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The reason for this is that these logics describe defeasible reasoning, and conditionals that appear in real-world contexts typically allow for exceptions, default assumptions, ceteris paribus conditions, or just simple uncertainty. An example, derived from Ernest W. Adams, [3] If Jones wins the election, Smith will retire after the election.
The act of combining simple objects or ideas into a complex whole, or the resulting combination itself. compositionality The principle in semantics that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. compound formula A formula representing a compound statement ...
A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
Simple propositions, on the other hand, do not have propositional parts. But they can also be conceived as having an internal structure: they are made up of subpropositional parts, like singular terms and predicates. [49] [48] For example, the simple proposition "Mars is red" can be formed by applying the predicate "red" to the singular term ...
[1] [13] Examples of such compound sentences might include: Wikipedia is a free online encyclopedia that anyone can edit, and millions already have. (conjunction) It is not true that all Wikipedia editors speak at least three languages. (negation) Either London is the capital of England, or London is the capital of the United Kingdom, or both ...
Each of the three distinct terms represents a category. From the example above, humans, mortal, and Greeks: mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, humans. Both of the premises are universal, as is the conclusion.
The proposition inferred from them is called the conclusion. [18] [19] For example, in the argument "all puppies are dogs; all dogs are animals; therefore all puppies are animals", the propositions "all puppies are dogs" and "all dogs are animals" act as premises while the proposition "all puppies are animals" is the conclusion. [21] [22]
Simple assertibles can be connected to each other to form compound or non-simple assertibles. [25] This is achieved through the use of logical connectives . [ 25 ] Chrysippus seems to have been responsible for introducing the three main types of connectives: the conditional ( if ), conjunctive ( and ), and disjunctive ( or ). [ 26 ]