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Graphs such as these are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.
In logic, the law of non-contradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that propositions cannot both be true and false at the same time, e. g. the two propositions "the house is white" and "the house is not white" are mutually exclusive.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).
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, [4] [1] or sometimes zeroth-order logic.
Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc.
The entailment relations of paraconsistent logics are propositionally weaker than classical logic; that is, they deem fewer propositional inferences valid. The point is that a paraconsistent logic can never be a propositional extension of classical logic, that is, propositionally validate every entailment that classical logic does.
With the advent of algebraic logic, it became apparent that classical propositional calculus admits other semantics.In Boolean-valued semantics (for classical propositional logic), the truth values are the elements of an arbitrary Boolean algebra; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element.
Computational logic is the use of logic to perform or reason about computation.It bears a similar relationship to computer science and engineering as mathematical logic bears to mathematics and as philosophical logic bears to philosophy.