Fitting semantics for modal logic
E504785
Kripke-style semantics
intuitionistic-style semantics
logical framework
possible-worlds semantics
semantics for modal logic
Fitting semantics for modal logic is a framework in mathematical logic that extends Kripke-style semantics to provide a more general and often intuitionistic treatment of modal operators.
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
Kripke-style semantics
ⓘ
intuitionistic-style semantics ⓘ logical framework ⓘ possible-worlds semantics ⓘ semantics for modal logic ⓘ |
| aimsAt |
more general semantics than standard Kripke frames
ⓘ
unified treatment of modal and intuitionistic operators ⓘ |
| appliesTo |
intuitionistic modal logics
ⓘ
modal logics ⓘ non-classical logics ⓘ |
| characteristicFeature |
combination of Kripke accessibility with intuitionistic preorder
ⓘ
evaluation of formulas at ordered pairs of worlds and states ⓘ intuitionistic treatment of implication and necessity ⓘ use of partial orders on worlds ⓘ |
| clarifies |
interaction between modality and intuitionistic implication
ⓘ
relationship between constructive truth and necessity ⓘ |
| ensures | monotonicity of truth with respect to the underlying order ⓘ |
| extends | Kripke semantics for modal logic ⓘ |
| field |
mathematical logic
ⓘ
modal logic ⓘ model theory ⓘ proof theory ⓘ |
| generalizes | Kripke semantics for modal logic ⓘ |
| hasComponent |
accessibility relation between worlds
ⓘ
preorder or partial order on worlds ⓘ valuation function respecting intuitionistic monotonicity ⓘ |
| influencedBy |
Kripke semantics for intuitionistic logic
ⓘ
classical Kripke semantics for modal logic ⓘ |
| influences |
research on intuitionistic modal logics
ⓘ
semantics for non-normal modal logics ⓘ |
| namedAfter | Melvin Fitting NERFINISHED ⓘ |
| relatedTo |
Kripke semantics for intuitionistic logic
ⓘ
neighborhood semantics ⓘ possible-worlds semantics for modal logic ⓘ topological semantics for modal logic ⓘ |
| supports |
constructive reasoning about necessity and possibility
ⓘ
intuitionistic interpretation of modal operators ⓘ |
| typicalApplication |
semantics of knowledge and belief in constructive settings
ⓘ
semantics of provability modalities ⓘ |
| usedFor |
completeness proofs for modal systems
ⓘ
correspondence results between syntax and semantics ⓘ soundness proofs for modal systems ⓘ |
Referenced by (1)
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