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- Adverb phrase as antecedent g. Fred works hard, but Tom does not do the same. - Verb phrase as antecedent h. Susan lies all the time, which everybody knows about. - Entire clause as antecedent i. Our politicians have been pandering again. This demotivates the voters. - Entire sentence as antecedent j. Rob is a dentist and, as such, he fixes ...
In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") [2] and denying the consequent, [3] is a deductive argument form and a rule of inference.
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as "P implies Q. P is true. Therefore, Q ...
– The anaphor they has a split antecedent, referring to both Carol and Bob. b. When Carol i helps Bob i and Bob i helps Carol i, they i can accomplish any task. – The anaphor they has a split antecedent, referring to both Carol and Bob. Coreferring noun phrases a. The project leader i is refusing to help. The jerk i thinks only of himself i.
An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the protasis. [1] Examples: If , then . This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q.
The antecedent, therefore, becomes the new goal: Fritz is a frog 2. Again substituting Fritz for X, rule #1 becomes: If Fritz croaks and Fritz eats flies – Then Fritz is a frog Since the consequent matches the current goal ("Fritz is a frog"), the inference engine now needs to see if the antecedent ("Fritz croaks and eats flies") can be proven.
In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates Antecedent Strengthening. To see why, observe that if P → Q {\displaystyle P\rightarrow Q} holds at every world accessible from w {\displaystyle w} , the monotonicity of the material conditional guarantees ...
The name denying the antecedent derives from the premise "not P", which denies the "if" clause (antecedent) of the conditional premise. The only situation where one may deny the antecedent would be if the antecedent and consequent represent the same proposition, in which case the argument is trivially valid (and it would beg the question ...