Time is the grand stage where human activities take place (rational or otherwise). And the view of a branching temporal universe, or tree of possible events, with our actual history linearly advancing through it, is a widely shared cultural idea, not confined to Academia (cf. Borges brilliant 1941 essay El Jard́ın de senderos que se bifurcan). Even though logic is often considered a study of tim...

SAT and QBF solving techniques have applications in various areas. One area of the applications of SAT-solving is formal verification of temporal properties of transition system models. Because of the restriction on the structure of formulas, complicated verification problems cannot be naturally represented with SAT-formulas succinctly. This paper investigates QBF-applications in this area, aim...

The high diversity of tree species has traditionally been considered an important controller of belowground processes in tropical rainforests. However, soil water availability and resources are also primary regulators of soil bacteria in many ecosystems. Separating the effects of these biotic and abiotic factors in the tropics is challenging because of their high spatial and temporal heterogene...

A temporal clausal resolution method was originally developed for linear time temporal logic and further extended to the branching-time framework of Computation Tree Logic (CTL). In this paper, following our general idea to expand the applicability of this efficient method to more expressive formalisms useful in a variety of applications in computer science and AI requiring branching time logic...

In this paper we extend our clausal resolution method for linear temporal logics to a branching-time framework. The branching-time temporal logics considered are Computation Tree Logic (CTL), often regarded as the simplest useful logic of this class, and Extended CTL (ECTL), which is CTL extended with fairness operators. The key elements of the resolution method, namely the normal form, the con...

In addition to providing a sound basis for analysis, formal methods can support other development activities; in our case the target is specification-based testing at the system level. We use the formal method of model checking to either generate new test sets or analyze existing test sets with respect to safety properties expressed in a temporal logic. We consider two types of tests: failing t...

In this paper we extend our clausal resolution method for linear time temporal logics to a branching-time framework. Thus, we propose an e cient deductive method useful in a variety of applications requiring an expressive branching-time temporal logic in AI. The branching-time temporal logic considered is Computation Tree Logic (CTL), often regarded as the simplest useful logic of this class. T...

In this paper, we use the constructs of branching temporal logic to formalize reasoning about a class of general flow systems, including discretetime transition systems, continuous-time differential inclusions, and hybrid-time systems such as hybrid automata. We introduce Full General Flow Logic, GFL, which has essentially the same syntax as the well-known Full Computation Tree Logic, CTL, but ...