A Concept of Possibility for Real-World Events
Daniel G. Schwartz
TL;DR
This work replaces the purely subjective original notion of possibility with a context-aware, objective measure for real-world events by modeling prerequisites and constraints as probabilities and applying Łukasiewicz min–max logic. It defines contextual constructs, a valuation function, and completeness notions, enablingPoss(E) to be computed as a minimum of constituent probabilities; it then extends to complex, precursor-driven events and provides a vehicle waypoint navigation example to illustrate dynamic planning. The paper also contrasts this approach with standard probability theory, arguing that it yields more intuitive feasibility assessments for planning tasks, and discusses broad application opportunities in robotics, organizational planning, networks, and games. The contribution lies in a formally developed, computation-friendly alternative to traditional probability for evaluating the feasibility or ease of executing plans in uncertain, context-dependent settings, with potential to inform real-time decision-making and routing.
Abstract
This paper offers a new concept of {\it possibility} as an alternative to the now-a-days standard concept originally introduced by L.A. Zadeh in 1978. This new version was inspired by the original but, formally, has nothing in common with it other than that they both adopt the Łukasiewicz multivalent interpretation of the logical connectives. Moreover, rather than seeking to provide a general notion of possibility, this focuses specifically on the possibility of a real-world event. An event is viewed as having prerequisites that enable its occurrence and constraints that may impede its occurrence, and the possibility of the event is computed as a function of the probabilities that the prerequisites hold and the constraints do not. This version of possibility might appropriately be applied to problems of planning. When there are multiple plans available for achieving a goal, this theory can be used to determine which plan is most possible, i.e., easiest or most feasible to complete. It is speculated that this model of reasoning correctly captures normal human reasoning about plans. The theory is elaborated and an illustrative example for vehicle route planning is provided. There is also a suggestion of potential future applications.