For the idea in philosophy of mind, see Multiple realizability.
In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them.[1] Formulas from a formal theory are "realized" by objects, known as "realizers", in a way that knowledge of the realizer gives knowledge about the truth of the formula. There are many variations of realizability; exactly which class of formulas is studied and which objects are realizers differ from one variation to another.
Realizability can be seen as a formalization of the BHK interpretation of intuitionistic logic; in realizability the notion of "proof" (which is left undefined in the BHK interpretation) is replaced with a formal notion of "realizer". Most variants of realizability begin with a theorem that any statement that is provable in the formal system being studied is realizable. The realizer, however, usually gives more information about the formula than a formal proof would directly provide.
Beyond giving insight into intuitionistic provability, realizability can be applied to prove the disjunction and existence properties for intuitionistic theories and to extract programs from proofs, as in proof mining. It is also related to topos theory via realizability topoi.
of realizability; exactly which class of formulas is studied and which objects are realizers differ from one variation to another. Realizability can...
physical states to mental states. Multiple realizability in general is not restricted to the multiple realizability of mental states. Many kinds of things...
the type identity theory is the argument from multiple realizability. The multiple realizability thesis asserts that mental states can be realized in multiple...
example of multiple realizability. This is sometimes called the "likelihood argument", as it focuses on the claim that multiple realizability is more likely...
Net realizable value (NRV) is a measure of a fixed or current asset's worth when held in inventory, in the field of accounting. NRV is part of the Generally...
{\displaystyle {\mathcal {K}}_{1}} . In Kleene's notion of recursive realizability, any predicate is assigned realizing numbers, i.e. a subset of N {\displaystyle...
the view that we fix a computational system up front, and then give a realizability interpretation of propositions to give them constructive content. For...
the multiple realizability argument, and it is not clear that token physicalism is susceptible to objections from multiple realizability. There are two...
Pěstování Matematiky (in Czech), 80: 477–480. Hakimi, S. L. (1962), "On realizability of a set of integers as degrees of the vertices of a linear graph. I"...
intuitionism. Using tools from recursion theory, he introduced recursive realizability, an important technique for interpreting intuitionistic statements....
{R} ^{3})=\Omega _{\mathbb {R} /\mathbb {Q} }^{1}} is an obstacle to realizability: its nonzero elements come from elements of R ⊗ Z R / 2 π Z {\displaystyle...
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of...
is not realizable in the Euclidean plane, but it is realizable in the complex plane. On the other hand, examples 2 and 5 above are realizable and the...
junctions and rapid single flux quantum technology, are becoming more nearly realizable with the discovery of nanoscale superconductors. Fiber-optic and photonic...
remains the dominant theory. Type identity was criticized using multiple realizability. Searle's Chinese room argument criticized functionalism and holds that...
between regions and between different types of outlet: The ideal, rarely realizable in practice, would consist of estimates of expenditure for each detailed...
Torque bursts two to three times higher than the maximum design torque are realizable. The brushless wound-rotor synchronous doubly-fed (BWRSDF) machine is...
would yield a chain of bi-connected 4-rings. These structures may not be realizable. The thinnest carbon nanotube proper is the armchair structure with type...
complete category. It is used to form the effective topos and other realizability toposes. Let C be a category with finite limits. Then the exact completion...
universal and inalienable is to be taken seriously, the rights must be realizable given the features of the modern liberal state. She concluded "The Rights...
the existence property. Kleene's method introduced the technique of realizability, which is now one of the main methods in the study of constructive theories...
theoretical but realizable ideal. By virtue of the cogency, clarity, and veracity of his portrayal of some of the key characteristics of realizable-ideal democracy...
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