What is the ideal theory of how to handle logical uncertainty?

Some possibly relevant work:

• Bayesian Networks for Logical Reasoning by Williamson
• Unifying Logical and Probabilistic Reasoning by Haenni
• Recursive Causality in Bayesian Networks and Self-Fibring Networks by Williamson and Gabbay
• Possible Semantics for a Common Framework of Probabilistic Logics by Haenni, Romeijn, Wheeler, and Williamson
• Reasoning with limited resources and assigning probabilities to arithmetical statements by Gaifman
• Non-deductive Logic in Mathematics by Franklin
• A Derivation of Quasi-Bayesian Theory by Cozman
• Slightly More Realistic Personal Probability by Hacking
• On Not Being Rational by Savage
• Knowledge and the Problem of Logical Omniscience by Parikh
• Belief, Awareness, and Limited Reasoning by Fagin and Halpern
• A Nonstandard Approach to the. Logical Omniscience Problem by Fagin, Halpern, and Vardi
• Old Evidence and Logical Omniscience in Bayesian Confirmation Theory by Garber
• Old Evidence, Logical Omniscience & Bayesianism by Fitelson
• A deduction model of belief by Konolige
• Using the Probabilistic Logic Programming Language P-log for Causal and Counterfactual Reasoning and Non-naive Conditioning by Baral and Hunsaker
• Decision Theory without Logical Omniscience by Lipman
• Objective Probabilities in Number Theory by Ellenberg and Sober
• Sentences, Propositions and Logical Omniscience by Parikh
• Maximum Entropy Probabilistic Logic by Paskin
• Towards a philosophy of real mathematics by Corfield
• Some puzzles about probability and probabilistic conditionals by Parikh
• Probabilistic Conditionals Are Almost Monotonic by Johnson and Parikh
• Probabilistic Proofs and the Collective Epistemic Goals of Mathematicians by Fallis
• Probabilistic Proofs and Transferability by Easwaran
• Randomized Arguments are Transferable by Jackson
• The philosophy of mathematical practice by Paolo Mancosu
• Dynamic Probability, Computer Chess, and the Measurement of Knowledge by Good
• Fully abstract compositional semantics for logic programs by Gaifman and Shapiro
• Putting Logic in its Place by Christensen
• A Hybrid Framework for Representing Uncertain Knowledge by Saffiotti