For the sake of brevity, we will concentrate on the multiplicative fragment of linear logic, i.e., which connectives are tensor, par, linear implication, and negation.
Implications are also commonly introduced into linear logic via definitions: the linear implication B ⊸ C can be defined as ¬B ⅋ C, while the intuitionistic implication B ⇒ C can be defined as !B ⊸ C. The operators ! and ?
Each nonlinear process system is described by fuzzy convolution models, which comprise a number of quasi-linear fuzzy implications (FIs).
In linear logic, this implication is equivalent to its contrapositive form: the type ¬β ⊸ ¬α can be lead to interpreting the same function as a process that transforms a demand for a value of type β into a demand for a value of type α (notice that this does not happen with functions of intuitionistic type since, for example, input argument may be vacuous) [Curien 2003].
This fuzzy model is defined by a set of fuzzy implications with linear consequent parts, each of which establishes a local linear input output relationship between the variables of the model.
Here, we discuss the implications of linear correlations between kinetic rates and binding affinity constants and the relevance of the computational approaches to QSKR modeling.
Due to the growing awareness of potential impacts of roads, managers demand well-designed studies about the implications of linear infrastructures on ecosystems.
First, we discuss the definition and the properties of linear processes and the implications that such properties have on the operational strand.
The failure of the linear model has many implications for the genetic/genomic analyses of PTB.
It is valuable to contrast the morphology of fibrils formed at low pH with that of fibrils grown at physiological pH because it highlights the structural implications of linear heterogeneity in the latter.
So what should we do?" When I ask whether 6 Music and Asian Network will close, his professorial voice flattens and he slips behind a screen of jargon – "You'll see some changes in the linear portfolios" – but the implication seems clear.
