{"about":"This a common question on this board:

What is reasoning?

In computer science and AI when we say "reasoning" we mean that we have a\ntheory and we can derive the consequences of the theory by application of some\ninference procedure.

A theory is a set of facts and rules about some environment of interest: the\nreal world, mathematics, language, etc. Facts are things we know (or assume)\nto be true: they can be direct observations, or implied, guesses. Rules are\nconditionally true and so most easily understood as implications: if we know\nsome facts are true we can conclude that some other facts must also be true.\nAn inference procedure is some system of rules, separate from the theory, that\ntells us how we can combine the rules and facts of the theory to squeeze out\nnew facts, or new rules.

There are three types of reasoning, what we may call modes of inference:\ndeduction, induction and abduction. Informally, deduction means that we start\nwith a set of rules and derive new unobserved facts, implied by the rules;\ninduction means that we start with a set of rules and some observations and\nderive new rules that imply the observations; and abduction means that we\nstart with some rules and some observations and derive new unobserved facts\nthat imply the observations.

It's easier to understand all this with examples.

One example of deductive reasoning is planning, or automated planning and\nscheduling, a field of classical AI research. Planning is the "model-based\napproach to autonomous behaviour", according to the textbook on planning by\nGeffner and Bonnet. An autonomous agent starts with a "model" that describes\nthe environment in which the agent is to operate as a set of entities with\ndiscrete states, and a set of actions that the agent can take to change those\nstates. The agent is given a goal, an instance of its model, and it must find\na sequence of actions, that we call a "plan", to take the entities in the\nmodel from their current state to the state in the goal. This is usually\nachieved by casting the planning problem as pathfinding over a graph with a\nsearch algorithm like A*. Here, the agent's model is a theory, the search\nalgorithm is the inference procedure, and the plan is a consequence of the\ntheory. Deductive reasoning can be sound, as long as the facts and rules in\nthe theory are correct: from correct premises we can deduce correct\nconclusions. We know of sound deductive inference rules, e.g. A*, and\nResolution, used in automated theorem proving and SAT-Solving, are sound.

The classic example of inductive reasoning is inferring the colour of swans.\nMost swans are white (apparently) so if we have only seen white swans we have\nno reason to believe there are any other colours: we are forced to infer that\nall swans are white. We may only be disabused of our fallacy if we happen to\nobserve a swan that is not white, e.g. a black swan. But who is to say when\nsuch a magnificent creature will grace us with its presence, outside of\nTchaikovsky's ballets? Induction is thus revealed to be unsound: even given\ntrue premises we can still arrive at the wrong conclusions. Another example is\nthe scientific method: imagine an idealised scientist, perfectly spherical, in\na frictionless vacuum. She starts with a scientific theory, then goes out into\nthe world and makes new observations about a phenomenon not described by her\ntheory. She constructs a hypothesis to extend her theory so as to explain the\nnew observations. The hypothesis is a set of rules, where the premises are the\nconsequences of the rules in her initial theory. Then, being an idealised\nscientist, she goes looking for new observations to refute her hypothesis.\nScience only gives us the tools to know when we're wrong.

Abductive reasoning is the mode of inference exemplified by Sherlock Holmes.\nWe can imagine Sherlock and Watson standing outside a tavern in London,\nwatching as a gentleman of interest steps out of the tavern with egg on his\nlapel. "Ah, my dear Watson, what can we conclude from this observation?". "Why\nmy dear Holmes, we can conclude that the man had eggs for breakfast". Holmes\nand Watson can arrive at this conclusion, about a fact that they have not\ndirectly observed, because they have a theory with a rule that says "if one\neats eggs, one may get some on one's lapels". Working backwards from this\nrule, and their observation of egg on the man's lapels, they can guess that\nhe had eggs even if they didn't directly observe him doing so. Abduction is\nalso unsound: the man may have swapped coats with an accomplice, who was the\none who had eggs for breakfast instead.

And now you know what "reasoning" means. So the next time someone asks: "what\nis reasoning?", you can let them know and turn the discussion to more\ninteresting, more productive directions.","created_time":1443306658,"created":"10 years ago","id":"YeGoblynQueenne","karma":23100}