Search results
Results From The WOW.Com Content Network
In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2][3][4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true. The rule makes it possible to shorten longer proofs ...
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning. [1] This contrasts with Hilbert-style systems, which instead use axioms as much as possible to express the logical laws of deductive reasoning.
Transformation rules. In propositional logic, disjunction elimination[1][2] (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference that if a statement implies a statement and a statement ...
from line 1 by rule (B) 3. Bp: from line 2 by conjunction elimination 4. BBp: from line 3 by rule (E) 5. B¬Bp: from line 2 by conjunction elimination 6. BBp & B¬Bp: from lines 4 and 5 by conjunction introduction: 7. ¬(BBp & B¬Bp) by rule (F) 8. ¬B(p & ¬Bp) from lines 6 and 7 by reductio ad absurdum, discharging assumption 1
In propositional logic, disjunctive syllogism (also known as disjunction elimination and or elimination, or abbreviated ∨E), [7][8][9][10] is a valid rule of inference. If it is known that at least one of two statements is true, and that it is not the former that is true; we can infer that it has to be the latter that is true.
In propositional logic, tautology is either of two commonly used rules of replacement. [1][2][3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction: and the principle of idempotency of conjunction: Where " " is a metalogical symbol ...
Propositional calculus. Not to be confused with Propositional analysis. The propositional calculus[a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and ...
Transformation rules. In logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens ...