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We introduce LTLf+ and PPLTL+, two logics to express properties of infinite traces, that are based on the linear-time temporal logics LTLf and PPLTL on finite traces. LTLf+/PPLTL+ use levels of Manna and Pnueli's LTL safety-progress hierarchy, and thus have the same expressive power as LTL. However, they also retain a crucial characteristic of the reactive synthesis problem for the base logics: the game arena for strategy extraction can be derived from deterministic finite automata (DFA). Consequently, these logics circumvent the notorious difficulties associated with determinizing infinite trace automata, typical of LTL reactive synthesis. We present DFA-based synthesis techniques for LTLf+/PPLTL+, and show that synthesis is 2EXPTIME-complete for LTLf+ (matching LTLf) and EXPTIME-complete for PPLTL+ (matching PPLTL). Notably, while PPLTL+ retains the full expressive power of LTL, reactive synthesis is EXPTIME-complete instead of 2EXPTIME-complete. The techniques are also adapted to optimally solve satisfiability, validity, and model-checking, to get EXPSPACE-complete for LTLf+ (extending a recent result for the guarantee level using LTLf), and PSPACE-complete for PPLTL+.

Responsibility is one of the key notions in machine ethics and in the area of autonomous systems. It is a multi-faceted notion involving counterfactual reasoning about actions and strategies. In this paper, we study different variants of responsibility in a strategic setting based on LTLf. We show a connection with notions in reactive synthesis, including synthesis of winning, dominant, and best-effort strategies. This connection provides the building blocks for a computational grounding of responsibility including complexity characterizations and sound, complete, and optimal algorithms for attributing and anticipating responsibility.

We develop a general framework for agent abstraction based on the situation calculus and the ConGolog agent programming language. We assume that we have a high-level specification and a low-level specification of the agent, both represented as basic action theories. A refinement mapping specifies how each high-level action is implemented by a low-level ConGolog program and how each high-level fluent can be translated into a low-level formula. We define a notion of sound abstraction between such action theories in terms of the existence of a suitable bisimulation between their respective models. Sound abstractions have many useful properties that ensure that we can reason about the agent's actions (e.g., executability, projection, and planning) at the abstract level, and refine and concretely execute them at the low level. We also characterize the notion of complete abstraction where all actions (including exogenous ones) that the high level thinks can happen can in fact occur at the low level. To facilitate verifying that one has a sound/complete abstraction relative to a mapping, we provide a set of necessary and sufficient conditions. Finally, we identify a set of basic action theory constraints that ensure that for any low-level action sequence, there is a unique high-level action sequence that it refines. This allows us to track/monitor what the low-level agent is doing and describe it in abstract terms (i.e., provide high-level explanations, for instance, to a client or manager)., Comment: 60 pages, 1 figure

Achieving seamless coordination in cooperative games is a crucial challenge in artificial intelligence, particularly when players operate under incomplete information. A common strategy to mitigate this information asymmetry involves leveraging explicit communication. However, direct communication is not always feasible due to factors such as transmission loss. We explore how effective coordination can be achieved without verbal communication, relying solely on observing each other's actions. We demonstrate how an autonomous agent can learn to cooperate by interpreting its partner's actions, which are used to hint at its intents. Our approach involves developing an agent strategy by constructing deterministic finite automata for each possible action and integrating them into a non-Markovian finite-state transducer. This transducer represents a non-deterministic strategy for the agent that suggests actions to assist its partner during gameplay. Experimental results in a testbed called Gnomes at Night show that the learned no-communication coordination strategy achieves significantly higher success rates and requires fewer steps to complete the game compared to uncoordinated scenarios, performing almost as well as an oracle baseline with direct communication., Comment: This paper is currently under review at AAAI 2025

Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in its action selection mechanism, thereby leading to possible goal failure. We study the trembling-hand problem in the context of reasoning about actions and planning for temporally extended goals expressed in Linear Temporal Logic on finite traces (LTLf), where we want to synthesize a strategy (aka plan) that maximizes the probability of satisfying the LTLf goal in spite of the trembling hand. We consider both deterministic and nondeterministic (adversarial) domains. We propose solution techniques for both cases by relying respectively on Markov Decision Processes and on Markov Decision Processes with Set-valued Transitions with LTLf objectives, where the set-valued probabilistic transitions capture both the nondeterminism from the environment and the possible action instruction errors from the agent. We formally show the correctness of our solution techniques and demonstrate their effectiveness experimentally through a proof-of-concept implementation., Comment: The paper is accepted by IJCAI 2024

