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Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. [2] A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (equiv ...
ABA is an applied science devoted to developing procedures which will produce observable changes in behavior. [3] [9] It is to be distinguished from the experimental analysis of behavior, which focuses on basic experimental research, [10] but it uses principles developed by such research, in particular operant conditioning and classical conditioning.
Not all tautologies of classical logic lift to Ł3 "as is". For example, the law of excluded middle, A ∨ ¬A, and the law of non-contradiction, ¬(A ∧ ¬A) are not tautologies in Ł3. However, using the operator I defined above, it is possible to state tautologies that are their analogues: A ∨ IA ∨ ¬A (law of excluded fourth)
However, the term tautology is also commonly used to refer to what could more specifically be called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias . Illustrating a general tendency in applied logic, Aristotle 's law of noncontradiction states that "It is impossible that the same thing can at the same time both ...
The Autism Treatment Evaluation Scale (ATEC) is a 77-item diagnostic assessment tool that was developed by Bernard Rimland and Stephen Edelson at the Autism Research Institute.
Of its five connectives, {∧, ∨, →, ¬, ⊥}, only negation "¬" can be reduced to other connectives (see False (logic) § False, negation and contradiction for more). Neither conjunction, disjunction, nor material conditional has an equivalent form constructed from the other four logical connectives.