منابع مشابه
Modes of Adjointness
The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues relate...
متن کاملEssential self - adjointness
1. Cautionary example 2. Criterion for essential self-adjointness 3. Examples of essentially self-adjoint operators 4. Appendix: Friedrichs' canonical self-adjoint extensions 5. The following has been well understood for 70-120 years, or longer, naturally not in contemporary terminology. The differential operator T = d 2 dx 2 on L 2 [a, b] or L 2 (R) is a prototypical natural unbounded operator...
متن کاملOn monotone modalities and adjointness
We fix a logical connection (Stone Pred : Set op −→ BA given by 2 as a schizophrenic object) and study coalgebraic modal logic that is induced by a functor T : Set −→ Set which is finitary, standard, preserves weak pullbacks and finite sets. We prove that for any such T , the cover modality nabla is a left (and its dual delta is a right) adjoint relative to Pω. We then consider monotone unary m...
متن کاملPartiality and Adjointness in Modal Logic
Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standa...
متن کاملContinuation semantics and self-adjointness
We give an abstract categorical presentation of continuation semantics by taking the continuation type constructor : (or cont in Standard ML of New Jersey) as primitive. This constructor on types extends to a contravariant functor on terms which is adjoint to itself on the left; restricted to the subcategory of those programs that do not manipulate the current continuation, it is adjoint to its...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1986
ISSN: 0168-0072
DOI: 10.1016/0168-0072(86)90056-4