Logical truth

A fact is a true datum about one or more aspects of a circumstance, or an occurrence in the real world. Standard reference works are often used to check facts. Scientific facts are verified by careful, repeatable observation or measurement by experiments or other means. Generally speaking, facts are independent of belief, knowledge and opinion. Facts are different from inferences, theories, values, and objects.

logical formula which is true in every possible interpretation

value indicating the relation of a proposition to truth

logical correctness of an argument's steps, regardless of the truth of the premises

statement which is true regardless of the truth or falsity of its constituent parts

sufficient evidence or a sufficient argument for the truth of a proposition

Way of arriving to a mathematical proof

term in logic

mathematical function

1951 philosophy article by Willard Van Orman Quine

establishment of a theorem using inference from the axioms

In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x+3=y is satisfiable because it is true when x=3 and y=6, while the formula x+1=x is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, x+3=3+x is valid over the integers, but x+3=y is not.

statement that can be expressed in the form of a conditional statement with a false antecedent

form for logical arguments, obtained by abstracting from the subject matter of its content terms

concept in logic; syntactic transformation on formal expressions

Condition required for a semantic statement to be true

rule for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language