TLDR: A new concept of possibility for real-world events is introduced, offering an objective method to calculate an event’s feasibility based on the probabilities of its prerequisites and the absence of its constraints. This approach, which uses Łukasiewicz logic, contrasts with traditional subjective possibility theory and is particularly useful for planning and decision-making in areas like robotics, project management, and vehicle navigation.
A new perspective on understanding the “possibility” of real-world events has been introduced, offering an alternative to the long-standing concept established by Lotfi A. Zadeh in 1978. This novel approach, detailed by Daniel G. Schwartz, aims to provide a more objective and computationally driven method for assessing whether an event can occur, focusing specifically on its feasibility or ease of completion.
The core of this new theory lies in viewing an event as being influenced by two main factors: prerequisites and constraints. Prerequisites are conditions that must be met for an event to happen, while constraints are factors that might hinder or prevent its occurrence. Instead of relying on subjective assessments, this model calculates an event’s possibility as a function of the probabilities that its prerequisites will hold true and its constraints will not.
For instance, consider a company planning to launch a new product line. The prerequisites might include securing “sufficient capital” and having “sufficient employees.” If there’s also a potential “environmental issue” that could impede factory construction, this becomes a constraint. The possibility of launching the new product would then be determined by combining the probabilities of having the capital, having the employees, and the environmental issue *not* being a problem. The mathematical framework for this combination uses Łukasiewicz multivalent logic, where logical “and” is interpreted as the minimum of probabilities, “or” as the maximum, and “not” as one minus the probability.
This approach distinguishes itself from traditional probability theory, which measures the likelihood of an event actually happening. Instead, this new possibility concept quantifies the “ease” or “feasibility” with which an event *could* happen. This distinction is particularly valuable in planning and decision-making. When faced with multiple plans to achieve a goal, this theory can help identify the plan that is “most possible,” meaning the easiest or most feasible to execute. The author suggests that this model closely mirrors how humans intuitively reason about plans.
Real-World Application: Vehicle Route Planning
To illustrate its practical utility, the paper presents an example of vehicle waypoint navigation in a “smart city.” Imagine a self-driving car needing to navigate from point A to point H through a network of city streets. Each segment of the journey, or “leg,” has its own set of prerequisites and constraints. Prerequisites might include the vehicle being in proper operating condition and the driver (human or AI) being competent. Constraints could involve high traffic volume, adverse weather conditions, traffic accidents, or road construction.
For each leg, the possibility of traversing it successfully at the designated speed limit is calculated. These calculations incorporate real-time data for probabilities, such as historical traffic patterns for congestion or immediate reports of accidents. As the vehicle progresses, it dynamically reassesses the possibility of different paths, choosing the one with the highest possibility degree. This ensures the vehicle selects the easiest or most feasible route, adapting to changing conditions.
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Broader Implications and Future Directions
The research emphasizes that while probability theory is about prediction, this possibility theory is about feasibility. This makes it a powerful tool for evaluating alternative plans across various domains. The paper outlines several potential application areas:
- Robotics: Assisting robots in selecting the most feasible sequence of actions to achieve a goal, especially when the success of individual actions is uncertain.
- Organizational Project Planning: Enhancing project management tools like Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) by providing insights into the feasibility of different project timelines and task sequences, beyond just time estimates.
- Computer Networks: Offering a measure of transmission feasibility for data packets, considering network constraints like congestion, bandwidth limitations, and environmental factors.
- Computer Games: Modeling more realistic and human-like decision-making for non-player characters, allowing them to choose actions based on perceived ease or feasibility.
This new concept of possibility provides an objective and computational framework for understanding and evaluating the ease or feasibility of real-world events. By integrating probabilities of prerequisites and constraints, it offers a valuable tool for informed decision-making in complex planning scenarios. For a deeper dive into the formal definitions and proofs, you can access the full research paper here: A Concept of Possibility for Real-World Events.
