Fluent calculus

Thefluent calculusis a formalism for expressing dynamical domains infirst-order logic.It is a variant of thesituation calculus;the main difference is that situations are considered representations of states. A binary function symbol$\circ$is used to concatenate the terms that represent facts that hold in a situation. For example, that the box is on the table in the situation$s$is represented by the formula$\exists t.s=on(box,table)\circ t$.Theframe problemis solved by asserting that the situation after the execution of an action is identical to the one before but for the conditions changed by the action. For example, the action of moving the box from the table to the floor is formalized as:

$State(Do(move(box,table,floor),s))\circ on(box,table)=State(s)\circ on(box,floor)$

This formula states that the state after the move is added the term$on(box,floor)$and removed the term$on(box,table)$.Axioms specifying that$\circ$iscommutativeand non-idempotentare necessary for such axioms to work.

See also

• Fluent (artificial intelligence)
• Frame problem
• Situation calculus
• Event calculus

References

• M. Thielscher (1998).Introduction to the fluent calculus.Electronic Transactions on Artificial Intelligence,2(3–4):179–192.
• M. Thielscher (2005).Reasoning Robots - The Art and Science of Programming Robotic Agents.Volume 33 of Applied Logic Series.Springer, Dordrecht.