Situation calculus has been widely applied in Artificial Intelligence related fields. This formalism is considered as a dialect of logic programming language and mostly used in dynamic domain modeling. However, type systems are hardly deployed in situation calculus in the literature. To achieve a correct and sound typed program written in situation calculus, adding typing elements into the current situation calculus will be quite helpful. In this paper, we propose to add more typing mechanisms to the current version of situation calculus, especially for three basic elements in situation calculus: situations, actions and objects, and then perform rigid type checking for existing situation calculus programs to find out the well-typed and ill-typed ones. In this way, type correctness and soundness in situation calculus programs can be guaranteed by type checking based on our type system. This modified version of a lightweight situation calculus is proved to be a robust and well-typed system.
There are also some attempts on modifying situation calculus only based on a lightweight version of the original one. Gerhard @cite_6 proposed a new logic dialect of situation calculus with the situation terms suppressed, namely, [height=0.3cm] es.png . That is, it is merely a similar formalism as a part of the current situation calculus. Moreover, in this paper, the authors consider how to map sentences between [height=0.3cm] es.png and situation calculus and try to prove [height=0.3cm] es.png is powerful enough to handle most cases as the situation calculus does, but mention little about how to type their new logic system as a fragment of situation calculus.
@cite_6
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In a recent paper, we presented a new logic called ES for reasoning about the knowledge, action, and perception of an agent. Although formulated using modal operators, we argued that the language was in fact a dialect of the situation calculus but with the situation terms suppressed. This allowed us to develop a clean and workable semantics for the language without piggybacking on the generic Tarski semantics for first-order logic. In this paper, we reconsider the relation between ES and the situation calculus and show how to map sentences of ES into the situation calculus. We argue that the fragment of the situation calculus represented by ES is rich enough to handle the basic action theories defined by Reiter as well as Golog. Finally, we show that in the full second-order version of ES, almost all of the situation calculus can be accommodated.