Generalization similar object types are abstracted into a higher level object type via the is-a relationship 3 (for example, an employee is a person). Association: several object types are considered as a higher level set object- type via the is-a-member-of relationship (for example, the sets \men" and \women" are members of the set \sex-groups"). Association is also likely to be encountered under the names of membership (e.g. [307]), grouping (e.g. [174]), or collection (e.g. [156]). Classi cation may be regarded as orthogonal to the other three { whereas the others construct bigger things from smaller things (on the same meta- level), classi cation results in a shift of meta-level, in accordance with the philosophical notions of intension and extension [56, 96]. The intension of
Generalization a. If any element is A-moved out of the embedded clause, LDA is obligatory.
Generalization. An algorithm A that solves the problem P in a system S is a generalization of the algorithm Aj that solves the same problem P in Sj, denoted by Aj A, if A also solves P in Sj and the opposite does not happen (i.e., Aj does not solve P in S).
Generalization. The computation of the generalization depends crucially on the anti-unification process in HDTP. First-order anti-unification was introduced by Xxxxxxx [28] in the context of inductive learning. Figure 3 gives several examples for anti-unifications. Terms are generalized resulting in an anti- instance, where differing subterms are replaced by variables3. The original terms can be restored {X → b} {X → a} f (X, c) {X → b} Y {Y → f (a, b)} {Y → g(a, b)} a \t b \z f (a, c) f (b, c) J zz f (a, b) g(a, b) (a) (b) (c) Figure 3: Xxxxxxx’x first-order anti-unification. by replacing the new variables by appropriate subterms. This idea can be made more precise by introducing the notion of a substitution: (• { → → } / ∈ { } / → Definition 3 (Substitution) Assume a term algebra Term(Σ, V ) is given. A substitution on terms is a partial function σ : V Term(Σ, V ) mapping variables to terms, formally represented by σ = x1 t1, . . . , xn tn (provided xi = x j for i, j 1, . . . , n , i = j and sorts of xi and ti match). An application of a substitution σ on a term is defined by induction over the term structure: apply(x, σ ) = t if x → t ∈ σ x otherwise • apply( f (s1, . . . , sm), σ ) = f (apply(s1, σ ), . . . , apply(sm, σ )) We say that a term t′ is an instance of t and t is an anti-instance of t′, if there is a substitution σ −→ such that apply(t, σ ) = t′. In this case we write t σ t′ or simply t → t′. Using substitutions, generalizations can be defined as follows: Definition 4 (Generalization) A generalization for a pair of terms ⟨s,t⟩ is a triple ⟨g, σ, τ⟩ with ←− g
Generalization. ❖ In German predicate constructions, formal agreement between the subject and the ellipsis remnant is only possible when the interpretation is compatible with N(P) ellipsis. [the N].f≠s is [ the only N.formal who ].formal [the N].f≠s is [ the only Ø[+ANIM] who ].*formal/ ✓semantic Further evidence
Generalization. In addition, a number of methods that we develop in OPPORTUNITY are generalizeable to other context recognition systems than activity recognition. We demonstrate this by showing how specific cognitive states (e.g. attention, expectation) can be detected on the basis of EEG signals, using the approaches developed within OPPORTUNITY, towards Brain-Computer Interfaces (BCI).
