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exam [2011/07/19 14:00] 131.246.18.253 [Calculi] |
exam [2011/07/19 14:16] 131.246.18.253 [Calculi] |
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| * A deductive system is sound if all provable formulas are valid. It is complete if all valid formulas are provable. | * A deductive system is sound if all provable formulas are valid. It is complete if all valid formulas are provable. | ||
| * Validity is a semantic property ($A \models B$), while provability a syntactic one ($A \vdash B$). So, in other words we have: | * Validity is a semantic property ($A \models B$), while provability a syntactic one ($A \vdash B$). So, in other words we have: | ||
| - | * Soundness: $A \vdash B \rightarrow A \models B$ | + | * Soundness: $A \vdash B \longrightarrow A \models B$ |
| - | * Completeness: $A \models B \rightarrow A \vdash B$ | + | * Completeness: $A \models B \longrightarrow A \vdash B$ |
| :?: What are the advantages/disadvantages of the Hilbert calculus compared to the Gentzen calculus. | :?: What are the advantages/disadvantages of the Hilbert calculus compared to the Gentzen calculus. | ||
exam.txt · Last modified: 2011/08/02 15:29 by 188.107.127.174
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