probability logic;modality;Lukasiewicz logic;possible-world semantics

The paper introduces a predicate version of two-layered fuzzy probability logic, extending the known propositional probability logic based on the infinite-valued logic of Lukasiewicz. The proposed first-order framework, enriched additionally by S5-style alethic modalities, significantly increases the expressive power of fuzzy probability logic while retaining semantic clarity. Although the present initial study is limited in scope to the semantics of the proposed probability logic, it lays grounds for further developments, including axiomatization, expansions to more expressive predicate probability logics, and modeling of complex probabilistic reasoning in fields such as decision theory, judgment aggregation, and game theory.

The paper introduces a predicate version of two-layered fuzzy probability logic, extending the known propositional probability logic based on the infinite-valued logic of Lukasiewicz. The proposed first-order framework, enriched additionally by S5-style alethic modalities, significantly increases the expressive power of fuzzy probability logic while retaining semantic clarity. Although the present initial study is limited in scope to the semantics of the proposed probability logic, it lays grounds for further developments, including axiomatization, expansions to more expressive predicate probability logics, and modeling of complex probabilistic reasoning in fields such as decision theory, judgment aggregation, and game theory.