deductive reasoning
In plain wordsReasoning in which true starting points guarantee a true conclusion: if every square is a rectangle and this shape is a square, then it must be a rectangle.
Truth-preserving inference: when the premises are true, a deductively drawn conclusion cannot be false, because affirming the premises while denying the conclusion would be self-contradictory. Logicians call such an argument valid, and call it sound when its premises are in fact true. Deduction adds no information beyond what the premises already contain, but it makes implicit consequences explicit, which can require enormous effort, as in mathematical proof. Formal logic codifies valid deduction in rules of inference such as modus ponens; automated theorem provingautomated theorem proving, n.: Getting computers to prove mathematical or logical statements by themselves, by searching for a chain of valid steps that leads from basic assumptions to the statement., logic programminglogic programming, n.: A style of programming in which you write down facts and rules in logic and then ask questions; the computer works out the answers itself by logical deduction. and description logicdescription logic, n.: A family of precise logical languages for defining categories and how they relate, such as 'a parent is a person with at least one child', designed so that a computer's reasoning about them always finishes. reasoners mechanize it, and proof assistantsinteractive theorem proving, n.: Writing a proof in a precise computer language so that software checks every step: the person supplies the ideas, the computer fills in small steps and guarantees that nothing is wrong. check it. Because validity can be checked mechanically, deductive tasks — proofs, logic puzzles and multi-step entailment benchmarks such as ProofWriter and FOLIO — are widely used to test whether language modelslarge language model, n.: A computer program trained on enormous amounts of text to predict the words that come next. At vast scale, that simple skill lets it chat, answer questions, translate, summarize and write code. reason reliably or rely on surface patterns.
Origin
Aristotle's syllogistic (4th century BCE) was the first systematic theory of deduction. Gottlob Frege's predicate logic (1879) and the 20th-century proof theory of David Hilbert, Gerhard Gentzen and others gave it modern form, and mechanizing it was one of AI's first goals.
Usage note
In everyday English and detective fiction, 'deduction' often names what logicians call abduction: Sherlock Holmes's famous 'deductions' are mostly inferences to the best explanation.
Related
- inductive reasoninginductive reasoning, n.: Reasoning from particular examples to a general rule or prediction — every swan I have seen is white, so swans are probably white — which is useful but can always turn out wrong.
- abductive reasoningabductive reasoning, n.: Reasoning from an observation to its most likely explanation — the grass is wet, so it probably rained — the kind of educated guess that doctors and detectives make.
- first-order logicfirst-order logic, n.: A precise formal language for statements about objects and their relations, using 'for all' and 'there exists', such as 'every person has a mother'. It is the standard logic of mathematics and of classic AI.
- automated theorem provingautomated theorem proving, n.: Getting computers to prove mathematical or logical statements by themselves, by searching for a chain of valid steps that leads from basic assumptions to the statement.
- reasoningreasoning, n.: Working out conclusions step by step from facts, rules or evidence, as in solving a math problem or planning a trip. Whether today's AI truly reasons, or imitates reasoning, is debated.
- resolutionresolution, n.: A mechanical step of logical reasoning: from 'A or B' and 'not A or C', conclude 'B or C'. Repeating it can demonstrate any conclusion that genuinely follows from what is known.
- inductive reasoninginductive reasoning, n.: Reasoning from particular examples to a general rule or prediction — every swan I have seen is white, so swans are probably white — which is useful but can always turn out wrong.
- abductive reasoningabductive reasoning, n.: Reasoning from an observation to its most likely explanation — the grass is wet, so it probably rained — the kind of educated guess that doctors and detectives make.
Sources
- Gentzen, G. (1935). Untersuchungen über das logische Schließen. Mathematische Zeitschrift 39, 176–210 and 405–431.
Mentioned in
abductive reasoningabductive reasoning, n.: Reasoning from an observation to its most likely explanation — the grass is wet, so it probably rained — the kind of educated guess that doctors and detectives make., inductive reasoninginductive reasoning, n.: Reasoning from particular examples to a general rule or prediction — every swan I have seen is white, so swans are probably white — which is useful but can always turn out wrong.