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 classical logic, a 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 the works of Theophrastus and Eudemus for the first investigation of this kind of syllogisms.[1][2]
^"History of Logic: Theophrastus of Eresus" in Encyclopædia Britannica Online.
^Susanne Bobzien,"The Development of Modus Ponens in Antiquity: "From Aristotle to the 2nd Century AD", Phronesis, Vol. 47, No. 4 (2002), pp. 359-394.
and 28 Related for: Hypothetical syllogism information
In classical logic, a hypotheticalsyllogism is a valid argument form, a deductive syllogism with a conditional statement for one or both of its premises...
disjunction elimination. Other forms of syllogism include: hypotheticalsyllogism categorical syllogism Disjunctive syllogism holds in classical propositional...
not win the Super Bowl Much like modus ponens and modus tollens, hypotheticalsyllogism (sometimes abbreviated as HS) contains two premises and a conclusion...
sky. There are no clouds in the sky. Thus, it is not raining. A hypotheticalsyllogism is an inference that takes two conditional statements and forms...
argument form and a rule of inference. Modus tollens is a mixed hypotheticalsyllogism that takes the form of "If P, then Q. Not Q. Therefore, not P."...
true. Therefore, Q must also be true." Modus ponens is a mixed hypotheticalsyllogism and is closely related to another valid form of argument, modus...
Hypotheticalsyllogism (HS2) ( p → q ) → ( ( q → r ) → ( p → r ) ) {\displaystyle (p\to q)\to ((q\to r)\to (p\to r))} - another form of Hypothetical syllogism...
q\to (r\to q)} by φ0. We also use repeatedly the method of the hypotheticalsyllogism metatheorem as a shorthand for several proof steps. (1) φ 0 {\displaystyle...
(p\to r))} - another form of Hypothetical syllogism. We also use the method of the hypotheticalsyllogism metatheorem as a shorthand for several proof...
Prior Analytics. He was responsible for the introduction of the hypotheticalsyllogism and temporal modal logic. Further innovations include inductive...
left unsatisfied in the derivation, then the derivation is a proof of a hypothetical statement: "if the premises hold, then the conclusion holds." In a Hilbert...
syllogistic fallacy. Types of syllogism to which it applies include statistical syllogism, hypotheticalsyllogism, and categorical syllogism, all of which must have...
arguments from analogy. Common deductive argument forms are hypotheticalsyllogism, categorical syllogism, argument by definition, argument based on mathematics...
multi-premise syllogism, sorites, climax, or gradatio) is a string of any number of propositions forming together a sequence of syllogisms such that the...
A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization...
From Hamilton 1860:241–242: “2°, "If the essential nature of an HypotheticalSyllogism consist in this, – that the subsumption affirms or denies one or...
therefore, statement A is true of all things B.") Type of syllogism (disjunctive, hypothetical, legal, poly-, prosleptic, quasi-, statistical) "History...
world, cosmos, or universe was said, by Kant, to originate from the hypotheticalsyllogism (If A is x, then B is y; A is x; Therefore, B is y). Schopenhauer...
filename extension Heat sink Higman–Sims group, in mathematics Hypotheticalsyllogism, a proof rule in classical logic Horizon scanning, a method from...
Avicenna's system of logic was responsible for the introduction of hypotheticalsyllogism, temporal modal logic and inductive logic. Other important developments...
{\displaystyle P\leftrightarrow Q} ). Of the possible forms of "mixed hypotheticalsyllogisms," two are valid and two are invalid. Affirming the antecedent (modus...
Global Information
