Bayesian Entailment Hypothesis: How Brains Implement Monotonic and Non-monotonic Reasoning
This addresses how brains might implement logical reasoning, offering a theoretical framework for cognitive science and AI, though it is incremental on existing Bayesian hypotheses.
The paper proposes a Bayesian account of entailment, showing it can model both monotonic and non-monotonic reasoning, with preferential entailment as an approximation via maximum a posteriori estimation.
Recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic, as the laws of thought, is a product and practice of the human brain, it leads to another hypothesis that there is a Bayesian algorithm and data-structure for logical reasoning. In this paper, we give a Bayesian account of entailment and characterize its abstract inferential properties. The Bayesian entailment is shown to be a monotonic consequence relation in an extreme case. In general, it is a sort of non-monotonic consequence relation without Cautious monotony or Cut. The preferential entailment, which is a representative non-monotonic consequence relation, is shown to be maximum a posteriori entailment, which is an approximation of the Bayesian entailment. We finally discuss merits of our proposals in terms of encoding preferences on defaults, handling change and contradiction, and modeling human entailment.