Inference and reasoning
Neither 'inference' nor 'reasoning' has a single precise meaning. If Johnson-Laird wants to identify inference with reasoning, I can't see a crucial objection. It does not violate fixed usage in ordinary language or logic. So he can say : inference is all reasoning from premises to conclusion.
Yet while I can't see a crucial objection, I can't also but note that premises/ conclusion is a bed of Procrustes model for reasoning. When I apply a rule to a case or calculate efficient means to a distinctly conceived end, it is not at all clear that I am reasoning from premises to a conclusion, yet I am certainly reasoning and using inference. But here we will keep to the premises/ conclusion model.
Confusion about implication
I think Johnson-Laird goes astray in introducing the idea of implication. Implication holds or fails to hold between propositions or statements : If p then q; p; therefore q. It doesn't matter what propositions or statements we take 'p' and 'q' to be, hence we can just use place-holders such as 'p' and 'q'. Inference is psychological and holds (roughly) between beliefs : I infer that the pavements are wet because you have told me that it has been raining and I believe you. In inference it matters very much what the specific beliefs are.
Characterising deduction and induction
Johnson-Laird's permutations of particular to particular, particular to general, and general to general are quite unnecessary. It is sufficient to say that :
A conclusion cannot be false if [not 'given'] the premises are true.
The conclusion can only be probable if the premises are true.
So in a deductively valid argument a conclusion cannot be false if the premsies are true : the truth of the premises (if they are true) necessitates the truth of the conclusion.
In an inductively strong argument, by contrast, the conclusion is unlikely to be false if the premises are true.
Deduction : All politicians are honorable; X is a politician; therefore X is honorable. (If - IF - the premises are true, the conclusion cannot be false. I hope we all gain a great deal of comfort from that.)
Induction : If all known cases of infection X (a statistically significant number) involve the Y virus then I might infer that all cases of X involve Y. I have acquired a belief about all cases on the basis of evidence that is not conclusive. But if my premises are true, in this or some better example, the conclusion is unlikely to be false. No more than that. This is a fair example of how induction might operate.
I here exclude mathematical induction, which differs in important ways from the ordinary induction considered here.
Induction includes inference to the best explanation (IBE) and abduction
If we adopt the fairly standard characterisation of inductive inference as I've set it out above, and steer clear of Johnson-Laird's permutations of particular to particular, particular to general, and general to general, we can readily subsume IBE under inductive inference.
Given evidence E and a range of potential explanations (H1 ... Hn) infer to the explanation that best explains E. (I set aside what constitutes the best explanation : I assume that there might be one.)
To illustrate : suppose something occurs which I need to explain, say one of my windows has been smashed and there is a set of footprints leading from the garden gate to the window. I note that the footprints are exceptionally large. The evidence may also contain indications that it was a local crime. I cast my mind and remember Joe Blow, the notorious local crook who has just such exceptionally large feet. Joe Blow's being the one who smashed the window is, or might be, the explanation that best fits the evidence.
I have not considered 'abduction', which I equate with inference to the best explanation. This may be unsubtle of me but in sum (1) I have found a place for IBE in inductive reasoning by providing an improved account of the contrast between induction and deduction, removing the clutter about particular and general; and (2) I have kept implication out of the picture, reserving it for the sphere of logic.
Much more is problematic about IBE than at first sight appears - see Yemima Ben-Menahem in References - but I keep it in my toolkit of inference.
D.Q. McInerny, Being Logical, ISBN 10: 0812971159 / ISBN 13: 9780812971156
Published by Random House USA Inc, 2005.
Peter Lipton, Inference to the Best Explanation, ISBN 10: 0415242037 / ISBN 13: 9780415242035
Published by Taylor Francis Ltd, United Kingdom, 2004.
Brian Skyrms, Choice and Chance: An Introduction to Inductive Logic (Second Edition), ISBN 10: 0822101343 / ISBN 13: 9780822101345
Published by Dickenson Pub. Co.
Gilbert Harman, 'Logic and Reasoning', Synthese
Vol. 60, No. 1, Foundations: Logic, Language, and Mathematics, Part I (Jul., 1984), pp. 107-127.
Ruth Weintraub, 'Induction and inference to the best explanation', Philosophical Studies: An International Journal for Philosophy in the Analytic
Tradition, Vol. 166, No. 1 (October 2013), pp. 203-216.
Yemima Ben-Menahem, 'The Inference to the Best Explanation', Erkenntnis (1975-), Vol. 33, No. 3 (Nov., 1990), pp. 319-344.