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...

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

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

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...

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

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...

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

In model theory, a branch of mathematical logic, a C-minimal theory is a theory that is "minimal" with respect to a ternary relation C with certain properties...

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

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...

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

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...

Logic redundancy occurs in a digital gate network containing circuitry that does not affect the static logic function. There are several reasons why logic...

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...

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...

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

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...

{\displaystyle {\mathsf {PA}}\vdash \psi \iff {\mathsf {HA}}\vdash \psi } . Minimal logic proves double-negation elimination for negated formulas, ¬ ¬ ( ¬ α )...

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...

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...

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

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

the principle is as a special case of Frege's theorem, already in minimal logic. Another derivation makes use of A → ¬ B {\displaystyle A\to \neg B}...

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...

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...