### Summary

Situation Calculus is a mathematical language used in artificial intelligence for representing and reasoning about dynamical systems. It helps model how actions change the state of the world and facilitates the computation of the consequence of actions.

### ELI5

Imagine playing a video game. Every action you make, like moving your character or opening a door, changes the state of the game world. Situation Calculus is like a special language that helps computers understand and predict these changes, just like when you know that opening a door will let you enter a room.

### In-depth explanation

Situation Calculus is a logic-based technique which provides a framework for reasoning about dynamic systems. At the heart of the situation calculus is the idea of a ‘situation’: a snapshot of the world at some point in time. Situations change with the occurrence of actions, leading to new situations.

The basic elements of Situation Calculus are:

• Constants representing objects in the world.
• Functions that return the properties of objects
• Predicates that stand for the relations between the objects and facts about the world.

Results are obtained by having first-order logic formulas that specify the preconditions and effects of actions using these elements. Crucially, Situation Calculus formulations are logical theories that are typically used to verify whether specific properties hold in all possible behaviors of the system, such as safety conditions.

A key point of Situation Calculus is to reason on the effect of sequences of actions, which forms a major part of AI’s planning and decision making. For instance, in a robotic deployment setting, the robot might use such a calculus to reason about the series of actions it needs to perform from a start state (e.g., at point A) to accomplish a goal state (e.g., move to point B).

Situation Calculus is typically based on first-order logic, with its expressivity allows representing complex scenarios. However, it’s worth mentioning that this also implies complexity in reasoning.

As part of the larger field of Knowledge Representation and Reasoning, Situation Calculus has connections with many other concepts in AI, particularly those concerned with modeling and managing change in AI systems.

First-Order Logic, Knowledge Representation, Reasoning, Dynamical Systems, AI Planning, Decision Making