Situation Calculus

The situation calculus is a logical language for representing changes. It was first introduced by McCarthy in 1963,1 and described in further details by McCarthy and Hayes [29] in 1969. The basic concepts in the situation calculus are situations, actions and fluents. Briefly, actions are what make the dynamic world change from one situation to another when performed by agents. Fluents are situation-dependent functions used to describe the effects of actions. There are two kinds of them, relational fluents and functional fluents. The former have only two values: true or false, while the latter can take a range of values. For instance, one may have a relational fluent called handempty which is true in a situation if the robot’s hand is not holding anything. We may need a relation like this in a robot domain. One may also have a functional fluent called battery-level whose value in a situation is an integer between 0 and 100 denoting the total battery power remaining on one’s laptop computer. According to McCarthy and Hayes [29], a situation is “the complete state of the universe at an instance of time”. But for Reiter [34], a situation is the same as its history which is the finite sequence of actions that has been performed since the initial situation S0. We shall discuss Reiter’s foundational axioms that make this precise later. Whatever the interpretation, the unique feature of the situation calculus is that situations are first-order objects that can be quantified over. This is what makes the situation calculus a powerful formalism for representing change, and distinguishes it from other formalisms such as dynamic logic [11]. To describe a dynamic domain in the situation calculus, one has to decide on the set of actions available for the agents to perform, and the set of fluents needed to describe the changes these actions will have on the world. For example, consider the classic blocks world where some blocks of equal size can be arranged into a set of towers on a table. The set of actions in this domain depends on what the imaginary agent can do. If we imagine the agent to be a one-handed robot that can be directed to grasp any block that is on the top of a tower, and either add it to the top of another tower or put it down on the table to make a new tower, then we can have the following actions [30]: