The definitions of actual cause given by Pearl and Halpern (HP) in the framework of causal models provided vital computational insight into an old philosophical problem but by no means resolved it. One source of concern is the lack of objective criteria for selecting possible worlds to be admitted into the counterfactual analysis, epitomized by the competition between multiple proposals by HP and others. Another concern is due to the modest expressivity of propositional-level structural equations which limits their applicability and, arguably, contributes to the the former problem. We tackle both of these issues using a novel approach. We build our definition of actual cause from first principles in the context of atemporal situation calculus (SC) action theories with sequential actions. As a result, we can successfully identify actual causes of conditions expressed in first-order logic. We validate the HP approach by providing a formal translation from causal models to SC and proving a relationship between our definitions of actual cause and that of HP. Using well-known and new examples, we show that long-standing disagreements between alternative definitions of actual causality can be mitigated by faithful SC modelling of the domains.

In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of weakly related or independent components. However, a theory may represent knowledge that is subject to change, as a result of executing actions that have effects on some of the initial properties mentioned in the theory. Having once computed a decomposition of a theory, it is advantageous to know whether a decomposition has to be computed again in the newly changed theory (obtained from taking into account changes resulting from execution of an action). In this article, we address this problem in the scope of the situation calculus, where a change of an initial theory is related to the notion of progression. Progression provides a form of forward reasoning; it relies on forgetting values of those properties, which are subject to change, and computing new values for them. We consider decomposability and inseparability, two component properties known from the literature, and contribute by studying the conditions (1) when these properties are preserved and (2) when they are lost wrt progression and the related operation of forgetting. To show the latter, we demonstrate the boundaries using a number of negative examples. To show the former, we identify cases when these properties are preserved under forgetting and progression of initial theories in local-effect basic action theories of the situation calculus. Our article contributes to bridging two different communities in knowledge representation, namely, research on modularity and research on reasoning about actions.

In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of components with weakly-related or independent signatures. This facilitates reasoning when signature of a query formula belongs to only one of the components. However, an initial theory may be subject to change due to execution of actions affecting features mentioned in the theory. Having once computed a decomposition of a theory, one would like to know whether a decomposition has to be computed again for the theory obtained from taking into account the changes resulting from execution of an action. In the paper, we address this problem in the scope of the situation calculus, where change of an initial theory is related to the well-studied notion of progression. Progression provides a form of forward reasoning; it relies on forgetting values of those features which are subject to change and computing new values for them. We prove new results about properties of decomposition components under forgetting and show when a decomposition can be preserved in progression of an initial theory.

It has been argued that causal rules are necessary for representing both implicit side-effects of actions and action qualifications, and there have been a number different approaches for representing causal rules in the area of formal theoriesof actions. These different approaches in general agree on rules without cycles. However, they differ on causal rules with mutual cyclic dependencies, both in terms of how these rules are supposed to be represented and their semantics. In this paper we show that by adding one more minimization to Lin's circumscriptive causal theory in the situation calculus, we can have a uniform representation of causal rules including those with cyclic dependencies. We also demonstrate that sometimes causal rules can be compiled into logically equivalent successor state axioms even in the presence of cyclical dependencies between fluents.

Reasoning about perception of depth and about spatial relations between moving physical objects is a challenging problem. We investigate the representation of depth and motion by means of depth profiles whereby each object in the world is represented as a single peak. We propose a logical theory, formulated in the situation calculus (SC), that is used for reasoning about object motion (including motion of the observer). The theory proposed here is comprehensive enough to accommodate reasoning about both sensor data and actions in the world. We show that reasoning about depth profiles is sound and complete with respect to actual motion in the world. This shows that in the conceptual neighbourhood diagram (CND) of all possible depth perceptions, the transitions between perceptions are logical consequences of the proposed theory of depth and motion.