Sentence examples for temporal formula from inspiring English sources

For each of these cases, after formally defining the game setting, we characterise the complexity of a range of problems relating to Nash equilibria (e.g., the computation or the verification of existence of a Nash equilibrium or checking whether a given temporal formula is satisfied on some Nash equilibrium).

A temporal formula \(\varphi\) defines the class of temporal frames in which it is valid.

Here the objective \(\varphi\) is a temporal formula, specified for instance in the logic LTL.

\] Therefore, Thus, validity of a temporal formula in a model is a first-order property, while validity in a frame is a second-order property.

Another example of a temporal formula that does not correspond to first-order sentence (unless linearity is assumed) is \ {G} F {p}\rightarrow F {G} {p}.\) On the other hand, some simple first-order definable properties of temporal frames, such as irreflexivity, expressed by \(\forall {t} \neg {t} \prec {t}),\) are not defined by any temporal formula.

In contrast, each instance of the reducer performs the actual evaluation of one more layer of the temporal formula to verify.

The algorithm also allows to generate full diagnostic information (examples and counterexamples) for temporal formulas.

We prove that under appropriate weak fairness assumptions all these specifications are stuttering bisimilar and that large classes of logic temporal formulas, namely all CTL⁎∖X formulas, are preserved.

The server view and the traveling agent's view of the system provide communication duality, while general temporal formulas for the IMDS allow automatic verification.

As we will see later, many but not all first-order definable properties of temporal frames are definable by temporal formulae and, vice versa, many but not all properties of temporal frames that are definable by temporal formulae are first-order definable.

Formally, this means, first, that the natural flows of time for Ockhamist semantics are tree-like rather than linear, and second, that temporal formulae are evaluated relative not only to a time instant, but also to a history containing that instant.