Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent...

yield full classical logic. Minimal logic + LEM + EFQ yields classical logic. PR entails but is not entailed by LEM in minimal logic. If the formula B in...

logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by...

the principle are provable in minimal logic, but the full principle itself is not provable even in intuitionistic logic. Consequentia mirabilis was a...

Intuitionistic logic Linear logic Many-valued logic Mathematical logic Metalogic Minimal logic Modal logic Non-Aristotelian logic Non-classical logic Noncommutative...

restricted to f-implicational formulas. Minimal logic: By limiting the natural deduction rules of this logic to Implication Introduction ( → {\displaystyle...

Constructive logic is a family of logics where proofs must be constructive (i.e., proving something means one must build or exhibit it, not just argue...

non-monotonic logic begins with restriction of the semantics of a suitable monotonic logic to some special models, for instance, to minimal models, and...

N} , hence the above sentential logic proof can be duplicated in the calculus: ⊢ ( ( m X ) X )  by the minimal logic axiom  A → A ⊢ ( ( m X ) ( ( m X...

Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion...

of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the logical structure of valid arguments. If an argument...

In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms...

axioms describe classical propositional logic; without axiom P4 we get positive implicational logic. Minimal logic is achieved either by adding instead the...

Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical...

Logic programming is a programming paradigm that includes languages based on formal logic, including Datalog and Prolog. This article describes the syntax...

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had...

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid...

excluded middle already over minimal logic. This also means that Piece's law entails classical logic over intuitionistic logic. This is shown below. Firstly...

M N O P Q R S T U V W X Y Z A System of Logic -- A priori and a posteriori -- Abacus logic -- Abduction (logic) -- Abductive validation -- Academia Analitica...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

strength of logics without the principle of explosion are discussed in minimal logic. Consequentia mirabilis – Clavius' Law Dialetheism – belief in the existence...

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can...

write one to the bus. Buffer amplifier Logic level Metastability Three-valued logic Four-valued logic Nine-valued logic Don't care Single pole, centre off...

business logic layer which is separate from other tiers or layers, such as the data access layer or service layer. Each layer "knows" only a minimal amount...

A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing...

elimination is a theorem of classical logic, but not of weaker logics such as intuitionistic logic and minimal logic. Double negation introduction is a theorem...

((P\land Q)\rightarrow R)} . This already holds in minimal logic, and thus also in classical logic, where the conditional operator " → {\displaystyle...

MINLOG – A proof assistant based on first-order minimal logic. Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck...

form of the logic in the original truth table. These terms can be used to write a minimal Boolean expression representing the required logic. Karnaugh maps...

In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent...