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
In philosophy of logic and logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion.
Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the conclusion of a given set of formulae according to the rule. An example of a rule that is not effective in this sense is the infinitary ω-rule.[1]
Popular rules of inference in propositional logic include modus ponens, modus tollens, and contraposition. First-order predicate logic uses rules of inference to deal with logical quantifiers.
^Boolos, George; Burgess, John; Jeffrey, Richard C. (2007). Computability and logic. Cambridge: Cambridge University Press. p. 364. ISBN 978-0-521-87752-7.
In philosophy of logic and logic, a ruleofinference, inferencerule or transformation rule is a logical form consisting of a function which takes premises...
This is a list ofrulesofinference, logical laws that relate to mathematical formulae. Rulesofinference are syntactical transform rules which one can...
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is...
interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, by contrast, focuses on rulesofinference, that...
In the field of artificial intelligence, an inference engine is a software component of an intelligent system that applies logical rules to the knowledge...
formal proof systems the same conveniency is provided by an explicit inferencerule; for example natural deduction calls it implication introduction. In...
with definitory rules, i.e. with the question of which rulesofinference determine whether an argument is valid or not. A separate topic of inquiry concerns...
Bayesian inference (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is a method of statistical inference in which Bayes' theorem is used to update the probability...
Unspoken rule, an assumed ruleof human behavior that is not voiced or written down Slide rule, a mechanical analog computer Ruleofinference or transformation...
Latin 'method of putting by placing'), implication elimination, or affirming the antecedent, is a deductive argument form and ruleofinference. It can be...
\\\end{aligned}}} A ruleofinference is a rule justifying a logical step from hypothesis to conclusion. There are several rulesofinference which utilize...
concept of a ruleofinference. Logical positivism was a movement in the early 20th century that tried to reduce the reasoning processes of science to...
abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations...
or elimination, or abbreviated ∨E), is a valid ruleofinference. If it is known that at least one of two statements is true, and that it is not the former...
another inferencerule, accompanying modus ponens. In this sense, DT corresponds to the natural conditional proof inferencerule which is part of the first...
natural deduction setting is to take as primitive rulesofinference negation introduction (from a derivation of P {\displaystyle P} to both Q {\displaystyle...
by a ruleofinference. It differs from a natural language argument in that it is rigorous, unambiguous and mechanically verifiable. If the set of assumptions...
Global Information