Authors: Ilić Stepić, Angelina 
Ognjanović, Zoran 
Perović, Aleksandar
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The Logic ILP for Intuitionistic Reasoning About Probability
Journal: Studia Logica
Issue Date: 2023
Rank: ~M21
ISSN: 0039-3215
DOI: 10.1007/s11225-023-10084-z
Abstract: 
We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form ⟨ H, μ⟩ that needs not be a probability space. More precisely, though H needs not be a Boolean algebra, the corresponding monotone function (we call it measure) μ: H⟶ [0 , 1] Q satisfies the following condition: if α , β , α∧ β , α∨ β∈ H , then μ(α∨ β) = μ(α) + μ(β) - μ(α∧ β) . Since the range of μ is the set [0 , 1] Q of rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability.
Keywords: Intuitionistic | Logic
Publisher: Springer Link

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