an:06081346
Zbl 1251.03027
Ili??-Stepi??, Angelina; Ognjanovi??, Zoran; Ikodinovi??, Neboj??a; Perovi??, Aleksandar
A \(p\)-adic probability logic
EN
Math. Log. Q. 58, No. 4-5, 263-280 (2012).
00306046
2012
j
03B48 03B25 03B42 68T27
probability logics; \(p\)-adic numbers; soundness; completeness
In this paper a propositional logic \(\mathcal L_{\mathbb Q_p}\) is introduced which is a generalization of Khrennikov's \(p\)-adic probability theory. It is shown that \(\mathcal L_{\mathbb Q_p}\) is sound and complete with respect to appropriate notions.
The first sections give background and motivation.
Thereafter, the main notions, such as \(\mathcal L_{\mathbb Q_p}\)-model and the satisfiability relation, are introduced.
The main content of Section three are five axioms and six inference rules, and a short discussion of these axioms and rules is given. In the next section, soundness and strong completeness of \(\mathcal L_{\mathbb Q_p}\) with respect to these axioms and rules are shown.
Section five contains decidability considerations. In the sixth and final section, the authors give their conclusions.
J??rgen Landes (Canterbury)