We study best-effort strategies (aka plans) in fully observable nondeterministic domains (FOND) for goals expressed in Linear Temporal Logic on Finite Traces (LTLf). The notion of best-effort strategy has been introduced to also deal with the scenario when no agent strategy exists that fulfills the goal against every possible nondeterministic environment reaction. Such strategies fulfill the goal if possible, and do their best to do so otherwise. We present a game-theoretic technique for synthesizing best-effort strategies that exploit the specificity of nondeterministic planning domains. We formally show its correctness and demonstrate its effectiveness experimentally, exhibiting a much greater scalability with respect to a direct best-effort synthesis approach based on re-expressing the planning domain as generic environment specifications., Comment: To appear at ECAI2023

In this paper, we study LTLf synthesis under environment specifications for arbitrary reachability and safety properties. We consider both kinds of properties for both agent tasks and environment specifications, providing a complete landscape of synthesis algorithms. For each case, we devise a specific algorithm (optimal wrt complexity of the problem) and prove its correctness. The algorithms combine common building blocks in different ways. While some cases are already studied in literature others are studied here for the first time., Comment: To appear at EUMAS2023

We consider an agent acting to fulfil tasks in a nondeterministic environment. When a strategy that fulfills the task regardless of how the environment acts does not exist, the agent should at least avoid adopting strategies that prevent from fulfilling its task. Best-effort synthesis captures this intuition. In this paper, we devise and compare various symbolic approaches for best-effort synthesis in Linear Temporal Logic on finite traces (LTLf). These approaches are based on the same basic components, however they change in how these components are combined, and this has a significant impact on the performance of the approaches as confirmed by our empirical evaluations., Comment: To appear at EUMAS2023

Goal Recognition is the task of discerning the correct intended goal that an agent aims to achieve, given a set of goal hypotheses, a domain model, and a sequence of observations (i.e., a sample of the plan executed in the environment). Existing approaches assume that goal hypotheses comprise a single conjunctive formula over a single final state and that the environment dynamics are deterministic, preventing the recognition of temporally extended goals in more complex settings. In this paper, we expand goal recognition to temporally extended goals in Fully Observable Non-Deterministic (FOND) planning domain models, focusing on goals on finite traces expressed in Linear Temporal Logic (LTLf) and Pure Past Linear Temporal Logic (PLTLf). We develop the first approach capable of recognizing goals in such settings and evaluate it using different LTLf and PLTLf goals over six FOND planning domain models. Empirical results show that our approach is accurate in recognizing temporally extended goals in different recognition settings., Comment: arXiv admin note: substantial text overlap with arXiv:2103.11692

We develop a general framework for abstracting the behavior of an agent that operates in a nondeterministic domain, i.e., where the agent does not control the outcome of the nondeterministic actions, based on the nondeterministic situation calculus and the ConGolog programming language. We assume that we have both an abstract and a concrete nondeterministic basic action theory, and a refinement mapping which specifies how abstract actions, decomposed into agent actions and environment reactions, are implemented by concrete ConGolog programs. This new setting supports strategic reasoning and strategy synthesis, by allowing us to quantify separately on agent actions and environment reactions. We show that if the agent has a (strong FOND) plan/strategy to achieve a goal/complete a task at the abstract level, and it can always execute the nondeterministic abstract actions to completion at the concrete level, then there exists a refinement of it that is a (strong FOND) plan/strategy to achieve the refinement of the goal/task at the concrete level., Comment: 20 pages, 2 figures

One major limitation to the applicability of Reinforcement Learning (RL) to many practical domains is the large number of samples required to learn an optimal policy. To address this problem and improve learning efficiency, we consider a linear hierarchy of abstraction layers of the Markov Decision Process (MDP) underlying the target domain. Each layer is an MDP representing a coarser model of the one immediately below in the hierarchy. In this work, we propose a novel form of Reward Shaping where the solution obtained at the abstract level is used to offer rewards to the more concrete MDP, in such a way that the abstract solution guides the learning in the more complex domain. In contrast with other works in Hierarchical RL, our technique has few requirements in the design of the abstract models and it is also tolerant to modeling errors, thus making the proposed approach practical. We formally analyze the relationship between the abstract models and the exploration heuristic induced in the lower-level domain. Moreover, we prove that the method guarantees optimal convergence and we demonstrate its effectiveness experimentally., Comment: This is an extended version of the paper presented at AAAI 2023, https://doi.org/10.1609/aaai.v37i6.25881

Most of the synthesis literature has focused on studying how to synthesize a strategy to fulfill a task. This task is a duty for the agent. In this paper, we argue that intelligent agents should also be equipped with rights, that is, tasks that the agent itself can choose to fulfill (e.g., the right of recharging the battery). The agent should be able to maintain these rights while acting for its duties. We study this issue in the context of LTLf synthesis: we give duties and rights in terms of LTLf specifications, and synthesize a suitable strategy to achieve the duties that can be modified on-the-fly to achieve also the rights, if the agent chooses to do so. We show that handling rights does not make synthesis substantially more difficult, although it requires a more sophisticated solution concept than standard LTLf synthesis. We also extend our results to the case in which further duties and rights are given to the agent while already executing.

Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as complex systems made of many components, each implementing a specific functionality. Any automaton can serve as a component; using specific components allows for a fine-grained control of the expressivity of the resulting class of automata; using prime automata as components implies specific expressivity guarantees. Moreover, specifying automata as cascades allows for describing the sample complexity of automata in terms of their components. We show that the sample complexity is linear in the number of components and the maximum complexity of a single component, modulo logarithmic factors. This opens to the possibility of learning automata representing large dynamical systems consisting of many parts interacting with each other. It is in sharp contrast with the established understanding of the sample complexity of automata, described in terms of the overall number of states and input letters, which implies that it is only possible to learn automata where the number of states is linear in the amount of data available. Instead our results show that one can learn automata with a number of states that is exponential in the amount of data available., Comment: Full version with appendix of a paper with the same title that appears in the proceedings of AAAI 2023

Devising a strategy to make a system mimicking behaviors from another system is a problem that naturally arises in many areas of Computer Science. In this work, we interpret this problem in the context of intelligent agents, from the perspective of LTLf, a formalism commonly used in AI for expressing finite-trace properties. Our model consists of two separated dynamic domains, D_A and D_B, and an LTLf specification that formalizes the notion of mimicking by mapping properties on behaviors (traces) of D_A into properties on behaviors of D_B. The goal is to synthesize a strategy that step-by-step maps every behavior of D_A into a behavior of D_B so that the specification is met. We consider several forms of mapping specifications, ranging from simple ones to full LTLf, and for each we study synthesis algorithms and computational properties.

Our work aims at developing reinforcement learning algorithms that do not rely on the Markov assumption. We consider the class of Non-Markov Decision Processes where histories can be abstracted into a finite set of states while preserving the dynamics. We call it a Markov abstraction since it induces a Markov Decision Process over a set of states that encode the non-Markov dynamics. This phenomenon underlies the recently introduced Regular Decision Processes (as well as POMDPs where only a finite number of belief states is reachable). In all such kinds of decision process, an agent that uses a Markov abstraction can rely on the Markov property to achieve optimal behaviour. We show that Markov abstractions can be learned during reinforcement learning. Our approach combines automata learning and classic reinforcement learning. For these two tasks, standard algorithms can be employed. We show that our approach has PAC guarantees when the employed algorithms have PAC guarantees, and we also provide an experimental evaluation., Comment: IJCAI 2022

We study temporally extended goals expressed in Pure-Past LTL (PPLTL). PPLTL is particularly interesting for expressing goals since it allows to express sophisticated tasks as in the Formal Methods literature, while the worst-case computational complexity of Planning in both deterministic and nondeterministic domains (FOND) remains the same as for classical reachability goals. However, while the theory of planning for PPLTL goals is well understood, practical tools have not been specifically investigated. In this paper, we make a significant leap forward in the construction of actual tools to handle PPLTL goals. We devise a technique to polynomially translate planning for PPLTL goals into standard planning. We show the formal correctness of the translation, its complexity, and its practical effectiveness through some comparative experiments. As a result, our translation enables state-of-the-art tools, such as FD or MyND, to handle PPLTL goals seamlessly, maintaining the impressive performances they have for classical reachability goals., Comment: 26 pages, 8 figures, 2 tables

Fully Observable Non-Deterministic (FOND) planning models uncertainty through actions with non-deterministic effects. Existing FOND planning algorithms are effective and employ a wide range of techniques. However, most of the existing algorithms are not robust for dealing with both non-determinism and task size. In this paper, we develop a novel iterative depth-first search algorithm that solves FOND planning tasks and produces strong cyclic policies. Our algorithm is explicitly designed for FOND planning, addressing more directly the non-deterministic aspect of FOND planning, and it also exploits the benefits of heuristic functions to make the algorithm more effective during the iterative searching process. We compare our proposed algorithm to well-known FOND planners, and show that it has robust performance over several distinct types of FOND domains considering different metrics.

