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The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method ...

Modus tollens is a valid argument form in propositional calculus in which p and q are propositions. If p implies q, and q is false, then p is false. Also known as an indirect ...

A generalization of a Heyting algebra which replaces Boolean algebra in "intuitionistic" logic.

A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

A statement which is rigorously not true. Regular two-valued logic allows statements to be only true or false, but fuzzy logic treats "truth" as a continuum which can have a ...

A constructive proof is a proof that directly provides a specific example, or which gives an algorithm for producing an example. Constructive proofs are also called ...

The branch of formal logic, also called functional calculus, that deals with representing the logical connections between statements as well as the statements themselves.

A premise is a statement that is assumed to be true. Formal logic uses a set of premises and syllogisms to arrive at a conclusion.

The symbol ¬ used to denote the negation operation ("NOT") in symbolic logic, also called "logical not."

A formal argument in logic in which it is stated that (1) P=>Q and R=>S (where => means "implies"), and (2) either P or R is true, from which two statements it follows that ...