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exam [2011/07/13 15:18] 131.246.18.253 [Core HOL] |
exam [2011/07/19 14:16] 131.246.18.253 [Calculi] |
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| :?: Why do we need calculi. | :?: Why do we need calculi. | ||
| + | * Basically, calculi are the tools we use to derive (and prove) theorems. Given a set of valid formulas and a sound calculus, new valid formulas (tautologies) can be derived. As far as I know, the semantic notion of "validity" corresponds to "provability" in the calculus, since it does not consider any notion of "truth". | ||
| :?: Please explain the following properties: Soundness (Correctness), Completeness, ... | :?: Please explain the following properties: Soundness (Correctness), Completeness, ... | ||
| + | * 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: | ||
| + | * Soundness: $A \vdash B \longrightarrow A \models B$ | ||
| + | * 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 ยท Last modified: 2011/08/02 15:29 by 188.107.127.174
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