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Absorption / modus tollens / modus ponendo tollens
Negation introduction
Rules of replacement
Associativity
Commutativity
Distributivity
Double negation
De Morgan's laws
Transposition
Material implication
Exportation
Tautology
Predicate logic
Rules of inference
Universal generalization / instantiation
Existential generalization / instantiation
A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.
A conditionalproof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to...
cause of Y Conditional probability, the probability of an event A given that another event B has occurred Conditionalproof, in logic: a proof that asserts...
also be characterized inferentially by modus ponens, modus tollens, conditionalproof, and classical reductio ad absurdum.[citation needed] Material implication...
hypothetical syllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises. Ancient references point to...
of proof of capacity was Signum (formerly burstcoin). The Proof of Capacity (PoC) consensus algorithm is used in some cryptocurrencies. Conditional Proof...
of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive...
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of...
accompanying modus ponens. In this sense, DT corresponds to the natural conditionalproof inference rule which is part of the first version of propositional...
The validity of this argument structure can be shown by using both conditionalproof (CP) and reductio ad absurdum (RAA) in the following way: Hurley,...
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated...
logic, a deduction theorem is a metatheorem that justifies doing conditionalproofs from a hypothesis in systems that do not explicitly axiomatize that...
science, the method of conditional probabilities is a systematic method for converting non-constructive probabilistic existence proofs into efficient deterministic...
this conjecture is given by Nathan Ng. In particular, Ng gives a conditionalproof that the function e − y / 2 M ( e y ) {\displaystyle e^{-y/2}M(e^{y})}...
conjecture has been stated) and conjectures for which it gives a conditionalproof. The consequences include: Roth's theorem on Diophantine approximation...
regular conditional probability is a concept that formalizes the notion of conditioning on the outcome of a random variable. The resulting conditional probability...
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y {\displaystyle...
without making any further assumptions. In order to directly prove a conditional statement of the form "If p, then q", it suffices to consider the situations...
two types of justification for a node. They are: Support list [SL] Conditionalproof (CP) Many kinds of truth maintenance systems exist. Two major types...
Christian theology, conditionalism or conditional immortality is a concept in which the gift of immortality is attached to (conditional upon) belief in Jesus...
and elimination are just special cases of implication introduction (conditionalproof) and elimination (modus ponens). In this case one must also add as...
the antecedent Theorem Axiom Axiomatic system Axiomatization Conditionalproof Invalid proof Degree of truth Truth Truth condition Truth function Double...
simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical...
premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not...
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to...