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...

minimal logic, the system defines intuitionistic logic. The statement P → ¬ ¬ P {\displaystyle P\to \neg \neg P} is valid (already in minimal logic,...

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

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

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

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...

one obtains (the implicational fragment of) minimal logic (as defined by Johansson). Intuitionistic logic: By adding Falsum Elimination ( ⊥ {\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...

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

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

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

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

The vi editor employed minimal logic that would aid the user. This included trivial aids such as how to join two lines together and maintain reasonable...

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

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

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...

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...

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

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

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 logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining...

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...

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...

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

In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to...

In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example...

of Horn clauses in the context of logic programming, showing that every set of definite clauses D has a unique minimal model M. An atomic formula A is logically...