In this research, we take into account the functional variety, topological complexity, and disturbance randomness of UDSs and define a new formula of resilience based on three parts of system severity, i.e. social severity affected by urban flooding, environmental severity caused by sewer overflow, and technological severity considering the safe operation of downstream facilities.
Every recursively enumerable (RE) set can be defined by a formula of the latter sort; these are just the Σ01-formulas.
In particular, the so-called Borel sets can be simply defined both by a formula of the form ∃XA x) and by a formula of the form ∀XB x), where A and B do not contain any set variables (in logician's terminology, Borel sets are the Δ11 sets).
To provide a logic with an algebraic semantics was to interpret its language in a class of algebras, define a notion of satisfaction of a formula in an algebra of the class and prove a soundness and completeness theorem, usually for the theorems of the logic only.
For the sake of argument, let's grant that the Skolemite has shown that our set-theoretic notions are relative and that, for every kind of set that we can define with a formula, there is an instance of this kind of set which is only countable.
We now define a relation of satisfaction between interpretations, variable-assignments, and formulas of L1K=.
An easy way to define a milestone-based formula for startups that are likely to require venture funding would be to base the formula on the valuation of the company at the various financing rounds.
The aim of this study was to explore the effect of a defined formula of Chinese medicinal herbs, GengNianAn (GNA, also called menopausal symptom-relieving formula) formula in relieving menopausal symptoms in ovariectomized women.
Moreover, it is easy to define a "reverse" translation that maps formulas of LPFO to formulas of LMSO and to prove that this translation maps theorems of the former to theorems of the latter.
The truth of a formula of TL at a given time instant \(t\) in a given temporal model \(\mathcal{M}\) is defined inductively as follows: A formula \(\varphi\) of TL is valid, denoted \(\models \varphi,\) if it is true at all time instants in all temporal models; a formula \(\varphi\) is satisfiable if it is true at some time instant in some temporal model.
