Timeline for Propositional logic --- syntactical completeness
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 23, 2014 at 18:31 | comment | added | zpavlinovic | Ok, this is what I had in mind when saying a subset of the FOL language. Thanks! | |
| Aug 23, 2014 at 16:24 | comment | added | Shaull | Well, PA is a first-order theory. There, propositional atoms are captured by 0-ary relations. In PA, there are no 0-ary relations, so you can't even say $p$. This makes this problem nonexistent. | |
| Aug 23, 2014 at 16:18 | comment | added | zpavlinovic | I'll try to do it here, as it is probably just my simple misunderstanding. Consider the theory of PA, and consider any propositional atom $p$. Then, again you cannot prove $p$ nor $\neg p$, hence incompleteness. We don't consider propositional atoms in PA? Basically, are we just focusing on a subset of FOL language in this case? | |
| Aug 23, 2014 at 15:50 | comment | added | Shaull | I don't really understand the question. Please elaborate, preferably as a new post. | |
| Aug 23, 2014 at 14:37 | comment | added | zpavlinovic | Simple follow-up question. Does one usually prove (in)completeness w.r.t. a subset of the language also? As far as I know, PA axioms do not tell anything about propositional atoms, so incompleteness would then trivially hold by my argument. | |
| Aug 23, 2014 at 14:11 | vote | accept | zpavlinovic | ||
| Aug 23, 2014 at 5:57 | history | answered | Shaull | CC BY-SA 3.0 |