Abstract
AbstractIn this paper, we present a logic $$\textbf{FPL}$$
FPL
(Frequentist Probability Logic) to reason about probabilities with a relative frequency interpretation. We show that it is possible to interpret the language of $$\textbf{FPL}$$
FPL
with the standard semantics for propositional logic. $$\textbf{FPL}$$
FPL
can give a peculiar frequentist interpretation of a probability operator. We then give a proof system for the language, prove that the traditional theorems of probability hold, and prove soundness and completeness.
Publisher
Springer Nature Switzerland
Reference17 articles.
1. Aldini, A., Seigneur, J.M., Ballester Lafuente, C., Titi, X., Guislain, J.: Design and validation of a trust-based opportunity-enabled risk management system. Inf. Comput. Secur. 25, 2–25 (2017)
2. Aldini, A., Curzi, G., Graziani, P., Tagliaferri, M.: Trust evidence logic. In: Vejnarová, J., Wilson, N. (eds.) Symbolic and Quantitative Approaches to Reasoning with Uncertainty: 16th European Conference (ECSQARU 2021). LNAI, vol. 12897, pp. 575–589. Springer (2021)
3. Aldini, A., Tagliaferri, M.: Logics to reason formally about trust computation and manipulation. In: Saracino, A., Mori, P. (eds.) Emerging Technologies for Authorization and Authentication. LNCS, vol. 11967, pp. 1–15. Springer (2020)
4. Antonelli, M., Lago, U.D., Pistone, P.: On counting propositional logic and wagner’s hierarchy. In: Coen, C.S., Salvo, I. (eds.) Proceedings of the 22nd Italian Conference on Theoretical Computer Science. CEUR Workshop Proceedings, vol. 3072. Technical University of Aachen (2021)
5. Casadei, R., Aldini, A., Viroli, M.: Combining trust and aggregate computing. In: Cerone, A., Roveri, M. (eds.) Software Engineering and Formal Methods, SEFM 2017. LNCS, vol. 10729, p. 507–522. Springer (2018)