We consider a modified version of the situation calculus built using a two-variable fragment of the first-order logic extended with counting quantifiers. We mention several additional groups of axioms that can be introduced to capture taxonomic reasoning. We show that the regression operator in this framework can be defined similarly to regression in Reiter's version of the situation calculus. Using this new regression operator, we show that the projection and executability problems (the important reasoning tasks in the situation calculus) are decidable in the modified version even if an initial knowledge base is incomplete. We also discuss the complexity of solving the projection problem via regression in this modified language in general. Furthermore, we define description logic based sublanguages of our modified situation calculus. They are based on the description logics ALCO(U) (or ALCQO(U), respectively). We show that in these sub-languages solving the projection problem via regression has better computational complexity than in the general modified situation calculus. We mention possible applications to formalization of Semantic Web services and some connections with reasoning about actions based on description logics.

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.

Organic Synthesis is a computationally challenging practical problem concerned with constructing a target molecule from a set of initially available molecules via chemical reactions. This paper demonstrates how organic synthesis can be formulated as a planning problem in Artificial Intelligence, and how it can be explored using the state-of-the-art domain independent planners. To this end, we develop a methodology to represent chemical molecules and generic reactions in PDDL 2.2, a version of the standardized Planning Domain Definition Language popular in AI. In our model, derived predicates define common functional groups and chemical classes in chemistry, and actions correspond to generic chemical reactions. We develop a set of benchmark problems. Since PDDL is supported as an input language by many modern planners, our benchmark can be subsequently useful for empirical assessment of the performance of various state-of-the-art planners.

In the area of reasoning about actions, one of the key computational problems is the projection problem: to find whether a given logical formula is true after performing a sequence of actions. This problem is undecidable in the general situation calculus; however, it is decidable in some fragments. We consider a fragment P of the situation calculus and Reiter's basic action theories (BAT) such that the projection problem can be reduced to the satisfiability problem in an expressive description logic ALCO(U) that includes nominals (O), the universal role (U), and constructs from the well-known logic ALC. It turns out that our fragment P is more expressive than previously explored description logic based fragments of the situation calculus. We explore some of the logical properties of our theories. In particular, we show that the projection problem can be solved using regression in the case where BATs include a general "static" TBox, i.e., an ontology that has no occurrences of fluents. Thus, we propose seamless integration of traditional ontologies with reasoning about actions. We also show that the projection problem can be solved using progression if all actions have only local effects on the fluents, i.e., in P, if one starts with an incomplete initial theory that can be transformed into an ALCO(U) concept, then its progression resulting from execution of a ground action can still be expressed in the same language. Moreover, we show that for a broad class of incomplete initial theories progression can be computed efficiently.

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 due to execution of actions that have effects on some properties 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 in the theory obtained from taking into account changes resulting from execution of an action. In the paper, 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. We undertake a study of the decomposability and inseparability properties known from the literature. We contribute by studying these properties wrt progression and the related notion of forgetting. We provide negative examples and identify cases when these properties are preserved under progression of initial theories and under forgetting in local-effect basic action theories of the situation calculus.