The logic FP(Ł,Ł) and two-sorted equational states

Serafina Lapenta, Sebastiano Napolitano, Luca Spada
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:280-287, 2023.

Abstract

The logic {FP(Ł{},Ł)} was introduced by L. Godo and T. Flaminio as an expansion of {Ł}ukasiewicz logic with a modality, to reason about the probability of vague events. We prove that {FP(Ł{},Ł)} is complete with respect to a class of two-sorted algebras, called equational states. They are an equational presentation of the well-known theory of states over lattice ordered groups.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-lapenta23a, title = {The logic {FP}({Ł},{Ł}) and two-sorted equational states}, author = {Lapenta, Serafina and Napolitano, Sebastiano and Spada, Luca}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {280--287}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/lapenta23a/lapenta23a.pdf}, url = {https://proceedings.mlr.press/v215/lapenta23a.html}, abstract = {The logic {FP(Ł{},Ł)} was introduced by L. Godo and T. Flaminio as an expansion of {Ł}ukasiewicz logic with a modality, to reason about the probability of vague events. We prove that {FP(Ł{},Ł)} is complete with respect to a class of two-sorted algebras, called equational states. They are an equational presentation of the well-known theory of states over lattice ordered groups.} }
Endnote
%0 Conference Paper %T The logic FP(Ł,Ł) and two-sorted equational states %A Serafina Lapenta %A Sebastiano Napolitano %A Luca Spada %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-lapenta23a %I PMLR %P 280--287 %U https://proceedings.mlr.press/v215/lapenta23a.html %V 215 %X The logic {FP(Ł{},Ł)} was introduced by L. Godo and T. Flaminio as an expansion of {Ł}ukasiewicz logic with a modality, to reason about the probability of vague events. We prove that {FP(Ł{},Ł)} is complete with respect to a class of two-sorted algebras, called equational states. They are an equational presentation of the well-known theory of states over lattice ordered groups.
APA
Lapenta, S., Napolitano, S. & Spada, L.. (2023). The logic FP(Ł,Ł) and two-sorted equational states. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:280-287 Available from https://proceedings.mlr.press/v215/lapenta23a.html.

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