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Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
In first-order logic, resolution condenses the traditional syllogisms of logical inference down to a single rule. To understand how resolution works, consider the following example syllogism of term logic: All Greeks are Europeans. Homer is a Greek. Therefore, Homer is a European. Or, more generally: .
In predicate logic, universal instantiation [1] [2] [3] (UI; also called universal specification or universal elimination, [citation needed] and sometimes confused with dictum de omni) [citation needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.
Absorption is a valid argument form and rule of inference of propositional logic. [1] [2] The rule states that if implies , then implies and .The rule makes it possible to introduce conjunctions to proofs.
Being a valid argument does not necessarily mean the conclusion will be true. It is valid because if the premises are true, then the conclusion has to be true. This can be proven for any valid argument form using a truth table which shows that there is no situation in which there are all true premises and a false conclusion. [2]
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.
In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa". [1]
A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).