# Deductive Reasoning Algorithm

A Deductive Reasoning Algorithm is a reasoning algorithm that can be applied by a deductive reasoning system (that can solve a deductive reasoning task which requires a deductive argument).

**AKA:**Deduction Process, Deductive Reasoning, Deductive Logic.**Context:**- The Evidence is associated to a set of Premises.
- The Background Knowledge must be expressed in a Logic formalism.
- It can/must (typically) apply Deduction Operationss, such as Modus Ponens and Modus Tollens.

**Example:**- Given: “
*IF human A THEN mortal A*” and “*human Socrates*” then “*mortal Socrates*”.

- Given: “
**Counter-Example(s):****See:**Expert System, First-Order Logic, Inductive Reasoning

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/deductive_reasoning Retrieved:2014-9-19.
**Deductive reasoning**, also**deductive logic**or**logical deduction**or, informally,**"top-down” logic**,^{[1]}is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.Deductive reasoning links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.

Deductive reasoning (top-down logic) contrasts with inductive reasoning (bottom-up logic) in the following way: In deductive reasoning, a conclusion is reached reductively by applying general rules that hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion is left. In inductive reasoning, the conclusion is reached by generalizing or extrapolating from initial information. As a result, induction can be used even in an open domain, one where there is epistemic uncertainty. Note, however, that the inductive reasoning mentioned here is not the same as induction used in mathematical proofs – mathematical induction is actually a form of deductive reasoning.

### 2009

- (Wordnet, 2009) ⇒ http://wordnet.princeton.edu/perl/webwn
- S: (n) tax write-off, tax deduction, deduction (a reduction in the gross amount on which a tax is calculated; reduces taxes by the percentage fixed for the taxpayer's income bracket)
- S: (n) deduction, discount (an amount or percentage deducted)
- S: (n) deduction, entailment, implication (something that is inferred (deduced or entailed or implied)) "his resignation had political implications"
- S: (n) deduction, deductive reasoning, synthesis (reasoning from the general to the particular (or from cause to effect))
- S: (n) subtraction, deduction (the act of subtracting (removing a part from the whole)) "he complained about the subtraction of money from their paychecks"
- S: (n) discount, price reduction, deduction (the act of reducing the selling price of merchandise)

- http://en.wiktionary.org/wiki/deduction
- 1. that which is deducted; that which is subtracted or removed
- 2. a sum that can be removed from tax calculations; something that is written off.
*You might want to donate the old junk and just take the deduction.* - 3. a conclusion; that which is deduced, concluded or figured out.
*He arrived at the deduction that the butler didn't do it.* - 4. the ability or skill to deduce or figure out; the power of reason.
*Through his powers of deduction, he realized that the plan would never work.* - 5. (logic)
- a. a process of reasoning that moves from the general to the specific, in which a conclusion follows necessarily from the premises presented, so that the conclusion cannot be false if the premises are true.
- b. a conclusion reached by this process

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- http://mdk12.org/instruction/curriculum/mathematics/glossary.shtml
- The process of reasoning that starts from statements accepted as true and applied to a new situation to reach a conclusion (eg, if 5+4 = 9, and 6 ...

- http://school.discoveryeducation.com/lessonplans/programs/conceptsInGeometry/
- Definition:The process of reasoning logically from given statements to a conclusion Context:The Pythagorean Theorem was proved using deductive ...

- http://www.apstudynotes.org/english/rhetorical-terms/diction/
- Reasoning that begins with a general principle and concludes with a specific instance that demonstrates the general principle. ...

- http://www.utexas.edu/academic/diia/assessment/iar/glossary.php
- a logic model in which assumptions or hypotheses are made on the basis of general principles.

- CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
- deduction: A deduction is an argument supporting a remote or inferred assertion. It is composed of a set of assertions which together entail the inferred assertion.

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