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Constructive Dilemma
Constructive dilemmaCopi and Cohen is a valid rule of inference of propositional logic. It is the inference that, if ''P'' implies ''Q'' and ''R'' implies ''S'' and either ''P'' or ''R'' is true, then either ''Q or S'' has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too. ''Constructive dilemma'' is the disjunctive version of modus ponens, whereas, destructive dilemma is the disjunctive version of ''modus tollens''. The constructive dilemma rule can be stated: :\frac where the rule is that whenever instances of "P \to Q", "R \to S", and "P \lor R" appear on lines of a proof, "Q \lor S" can be placed on a subsequent line. Formal notation The ''constructive dilemma'' rule may be written in sequent notation: : (P \to Q), (R \to S), (P \lor R) \vdash (Q \lor S) where \vdash is a metalogical symbol meaning that Q \lor S is a syntactic consequence of P \to Q, R \to S, and P \lor R in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Inference
In the philosophy of 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. r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |