User:IssaRice/Computability and logic/Logic versus theory: Difference between revisions
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Many terms in mathematical logic apply to both logics and to theories. In these cases, the terms mean different things depending on what object it applies to. This distinction is similar to the distinction between truth-in-all-interpretations and truth-in-intended-interpretation. | Many terms in mathematical logic apply to both logics and to theories. In these cases, the terms mean different things depending on what object it applies to. This distinction is similar to the distinction between [[../Intended interpretation versus all interpretations|truth-in-all-interpretations and truth-in-intended-interpretation]]. | ||
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! Term !! Meaning for logic !! Meaning for theory | ! Term !! Meaning for logic !! Meaning for theory | ||
|- | |- | ||
| Sound | | Sound || || | ||
|- | |- | ||
| Complete | | Complete || || | ||
|- | |- | ||
| Decidable | | Decidable || || | ||
|- | |- | ||
| Defines/expresses | | Provable || For a logic, "provable" means "provable using the proof system and logical axioms". || For a theory, "provable" means "provable using the proof system, logical axioms, and non-logical axioms". The non-logical axioms are specific to each theory. | ||
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| Defines/expresses? | |||
|} | |} | ||
Latest revision as of 21:09, 9 February 2019
Many terms in mathematical logic apply to both logics and to theories. In these cases, the terms mean different things depending on what object it applies to. This distinction is similar to the distinction between truth-in-all-interpretations and truth-in-intended-interpretation.
| Term | Meaning for logic | Meaning for theory |
|---|---|---|
| Sound | ||
| Complete | ||
| Decidable | ||
| Provable | For a logic, "provable" means "provable using the proof system and logical axioms". | For a theory, "provable" means "provable using the proof system, logical axioms, and non-logical axioms". The non-logical axioms are specific to each theory. |
| Defines/expresses? |