Yes / In this paper, we discuss a framework for synthesising manufacturing process controllers using situation calculus, a well-known second-order logic for reasoning about actions in AI. Using a library of high-level ConGolog programs and logical action theories for production resources, we demonstrate how to efficiently synthesise an ‘optimal’ plan, i.e. the plant that minimises the number of actions for a target high-level program of a process recipe. / University of Bradford / The full-text of this conference paper will be released for public view at the end of the publisher embargo on 8 Nov 2025.

Golog programs allow to model complex behaviour of agents by combining primitive actions defined in a Situation Calculus theory using imperative and non-deterministic programming language constructs. In general, verifying temporal properties of Golog programs is undecidable. One way to establish decidability is to restrict the logic used by the program to a Description Logic (DL), for which recently some complexity upper bounds for verification problem have been established. However, so far it was open whether these results are tight, and lightweight DLs such as EL have not been studied at all. Furthermore, these results only apply to a setting where actions do not consume time, and the properties to be verified only refer to the timeline in a qualitative way. In a lot of applications, this is an unrealistic assumption. In this work, we study the verification problem for timed Golog programs, in which actions can be assigned differing durations, and temporal properties are specified in a metric branching time logic. This allows to annotate temporal properties with time intervals over which they are evaluated, to specify for example that some property should hold for at least n time units, or should become specified within some specified time window. We establish tight complexity bounds of the verification problem for both expressive and lightweight DLs. Our lower bounds already apply to a very limited fragment of the verification problem, and close open complexity bounds for the non-metrical cases studied before.

This dissertation investigates high-level decision making for agents that are both goal and utility driven. We develop a partially observable Markov decision process (POMDP) planner which is an extension of an agent programming language called DTGolog, itself an extension of the Golog language. Golog is based on a logic for reasoning about action—the situation calculus. A POMDP planner on its own cannot cope well with dynamically changing environments and complicated goals. This is exactly a strength of the belief-desire-intention (BDI) model: BDI theory has been developed to design agents that can select goals intelligently, dynamically abandon and adopt new goals, and yet commit to intentions for achieving goals. The contribution of this research is twofold: (1) developing a relational POMDP planner for cognitive robotics, (2) specifying a preliminary BDI architecture that can deal with stochasticity in action and perception, by employing the planner. / Computing / M. Sc. (Computer Science)

This dissertation investigates high-level decision making for agents that are both goal and utility driven. We develop a partially observable Markov decision process (POMDP) planner which is an extension of an agent programming language called DTGolog, itself an extension of the Golog language. Golog is based on a logic for reasoning about action—the situation calculus. A POMDP planner on its own cannot cope well with dynamically changing environments and complicated goals. This is exactly a strength of the belief-desire-intention (BDI) model: BDI theory has been developed to design agents that can select goals intelligently, dynamically abandon and adopt new goals, and yet commit to intentions for achieving goals. The contribution of this research is twofold: (1) developing a relational POMDP planner for cognitive robotics, (2) specifying a preliminary BDI architecture that can deal with stochasticity in action and perception, by employing the planner. / Computing / M. Sc. (Computer Science)

In this thesis we study a reasoning module for agents that have cognitive abilities, such as memory, perception, action, and are expected to function autonomously for long periods of time. The module provides the ability to reason about action and change using the language of the situation calculus and variants of the basic action theories. The main focus of this thesis is on the logical problem of progressing an action theory. First, we investigate the conjecture by Lin and Reiter that a practical first-order definition of progression is not appropriate for the general case. We show that Lin and Reiter were indeed correct in their intuitions by providing a proof for the conjecture, thus resolving the open question about the first-order definability of progression and justifying the need for a second-order definition. Then we proceed to identify three cases where it is possible to obtain a first-order progression with the desired properties: i) we extend earlier work by Lin and Reiter and present a case where we restrict our attention to a practical class of queries that may only quantify over situations in a limited way; ii) we revisit the local-effect assumption of Liu and Levesque that requires that the effects of an action are fixed by the arguments of the action and show that in this case a first-order progression is suitable; iii) we investigate a way that the local-effect assumption can be relaxed and show that when the initial knowledge base is a database of possible closures and the effects of the actions are range-restricted then a first-order progression is also suitable under a just-in-time assumption. Finally, we examine a special case of the action theories with range-restricted effects and present an algorithm for computing a finite progression. We prove the correctness and the complexity of the algorithm, and show its application in a simple example that is inspired by video games.

In this thesis we study a reasoning module for agents that have cognitive abilities, such as memory, perception, action, and are expected to function autonomously for long periods of time. The module provides the ability to reason about action and change using the language of the situation calculus and variants of the basic action theories. The main focus of this thesis is on the logical problem of progressing an action theory. First, we investigate the conjecture by Lin and Reiter that a practical first-order definition of progression is not appropriate for the general case. We show that Lin and Reiter were indeed correct in their intuitions by providing a proof for the conjecture, thus resolving the open question about the first-order definability of progression and justifying the need for a second-order definition. Then we proceed to identify three cases where it is possible to obtain a first-order progression with the desired properties: i) we extend earlier work by Lin and Reiter and present a case where we restrict our attention to a practical class of queries that may only quantify over situations in a limited way; ii) we revisit the local-effect assumption of Liu and Levesque that requires that the effects of an action are fixed by the arguments of the action and show that in this case a first-order progression is suitable; iii) we investigate a way that the local-effect assumption can be relaxed and show that when the initial knowledge base is a database of possible closures and the effects of the actions are range-restricted then a first-order progression is also suitable under a just-in-time assumption. Finally, we examine a special case of the action theories with range-restricted effects and present an algorithm for computing a finite progression. We prove the correctness and the complexity of the algorithm, and show its application in a simple example that is inspired by video games.

