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A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises ...
Deductive reasoning is the psychological process of drawing deductive inferences.An inference is a set of premises together with a conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises.
An argument is defined as a pair of things, namely a set of sentences, called the premises, [g] and a sentence, called the conclusion. [ 38 ] [ 34 ] [ 37 ] The conclusion is claimed to follow from the premises, [ 37 ] and the premises are claimed to support the conclusion.
An informal fallacy in which a conclusion is not logically justified by sufficient or unbiased evidence; drawing a general conclusion from a too-small sample size. Henkin semantics A generalization of standard first-order semantics that allows for models where the range of quantifiers can be restricted, named after Leon Henkin.
In natural language, an instance of the paradox of entailment arises: It is raining. And It is not raining. Therefore George Washington is made of rakes. This arises from the principle of explosion, a law of classical logic stating that inconsistent premises always make an argument valid; that is, inconsistent premises imply any conclusion at all.
A non-monotonic logic is a formal logic whose entailment relation is not monotonic.In other words, non-monotonic logics are devised to capture and represent defeasible inferences, i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. [1]
In deductive reasoning, a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion must be true. An example of a sound argument is the following well-known syllogism: (premises) All men are mortal.
With the advent of algebraic logic, it became apparent that classical propositional calculus admits other semantics.In Boolean-valued semantics (for classical propositional logic), the truth values are the elements of an arbitrary Boolean algebra; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element.