is an infinitary Archimedean rule (ARCH). Our proof of the completeness of Σ+ is in keeping with the Kripke-style proof of completeness in modal logic. With the Fourier–Motzkin elimination method, we show both the decidability and Moss's conjecture that the rule (ARCH) is essentially finitary. The perspective of this article is mainly logical. At the end, we point to some further research continuing this piece of work from a coalgebraic perspective.