Name
Abstract | ||
|---|---|---|
Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general \({\varvec{A}}\)-frames over a given residuated lattice \({\varvec{A}}\) (i.e., the usual frames with a collection of admissible \({\varvec{A}}\)-valued sets). We describe in detail the relation between general Kripke and neighborhood \({\varvec{A}}\)-frames and prove that, if the logic of \({\varvec{A}}\) is finitary, all extensions of the corresponding logic E of \({\varvec{A}}\) are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1007/s00500-018-3369-5 | soft computing |
Keywords | Field | DocType |
Modal many-valued logics, Mathematical fuzzy logic, Neighborhood frames, Kripke semantics, General frames | Residuated lattice,Discrete mathematics,Kripke semantics,Generalization,Computer science,General frame,Theoretical computer science,Finitary,Frame semantics,Completeness (statistics),Modal | Journal |
Volume | Issue | ISSN |
23 | SP7 | 1433-7479 |
Citations | PageRank | References |
0 | 0.34 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petr Cintula | 1 | 601 | 50.37 |
| Paula Menchón | 2 | 0 | 0.34 |
| Carles Noguera | 3 | 462 | 33.93 |