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In this respect the hierarchical approach does not fit the framework outlined in Section 2, because the language does not feature a single unary truth predicate applying to sentences but rather many unary truth predicates or a single binary truth predicate (or even a single unary truth predicate applying to pairs of ordinal notations and sentences).
That is, the proposed MSPN models the joint distribution of multiscale unary potentials and object classes instead of single unary potentials in popular settings.
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To explain the sequential algorithm more clearly, we assume a simpler labeling problem on a single image with unary and smoothness energies but without the consistency term between the left and right images.
Constants can be simulated by the use of unary relations that are true of single things.
They are unary quantifiers because they require a single argument in order to form a sentence of the form $\forall x \ A$ or $\exists x \ A$.
For a compact representation, all chains of unary nodes are collapsed into a single arc, so that the resulting structure is linear in the length of the string.
An important class of these identity statements are statements of the form 'ƒ(x) = y', where ƒ is any unary function (i.e., function of a single variable), x is the argument of the function, and ƒ(x) is the value of the function for the argument x.
A unary connective $*$ is a perfect negation with respect to a single-conclusion consequence relation $\vdash $from the syntactic point of view if the relation $\vdash$ is strongly symmetrical with respect to $*$.
The tree edges can be unary (ordinary) or binary, i.e., pairs of unary edges originated from a single vertex.
Multiscale unary potentials at different scales can thus help overcome semantic ambiguities caused by only evaluating single local regions, while long-range spatial correlations can further refine image labeling.
The diagram is a representation of a one-component (unary) system, in contrast to a two-component (binary), three-component (ternary), or four-component (quaternary) system.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com