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sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on. The Epimenides...

formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way...

cannot imagine how F could be true; therefore F must be false. I cannot imagine how F could be false; therefore F must be true. Arguments from incredulity...

equality that must be true regardless of the value of its variables, or a statement that by definition (or construction) must be true. Where an accounting...

the first statement, and it must be true if and only if the original statement is true. Example 2 If an animal is a dog, then it has four legs. My cat has...

first part is false, and hence the second part must be true to ensure the two-part statement to be true, i.e., unicorns exist (this inference is known...

be wet. The street is wet. Therefore, it rained. Although it is possible that this conclusion is true, it does not necessarily mean it must be true....

paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc. It is a fragment of the more complex CTL*...

The inductive hypothesis holds true for n + 1 {\displaystyle n+1} , therefore it must be true ∀ n ∈ N {\displaystyle \forall n\in \mathbb...

no element of the domain of discourse for which the statement is true, then it must be false for all of those elements. That is, the negation of ∃ x ∈...

personal interpretations of the sentences) the sentence must be true if every sentence in the set is true. Logicians make precise accounts of logical consequence...

actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed...

The rule makes it possible to introduce disjunctions to logical proofs. It is the inference that if P is true, then P or Q must be true. An example in...

recognizing logically equivalent statements; and inferring what could be true or must be true from given facts and rules. Analytical reasoning is axiomatic in...

come out true. For if the first disjunct ( A ∧ B ) {\displaystyle (A\land B)} is not satisfied by a particular valuation, then A or B must be assigned...

Trek). 29c 16c "It Must Be True!" November 11, 1989 (1989-11-11) 216c Garfield presents a TV show to a live audience called It Must Be True! where he claims...

necessarily true statement must be true in all possible worlds. In modal logic, a proposition P {\displaystyle P} can be necessarily true or false (denoted...

is false or Y is true" (¬X ∨ Y). For example, given the statement "if you press the button then the light comes on", it must be true at any given moment...

man is free, and the ass is not, nevertheless for the same reason it must be true that in man likewise the case of a perfect equipoise between two courses...

the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false...