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.

PDDL+ is an extension of PDDL2.1 which incorporates fully-featured autonomous processes and allows for better modelling of mixed discrete-continuous domains. Unlike PDDL2.1, PDDL+ lacks a logical semantics, relying instead on state-transitional semantics enriched with hybrid automata semantics for the continuous states. This complex semantics makes analysis and comparisons to other action formalisms difficult. In this paper, we propose a natural extension of Reiter’s situation calculus theories inspired by hybrid automata. The kinship between PDDL+ and hybrid automata allows us to develop a direct mapping between PDDL+ and situation calculus, thereby supplying PDDL+ with a logical semantics and the situation calculus with a modern way of representing autonomous processes. We outline the potential benefits of the mapping by suggesting a new approach to effective planning in PDDL+.

We extend Reiter's temporal situation calculus by introducing continuous change due to passage of time in addition to discrete change due to actions. We define regression for hybrid action theories and show that hybrid action theories can capture hybrid automata.

The ability to model continuous change in Reiter's temporal situation calculus action theories has attracted a lot of interest. In this paper, we propose a new development of his approach, which is directly inspired by hybrid systems in control theory. Specifically, while keeping the foundations of Reiter's axiomatization, we propose an elegant extension of his approach by adding a time argument to all fluents that represent continuous change. Thereby, we insure that change can happen not only because of actions, but also due to the passage of time. We present a systematic methodology to derive, from simple premises, a new group of axioms which specify how continuous fluents change over time within a situation. We study regression for our new temporal basic action theories and demonstrate what reasoning problems can be solved. Finally, we formally show that our temporal basic action theories indeed capture hybrid automata.

Conformant planning has been traditionally studied in the form of classical planning extended with a mechanism for expressing unknown facts and/or disjunctive knowledge. Despite a sizable body of research, most approaches do not attempt to move beyond essentially propositional planning. We address this shortcoming by defining conformant planning in terms of the situation calculus semantics and use recent advances in the fields of first-order knowledge base progression and query answering to develop a sound and complete conformant planning algorithm capable of handling knowledge defined in an expressive fragment of first-order logic. We implement a prototype planner and evaluate its performance on several existing domains.