A model of a logic is a world where we can interpret the logic. Sometimes this is called semantics as opposed to the syntax of the logic. Then a tautology is defined to a sentence that is true in every possible model. Sometimes tautologies or logical truths are dismissed as being empty of content as they are merely deductively true.

2016年10月17日 · In mathematical logic, tautology means a propositional valid formula : a formula $\alpha$ is a tautoloy iff every truth assignment (for the sentence symbols in $\alpha$) satisfies it. The terms in natural language means : "saying the same thing twice". Thus, it stay for something redundant, not informative.

2016年5月23日 · To get an overview, consider also entry for "Circular reasoning" and "Tautology (logic)". Wikipedia currently says this about "tautology": In literary criticism and rhetoric, a tautology is a statement which repeats the same idea, using near-synonymous morphemes, words, or phrases, that is, "saying the same thing twice".

In logic, a tautology ... is a formula or assertion that is true in every possible interpretation. For propositional logic Wikipedia defines an interpretation as follows: The standard kind of interpretation in this setting is a function that maps each propositional symbol to one of the truth values true and false.

2019年9月26日 · In that world, "tautology" is firmly established as a "semantic" concept. (Or so I thought -- but see also Noah Schweber's answer which shows that he considers the word "tautology" to belong to the syntactic concept even when considering only logic. He and I agree about what is syntactic and what is semantic in that context, but not about the ...

2015年6月26日 · $\begingroup$ Is somebody demanding a proof from you? If so, you need to tell us which particular formal proof system they want you to use -- there are many possible ones which are structured quite differently (even though they prove the same things), and a hint that works with one may well be useless for another system.

2015年11月22日 · A tautology in first-order logic is a sentence that can be obtained by taking a tautology of propositional logic and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable).

2019年9月8日 · So, it's either contingent or a tautology. Ref; If a logic is a contradiction then it is said to be unsatisfiable. A formula is valid only if it is a tautology. Ref; A formula is invalid if it is contingent or a contradiction. Based on these definitions, I prepared a diagram showing how these concepts overlap:

2017年4月21日 · Is this predicate logic formula a tautology. 1. Satisfiability of predicate logic formulas. 0.

2019年9月30日 · Tautological Consequence (TautCon) is the rule by which you can introduce a previously established tautology. If it has been proven, or otherwise accepted, to be a tautology in the logic system being used, then you may use it. In this case you are using Law of Excluded Middle, which is accepted in classical logic, but not in constructive logic.