Sara Lapenta (Università di Salerno) will give a talk on
A Logic for Weighted Markov Chains
Abstract:
Furber, Mardare, and Mio introduced in [2] a modal operator on Archimedean Riesz spaces powerful enough to capture, when endowed with fixed-point operators, probabilistic CTL. Their logic is inherently infinitary, requiring both an infinitary language—featuring a unary operator for each real number—and an infinitary deduction rule. A key contribution is the definition of a transition semantics based on topological Markov chains, yielding a genuinely probabilistic modality and a perspective that departs from existing approaches to many-valued modal logic. The Riesz space setting naturally connects this framework to Lukasiewicz logic.
In this seminar, we revisit this framework in the setting of lattice-ordered groups and MV-algebras, showing that this allows us to avoid infinitary languages. Our approach builds on a recent duality for complete Archimedean lattice-ordered groups with strong order unit; see [1].
This is joint work in progress with Nick Bezhanishvili, Sebastiano Napolitano, and Luca Spada.
References:
[1] Abbadini, M., Marra, V., and Spada, L. Stone–Gelfand duality for metrically complete lattice-ordered groups. Journal of Symbolic Logic, 2025.
[2] Furber, R., Mardare, R., and Mio, M. Probabilistic Logics Based on Riesz Spaces. Logical Methods in Computer Science, 16(1:6), 2020.