my 2 cents: Deduction: p( C | do(P,R) ) Induction: p( C | do(P), R ) Abduction: p( P | do(C), R ) where C stands for conclusion, P for premises, R for prior

my 2 cents: Deduction: p( C | do(P,R) ) Induction: p( C | do(P), R ) Abduction: p( P | do(C), R ) where C stands for conclusion, P for premises, R for prior assumptions / remaining possible statements in the universe of discourse not covered by the premises and conclusion. Deduction can only take values in {0,1}. Deductive arguments are valid when that probability is 1, invalid when that probability is 0, sound when do(P,R) can be shown to be 1, and unsound when it cannot. Typically when trying to show that do(P,R)=1, we may assume or try to show that it can be simplified to do(P). Whether it can or not is often the source of soundness errors. Inductive arguments are effectively probabilistic reasoning about the posterior probability of the conclusion (i.e. a process equivalent to Bayesian inference, with regard to statements in the universe of discourse and their probability). Abductive arguments are statements of [high] likelihood, with the intent of exploring/generating/identifying [high-likelihood] data (i.e. useful premises). It can be compared to Maximum Likelihood Estimation in statistics. Quite often, R is simplified to be null (i.e., the universe of discourse is limited to only what we already know). The intent is typically to generate a subset of premises to act as a new, more manageable universe of discourse for subsequent deductive or inductive reasoning, when the original full universe of discourse would be intractable.