Logic-based formalizations of dynamical systems are central to the field of knowledge representation and reasoning. These formalizations can be used to model agents that act, reason,and perceive in a changing and incompletely known environment. A key aspect of reasoning about agents and their behaviors is the notion of joint ability. A team of agents is jointly able to achieve a goal if despite any incomplete knowledge or even false beliefs about the world or each other, they still know enough to be able to get to a goal state, should they choose to do so. A particularly challenging issue associated with joint ability is how team members can coordinate their actions. Existing approaches often require the agents to communicate to agree on a joint plan. In this thesis, we propose an account of joint ability that supports coordination among agents without requiring communication, and that allows for agents to have incomplete (or even false) beliefs about the world or the beliefs of other agents. We use ideas from game theory to address coordination among agents. We introduce the notion of a strategy for each agent which is basically a plan that the agent knows how to follow. Each agent compares her strategies and iteratively discards those that she believes are not good considering the strategies that the other agents have kept. Our account is developed in the situation calculus, a logical language suitable for representing and reasoning about action and change that is extended to support reasoning about multiple agents. Through several examples involving public, private, and sensing actions, we demonstrate how symbolic proof techniques allow us to reason about team ability despite incomplete specifications about the beliefs of agents.

Logic-based formalizations of dynamical systems are central to the field of knowledge representation and reasoning. These formalizations can be used to model agents that act, reason,and perceive in a changing and incompletely known environment. A key aspect of reasoning about agents and their behaviors is the notion of joint ability. A team of agents is jointly able to achieve a goal if despite any incomplete knowledge or even false beliefs about the world or each other, they still know enough to be able to get to a goal state, should they choose to do so. A particularly challenging issue associated with joint ability is how team members can coordinate their actions. Existing approaches often require the agents to communicate to agree on a joint plan. In this thesis, we propose an account of joint ability that supports coordination among agents without requiring communication, and that allows for agents to have incomplete (or even false) beliefs about the world or the beliefs of other agents. We use ideas from game theory to address coordination among agents. We introduce the notion of a strategy for each agent which is basically a plan that the agent knows how to follow. Each agent compares her strategies and iteratively discards those that she believes are not good considering the strategies that the other agents have kept. Our account is developed in the situation calculus, a logical language suitable for representing and reasoning about action and change that is extended to support reasoning about multiple agents. Through several examples involving public, private, and sensing actions, we demonstrate how symbolic proof techniques allow us to reason about team ability despite incomplete specifications about the beliefs of agents.

The Golog action programming language is a powerful means to express high-level behaviours in terms of programs over actions defined in a Situation Calculus theory. In particular for physical systems, verifying that the program satisfies certain desired temporal properties is often crucial, but undecidable in general, the latter being due to the language’s high expressiveness in terms of first-order quantification and program constructs. So far, approaches to achieve decidability involved restrictions where action effects either had to be contextfree (i.e. not depend on the current state), local (i.e. only affect objects mentioned in the action’s parameters), or at least bounded (i.e. only affect a finite number of objects). In this paper, we present a new, more general class of action theories (called acyclic) that allows for context-sensitive, non-local, unbounded effects, i.e. actions that may affect an unbounded number of possibly unnamed objects in a state-dependent fashion. We contribute to the further exploration of the boundary between decidability and undecidability for Golog, showing that for acyclic theories in the two-variable fragment of first-order logic, verification of CTL properties of programs over ground actions is decidable.

In this thesis, we study advanced reasoning about dynamical systems in a logical framework -- the situation calculus. In particular, we consider promoting the efficiency of reasoning about action in the situation calculus from three different aspects. First, we propose a modified situation calculus based on the two-variable predicate logic with counting quantifiers. We show that solving the projection and executability problems via regression in such language are decidable. We prove that generally these two problems are co-NExpTime-complete in the modified language. We also consider restricting the format of regressable formulas and basic action theories (BATs) further to gain better computational complexity for reasoning about action via regression. We mention possible applications to formalization of Semantic Web services. Then, we propose a hierarchical representation of actions based on the situation calculus to facilitate development, maintenance and elaboration of very large taxonomies of actions. We show that our axioms can be more succinct, while still using an extended regression operator to solve the projection problem. Moreover, such representation has significant computational advantages. For taxonomies of actions that can be represented as finitely branching trees, the regression operator can sometimes work exponentially faster with our theories than it works with the BATs current situation calculus. We also propose a general guideline on how a taxonomy of actions can be constructed from the given set of effect axioms. Finally, we extend the current situation calculus with the order-sorted logic. In the new formalism, we add sort theories to the usual initial theories to describe taxonomies of objects. We then investigate what is the well-sortness for BATs under such framework. We consider extending the current regression operator with well-sortness checking and unification techniques. With the modified regression, we gain computational efficiency by terminating the regression earlier when reasoning tasks are ill-sorted and by reducing the search spaces for well-sorted objects. We also study that the connection between the order-sorted situation calculus and the current situation calculus.