On If and Only

Embedding If and Only If

Compounds of indicative conditionals present some puzzling phenomena. Perhaps most striking, some nested indicative conditionals are uninterpretable. Proponents of NTV hold that indicative conditionals do not have truth values, and they use this to explain why nested indicative conditionals are sometimes uninterpretable: the embedded conditional does not provide the truth conditions needed by t...

Markets are efficient if and only if P = NP

I prove that if markets are efficient, meaning current prices fully reflect all information available in past prices, then P = NP , meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can “program” the market to solve NP -complete problems. Since P probably does not equal NP , ma...

If only we all cared.

Indicative and counterfactual 'only if' conditionals.

We report three experiments to test the possibilities reasoners think about when they understand a conditional of the form 'A only if B' compared to 'if A then B'. The experiments examine conditionals in the indicative mood (e.g., A occurred only if B occurred) and counterfactuals in the subjunctive mood (A would have occurred only if B had occurred). The first experiment examines the conjuncti...

A Tri-Phase Multimodal Evolutionary Search Performance Profile on the 'Hierarchical If and Only If' Problem

Previous work by the authors has explored performance profiles of simple evolutionary algorithms over a range of problems. These studies have revealed a consistent bimodal feature, where the optimal mutation rate occurs at the trough between two peaks in convergence time. However, careful examination revealed anomalies suggesting higher modality features in the performance profile under certain...