Report
Action Logic is Undecidable
| Τίτλος: | Action Logic is Undecidable |
|---|---|
| Συγγραφείς: | Kuznetsov, Stepan |
| Έτος έκδοσης: | 2019 |
| Συλλογή: | Computer Science Mathematics |
| Θεματικοί όροι: | Computer Science - Logic in Computer Science, Mathematics - Logic, F.4.1, I.2.3, F.4.1, I.2.3 |
| Περιγραφή: | Action logic is the algebraic logic (inequational theory) of residuated Kleene lattices. This logic involves Kleene star, axiomatized by an induction scheme. For a stronger system which uses an $\omega$-rule instead (infinitary action logic) Buszkowski and Palka (2007) have proved $\Pi_1^0$-completeness (thus, undecidability). Decidability of action logic itself was an open question, raised by D. Kozen in 1994. In this article, we show that it is undecidable, more precisely, $\Sigma_1^0$-complete. We also prove the same complexity results for all recursively enumerable logics between action logic and infinitary action logic; for fragments of those only one of the two lattice (additive) connectives; for action logic extended with the law of distributivity. Comment: 33 pages |
| Τύπος εγγράφου: | Working Paper |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/1912.11273 |
| Αριθμός Καταχώρησης: | edsarx.1912.11273 |
| Βάση Δεδομένων: | arXiv |
| Η περιγραφή δεν είναι διαθέσιμη |