And indeed, as Camp (2002, 157) observes, the set of implications valid according to his semantics is exactly the set of implications of the entailment system Efde.
As a result, a sound, complete, and non-redundant knowledge base is created, from which all implications, valid according to the semantics given by the enlarged formal context K sim, can be derived.
It is clear that the following diagram, where arrows stand for implications, is valid: contraction → quasicontraction ↓ ↓ ordered contraction → ordered quasicontraction.
From the above definition, it is easy to see that the following implications are valid: E is uniformly convex ⇒ E is locally uniformly convex ⇒ E is strictly convex.
Finally, we describe a follow-up study currently under way, which validates a complementary performance-based tool to assess the strategic component of PCK of business and economics using video vignettes, and discuss uses of both tools and implications for valid assessment of the professional knowledge of business and economics teachers.
In other words, the implications are valid regarding the knowledge formalised in the Boolean network and can also be checked by supplementary human expert knowledge or further literature research, e.g., for co-regulation of genes or possible or forbidden resulting states.
then the following implication is valid: if (p=p^{r}_{0}(x)), then mathbb{P} left widetilde{V}_{T} (x,p,phi,mathcal{C})=x right)=1.
Moreover, if condition (i) holds, then condition (ii) is equivalent to the following condition if p is such that there exists ((x,p,phi,mathcal {C} in Psi ^{0,x} (p,mathcal {C})) satisfying mathbb{P} left widetilde{V}_{T} (x,p,phi,mathcal{C}) geq x right)=1, (53) then the following implication is valid: if (p=p^{r}_{0}(x)), then mathbb{P} left widetilde{V}_{T} (x,p,phi,mathcal{C})=x right)=1.
The set of axioms provides a mechanism for temporal and spatial reasoning with the set of relations and can be used to derive all possible implications from any valid predicate on the proposed relations.
McCall refers to a result by R. Meyer showing that the valid implications of CFL form a subset of the set of valid material equivalences and briefly discusses giving up the syntactic restriction to first-degree implication.
