Search results
Results From The WOW.Com Content Network
A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must be true if every sentence in the set is true.
The hearer can now draw the contextual implications that +> Susan needs to be cheered up. +> Peter wants me to ring Susan and cheer her up. If Peter intended the hearer to come to these implications, they are implicated conclusions. Implicated premises and conclusions are the two types of implicatures in the relevance theoretical sense. [51]
An argument (consisting of premises and a conclusion) is valid if and only if there is no possible situation in which all the premises are true and the conclusion is false. For example a valid argument might run: If it is raining, water exists (1st premise) It is raining (2nd premise) Water exists (Conclusion)
In the implication " implies ", is called the antecedent and is called the consequent. [2] Antecedent and consequent are connected via logical connective to form a proposition . If X {\displaystyle X} is a man, then X {\displaystyle X} is mortal.
In a Hilbert system, the premises and conclusion of the inference rules are simply formulae of some language, usually employing metavariables.For graphical compactness of the presentation and to emphasize the distinction between axioms and rules of inference, this section uses the sequent notation instead of a vertical presentation of rules.
This function maps sentences of the first system to sentences of the second system while obeying the entailment relations between the original sentences. This means that if a sentence entails another sentence in the first logic, then the translation of the first sentence should entail the translation of the second sentence in the second logic.
Going from a statement to its converse is the fallacy of affirming the consequent.However, if the statement S and its converse are equivalent (i.e., P is true if and only if Q is also true), then affirming the consequent will be valid.
A is the premise and B is the conclusion of the implication A→B . A set C respects the implication A → B when ¬( C ⊆ A ) or C ⊆ B . A formal context is a triple (G,M,I) , where G and M are sets (of objects and attributes , respectively), and where I ⊆ G × M is a relation expressing which objects have which attributes.