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A second-order stimulus is a type of visual stimulus employed in psychophysics where objects are distinguished from their backgrounds through variations in contrast or texture. In contrast, a stimulus distinguished by differences in luminance is termed a first-order stimulus.
An example of second-order conditioning. In classical conditioning, second-order conditioning or higher-order conditioning is a form of learning in which a stimulus is first made meaningful or consequential for an organism through an initial step of learning, and then that stimulus is used as a basis for learning about some new stimulus.
In the monadic second-order logic of graphs, the variables represent objects of up to four types: vertices, edges, sets of vertices, and sets of edges. There are two main variations of monadic second-order graph logic: MSO 1 in which only vertex and vertex set variables are allowed, and MSO 2 in which all four types of variables are allowed ...
first order The first order logic of graphs is a form of logic in which variables represent vertices of a graph, and there exists a binary predicate to test whether two vertices are adjacent. To be distinguished from second order logic, in which variables can also represent sets of vertices or edges.-flap
The satisfiability problem for monadic second-order logic is undecidable in general because this logic subsumes first-order logic. The monadic second-order theory of the infinite complete binary tree, called S2S, is decidable. [8] As a consequence of this result, the following theories are decidable: The monadic second-order theory of trees.
Higher-order logic is an extension of first-order logic and second-order logic with higher-order quantifiers. There is a relation between the i {\displaystyle i} th order and non-deterministic algorithms the time of which is bounded by i − 1 {\displaystyle i-1} levels of exponentials.
Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for "∃y t∈y" Some first-order set theories include: Weak theories lacking powersets:
As a result, second-order logic has greater expressive power than first-order logic. For example, there is no way in first-order logic to identify the set of all cubes and tetrahedrons. But the existence of this set can be asserted in second-order logic as: ∃P ∀x (Px ↔ (Cube(x) ∨ Tet(x))). We can then assert properties of this set.