AI-Augmented Business Process Management Systems (ABPMSs) are an emerging class of process-aware information systems, empowered by trustworthy AI technology. An ABPMS enhances the execution of business processes with the aim of making these processes more adaptable, proactive, explainable, and context-sensitive. This manifesto presents a vision for ABPMSs and discusses research challenges that need to be surmounted to realize this vision. To this end, we define the concept of ABPMS, we outline the lifecycle of processes within an ABPMS, we discuss core characteristics of an ABPMS, and we derive a set of challenges to realize systems with these characteristics., Comment: 19 pages, 1 figure

Recently regular decision processes have been proposed as a well-behaved form of non-Markov decision process. Regular decision processes are characterised by a transition function and a reward function that depend on the whole history, though regularly (as in regular languages). In practice both the transition and the reward functions can be seen as finite transducers. We study reinforcement learning in regular decision processes. Our main contribution is to show that a near-optimal policy can be PAC-learned in polynomial time in a set of parameters that describe the underlying decision process. We argue that the identified set of parameters is minimal and it reasonably captures the difficulty of a regular decision process., Comment: IJCAI 2021

Goal Recognition is the task of discerning the correct intended goal that an agent aims to achieve, given a set of possible goals, a domain model, and a sequence of observations as a sample of the plan being executed in the environment. Existing approaches assume that the possible goals are formalized as a conjunction in deterministic settings. In this paper, we develop a novel approach that is capable of recognizing temporally extended goals in Fully Observable Non-Deterministic (FOND) planning domain models, focusing on goals on finite traces expressed in Linear Temporal Logic (LTLf) and (Pure) Past Linear Temporal Logic (PLTLf). We empirically evaluate our goal recognition approach using different LTLf and PLTLf goals over six common FOND planning domain models, and show that our approach is accurate to recognize temporally extended goals at several levels of observability.

In this paper we introduce Behavioral QLTL, which is a ``behavioral'' variant of linear-time temporal logic on infinite traces with second-order quantifiers. Behavioral QLTL is characterized by the fact that the functions that assign the truth value of the quantified propositions along the trace can only depend on the past. In other words such functions must be``processes''. This gives to the logic a strategic flavor that we usually associate to planning. Indeed we show that temporally extended planning in nondeterministic domains, as well as LTL synthesis, are expressed in Behavioral QLTL through formulas with a simple quantification alternation. While, as this alternation increases, we get to forms of planning/synthesis in which conditional and conformant planning aspects get mixed. We study this logic from the computational point of view and compare it to the original QLTL (with non-behavioral semantics) and with simpler forms of behavioral semantics.

Runtime monitoring is one of the central tasks in the area of operational decision support for business process management. In particular, it helps process executors to check on-the-fly whether a running process instance satisfies business constraints of interest, providing an immediate feedback when deviations occur. We study runtime monitoring of properties expressed in LTL on finite traces (LTLf), and in its extension LDLf. LDLf is a powerful logic that captures all monadic second order logic on finite traces, and that is obtained by combining regular expressions with LTLf, adopting the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its greater expressivity, \LDLf has exactly the same computational complexity of LTLf. We show that LDLf is able to declaratively express, in the logic itself, not only the constraints to be monitored, but also the de-facto standard RV-LTL monitors. On the one hand, this enables us to directly employ the standard characterization of LDLf based on finite-state automata to monitor constraints in a fine-grained way. On the other hand, it provides the basis for declaratively expressing sophisticated metaconstraints that predicate on the monitoring state of other constraints, and to check them by relying on standard logical services instead of ad-hoc algorithms. In addition, we devise a direct translation of LDLf formulae into nondeterministic finite-state automata, avoiding to detour to Buchi automata or alternating automata. We then report on how this approach has been effectively implemented using Java to manipulate LDLf formulae and their corresponding monitors, and the well-known ProM process mining suite as underlying operational decision support infrastructure.

We address two central notions of fairness in the literature of planning on nondeterministic fully observable domains. The first, which we call stochastic fairness, is classical, and assumes an environment which operates probabilistically using possibly unknown probabilities. The second, which is language-theoretic, assumes that if an action is taken from a given state infinitely often then all its possible outcomes should appear infinitely often (we call this state-action fairness). While the two notions coincide for standard reachability goals, they diverge for temporally extended goals. This important difference has been overlooked in the planning literature, and we argue has led to confusion in a number of published algorithms which use reductions that were stated for state-action fairness, for which they are incorrect, while being correct for stochastic fairness. We remedy this and provide an optimal sound and complete algorithm for solving state-action fair planning for LTL/LTLf goals, as well as a correct proof of the lower bound of the goal-complexity (our proof is general enough that it provides new proofs also for the no-fairness and stochastic-fairness cases). Overall, we show that stochastic fairness is better behaved than state-action fairness.

