enow.com Web Search

Search results

1. Results from the WOW.Com Content Network

2. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.

3. Metamath - Wikipedia

   en.wikipedia.org/wiki/Metamath

   The Metamath Proof Explorer (recorded in set.mm) is the main database. It is based on classical first-order logic and ZFC set theory (with the addition of Tarski-Grothendieck set theory when needed, for example in category theory). The database has been maintained for over thirty years (the first proofs in set.mm are dated September 1992). The ...

4. Propositional calculus - Wikipedia

   en.wikipedia.org/wiki/Propositional_calculus

   The assumption set lists the assumptions on which the given sentence of proof depends, which are referenced by the line numbers. [38] The annotation specifies which rule of proof was applied, and to which earlier lines, to yield the current sentence. [38] See the § Natural deduction proof example.

5. Model theory - Wikipedia

   en.wikipedia.org/wiki/Model_theory

   A set of sentences is called a (first-order) theory, which takes the sentences in the set as its axioms. A theory is satisfiable if it has a model M ⊨ T {\displaystyle {\mathcal {M}}\models T} , i.e. a structure (of the appropriate signature) which satisfies all the sentences in the set T {\displaystyle T} .

6. Formal proof - Wikipedia

   en.wikipedia.org/wiki/Formal_proof

   In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence, according to the rule of inference.

7. First-order logic - Wikipedia

   en.wikipedia.org/wiki/First-order_logic

   An interpretation (or model) of a first-order formula specifies what each predicate means, and the entities that can instantiate the variables. These entities form the domain of discourse or universe, which is usually required to be a nonempty set. For example, consider the sentence "There exists x such that x is a philosopher."

8. Complete theory - Wikipedia

   en.wikipedia.org/wiki/Complete_theory

   For a set of formulas : if and only if or . Maximal consistent sets are a fundamental tool in the model theory of classical logic and modal logic . Their existence in a given case is usually a straightforward consequence of Zorn's lemma , based on the idea that a contradiction involves use of only finitely many premises.

9. List of set identities and relations - Wikipedia

   en.wikipedia.org/wiki/List_of_set_identities_and...

   To investigate the left distributivity of set subtraction over unions or intersections, consider how the sets involved in (both of) De Morgan's laws are all related: () = = () always holds (the equalities on the left and right are De Morgan's laws) but equality is not guaranteed in general (that is, the containment might be strict).