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definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
A proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true in all possible worlds and under all interpretations of its non-logical terms, like the claim "either it is raining, or it is not". [15] These two definitions of formal logic are not identical, but they are closely related.
Logical constants are always given the same meaning by every interpretation of the standard kind, so that only the meanings of the non-logical symbols are changed. Logical constants include quantifier symbols ∀ ("all") and ∃ ("some"), symbols for logical connectives ∧ ("and"), ∨ ("or"), ¬ ("not"), parentheses and other grouping symbols ...
Forms of logical reasoning can be distinguished based on how the premises support the conclusion. Deductive arguments offer the strongest possible support. Non-deductive arguments are weaker but are nonetheless correct forms of reasoning. [28] [29] The term "proof" is often used for deductive arguments or very strong non-deductive arguments. [30]
A term used to describe non-standard or alternative logical systems that deviate from classical logic. diagonalization lemma A lemma used in the proof of Gödel's incompleteness theorems, stating that for any formula with one free variable, there exists a sentence that asserts its own unprovability.
The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...
In logic and semantics, the term statement is variously understood to mean either: a meaningful declarative sentence that is true or false, [citation needed] or; a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence. [1] [2]
The term was translated into English from Latin in the 16th century. The Latin version, petitio principii ' asking for the starting point ' , can be interpreted in different ways. Petitio (from peto ), in the post-classical context in which the phrase arose, means ' assuming ' or ' postulating ' , but in the older classical sense means ...