see also Mathematical proof, Proof theory, and Axiomatic system. A formal proof or derivation is a finite sequence of propositions (called well-formed formulas in the case of a formal language) each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system.

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  • see also Mathematical proof, Proof theory, and Axiomatic system. A formal proof or derivation is a finite sequence of propositions (called well-formed formulas in the case of a formal language) each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system. The notion of theorem is not in general effective, therefore there may be no method by which we can always find a proof of a given sentence or determine that none exists. The concept of natural deduction is a generalization of the concept of proof. The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus of some formal system to the previous well-formed formulae in the proof sequence. Formal proofs often are constructed with the help of computers in interactive theorem proving. Significantly, these proofs can be checked automatically, also by computer. Checking formal proofs is usually simple, whereas finding proofs is generally computationally hard.
  • Ein axiomatischer Beweis ist ein Beweis in einem axiomatischen Kalkül, das heißt ein Nachweis dafür, dass die zu beweisende Aussage alleine aus den Axiomen des jeweiligen Kalküls folgt. Jede Zeile eines axiomatischen Beweises ist entweder eine Einsetzungsinstanz eines Axioms oder das Ergebnis der Anwendung einer Schlussregel des jeweiligen Kalküls auf eine oder mehrere der vorangehenden Zeilen des Beweises.
  • La dimostrazione è una serie di ragionamenti logici che, partendo da una ipotesi, arrivano a dimostrare una tesi. Una dimostrazione consiste nel verificare - nel senso di mostrarne la ragionevole verità - un predicato, una frase; infatti, attraverso vari passaggi - e utilizzando per esempio assiomi e postulati - si rende innegabile un'affermazione.
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  • see also Mathematical proof, Proof theory, and Axiomatic system. A formal proof or derivation is a finite sequence of propositions (called well-formed formulas in the case of a formal language) each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference. The last sentence in the sequence is a theorem of a formal system.
  • Ein axiomatischer Beweis ist ein Beweis in einem axiomatischen Kalkül, das heißt ein Nachweis dafür, dass die zu beweisende Aussage alleine aus den Axiomen des jeweiligen Kalküls folgt. Jede Zeile eines axiomatischen Beweises ist entweder eine Einsetzungsinstanz eines Axioms oder das Ergebnis der Anwendung einer Schlussregel des jeweiligen Kalküls auf eine oder mehrere der vorangehenden Zeilen des Beweises.
  • La dimostrazione è una serie di ragionamenti logici che, partendo da una ipotesi, arrivano a dimostrare una tesi. Una dimostrazione consiste nel verificare - nel senso di mostrarne la ragionevole verità - un predicato, una frase; infatti, attraverso vari passaggi - e utilizzando per esempio assiomi e postulati - si rende innegabile un'affermazione.
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  • Formal proof
  • Axiomatischer Beweis
  • Dimostrazione
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