In synthesis, assumptions are constraints on the environment that rule out certain environment behaviors. A key observation here is that even if we consider systems with LTLf goals on finite traces, environment assumptions need to be expressed over infinite traces, since accomplishing the agent goals may require an unbounded number of environment action. To solve synthesis with respect to finite-trace LTLf goals under infinite-trace assumptions, we could reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTLf and in LTL have the same worst-case complexity (both 2EXPTIME-complete), the algorithms available for LTL synthesis are much more difficult in practice than those for LTLf synthesis. In this work we show that in interesting cases we can avoid such a detour to LTL synthesis and keep the simplicity of LTLf synthesis. Specifically, we develop a BDD-based fixpoint-based technique for handling basic forms of fairness and of stability assumptions. We show, empirically, that this technique performs much better than standard LTL synthesis.

We study the characterization and computation of general policies for families of problems that share a structure characterized by a common reduction into a single abstract problem. Policies $\mu$ that solve the abstract problem P have been shown to solve all problems Q that reduce to P provided that $\mu$ terminates in Q. In this work, we shed light on why this termination condition is needed and how it can be removed. The key observation is that the abstract problem P captures the common structure among the concrete problems Q that is local (Markovian) but misses common structure that is global. We show how such global structure can be captured by means of trajectory constraints that in many cases can be expressed as LTL formulas, thus reducing generalized planning to LTL synthesis. Moreover, for a broad class of problems that involve integer variables that can be increased or decreased, trajectory constraints can be compiled away, reducing generalized planning to fully observable non-deterministic planning., Comment: Proceedings IJCAI-17

In Reasoning about Action and Planning, one synthesizes the agent plan by taking advantage of the assumption on how the environment works (that is, one exploits the environment's effects, its fairness, its trajectory constraints). In this paper we study this form of synthesis in detail. We consider assumptions as constraints on the possible strategies that the environment can have in order to respond to the agent's actions. Such constraints may be given in the form of a planning domain (or action theory), as linear-time formulas over infinite or finite runs, or as a combination of the two. We argue though that not all assumption specifications are meaningful: they need to be consistent, which means that there must exist an environment strategy fulfilling the assumption in spite of the agent actions. For such assumptions, we study how to do synthesis/planning for agent goals, ranging from a classical reachability to goal on traces specified in \LTL and \LTLf/\LDLf, characterizing the problem both mathematically and algorithmically.

In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The two sets are apparently unrelated since of interest to independent parties, however they both account for (aspects of) the same world. We consider the case in which the agent is a reinforcement learning agent on the first set of features, while the restraining bolt is specified logically using linear time logic on finite traces LTLf/LDLf over the second set of features. We show formally, and illustrate with examples, that, under general circumstances, the agent can learn while shaping its goals to suitably conform (as much as possible) to the restraining bolt specifications.

Manufacturing is transitioning from a mass production model to a manufacturing as a service model in which manufacturing facilities 'bid' to produce products. To decide whether to bid for a complex, previously unseen product, a manufacturing facility must be able to synthesize, 'on the fly', a process plan controller that delegates abstract manufacturing tasks in the supplied process recipe to the appropriate manufacturing resources, e.g., CNC machines, robots etc. Previous work in applying AI behaviour composition to synthesize process plan controllers has considered only finite state ad-hoc representations. Here, we study the problem in the relational setting of the Situation Calculus. By taking advantage of recent work on abstraction in the Situation Calculus, process recipes and available resources are represented by ConGolog programs over, respectively, an abstract and a concrete action theory. This allows us to capture the problem in a formal, general framework, and show decidability for the case of bounded action theories. We also provide techniques for actually synthesizing the controller.

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.

In Markov Decision Processes (MDPs), the reward obtained in a state depends on the properties of the last state and action. This state dependency makes it difficult to reward more interesting long-term behaviors, such as always closing a door after it has been opened, or providing coffee only following a request. Extending MDPs to handle such non-Markovian reward function was the subject of two previous lines of work, both using variants of LTL to specify the reward function and then compiling the new model back into a Markovian model. Building upon recent progress in the theories of temporal logics over finite traces, we adopt LDLf for specifying non-Markovian rewards and provide an elegant automata construction for building a Markovian model, which extends that of previous work and offers strong minimality and compositionality guarantees.