Probabilistic Hybrid Action Models for Predicting Concurrent Percept-driven Robot Behavior

This article develops Probabilistic Hybrid Action Models (PHAMs), a realistic causal model for predicting the behavior generated by modern percept-driven robot plans. PHAMs represent aspects of robot behavior that cannot be represented by most action models used in AI planning: the temporal structure of continuous control processes, their non-deterministic effects, several modes of their interferences, and the achievement of triggering conditions in closed-loop robot plans. The main contributions of this article are: (1) PHAMs, a model of concurrent percept-driven behavior, its formalization, and proofs that the model generates probably, qualitatively accurate predictions; and (2) a resource-efficient inference method for PHAMs based on sampling projections from probabilistic action models and state descriptions. We show how PHAMs can be applied to planning the course of action of an autonomous robot office courier based on analytical and experimental results

Stochastic Fairness and Language-Theoretic Fairness in Planning in Nondeterministic Domains

We address two central notions of fairness in the literature of 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 differ for temporally extended goals. This important difference has been overlooked in the planning literature and has led to the use of a product-based reduction in a number of published algorithms which were stated for state-action fairness, for which they are incorrect, while being correct for stochastic fairness. We remedy this and provide a correct optimal 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 also pro- vides, for the no-fairness and stochastic-fairness cases, multiple missing lower bounds and new proofs of known lower bounds. Overall, we show that stochastic fairness is better behaved than state-action fairness

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

A Process Modelling Framework Based on Point Interval Temporal Logic with an Application to Modelling Patient Flows

This thesis considers an application of a temporal theory to describe and model the patient journey in the hospital accident and emergency (A&E) department. The aim is to introduce a generic but dynamic method applied to any setting, including healthcare. Constructing a consistent process model can be instrumental in streamlining healthcare issues. Current process modelling techniques used in healthcare such as flowcharts, unified modelling language activity diagram (UML AD), and business process modelling notation (BPMN) are intuitive and imprecise. They cannot fully capture the complexities of the types of activities and the full extent of temporal constraints to an extent where one could reason about the flows. Formal approaches such as Petri have also been reviewed to investigate their applicability to the healthcare domain to model processes. Additionally, to schedule patient flows, current modelling standards do not offer any formal mechanism, so healthcare relies on critical path method (CPM) and program evaluation review technique (PERT), that also have limitations, i.e. finish-start barrier. It is imperative to specify the temporal constraints between the start and/or end of a process, e.g., the beginning of a process A precedes the start (or end) of a process B. However, these approaches failed to provide us with a mechanism for handling these temporal situations. If provided, a formal representation can assist in effective knowledge representation and quality enhancement concerning a process. Also, it would help in uncovering complexities of a system and assist in modelling it in a consistent way which is not possible with the existing modelling techniques. The above issues are addressed in this thesis by proposing a framework that would provide a knowledge base to model patient flows for accurate representation based on point interval temporal logic (PITL) that treats point and interval as primitives. These objects would constitute the knowledge base for the formal description of a system. With the aid of the inference mechanism of the temporal theory presented here, exhaustive temporal constraints derived from the proposed axiomatic system’ components serves as a knowledge base. The proposed methodological framework would adopt a model-theoretic approach in which a theory is developed and considered as a model while the corresponding instance is considered as its application. Using this approach would assist in identifying core components of the system and their precise operation representing a real-life domain deemed suitable to the process modelling issues specified in this thesis. Thus, I have evaluated the modelling standards for their most-used terminologies and constructs to identify their key components. It will also assist in the generalisation of the critical terms (of process modelling standards) based on their ontology. A set of generalised terms proposed would serve as an enumeration of the theory and subsume the core modelling elements of the process modelling standards. The catalogue presents a knowledge base for the business and healthcare domains, and its components are formally defined (semantics). Furthermore, a resolution theorem-proof is used to show the structural features of the theory (model) to establish it is sound and complete. After establishing that the theory is sound and complete, the next step is to provide the instantiation of the theory. This is achieved by mapping the core components of the theory to their corresponding instances. Additionally, a formal graphical tool termed as point graph (PG) is used to visualise the cases of the proposed axiomatic system. PG facilitates in modelling, and scheduling patient flows and enables analysing existing models for possible inaccuracies and inconsistencies supported by a reasoning mechanism based on PITL. Following that, a transformation is developed to map the core modelling components of the standards into the extended PG (PG*) based on the semantics presented by the axiomatic system. A real-life case (from the King’s College hospital accident and emergency (A&E) department’s trauma patient pathway) is considered to validate the framework. It is divided into three patient flows to depict the journey of a patient with significant trauma, arriving at A&E, undergoing a procedure and subsequently discharged. Their staff relied upon the UML-AD and BPMN to model the patient flows. An evaluation of their representation is presented to show the shortfalls of the modelling standards to model patient flows. The last step is to model these patient flows using the developed approach, which is supported by enhanced reasoning and scheduling

Decision-Theoretic Golog with Qualitative Preferences

Personalization is becoming increasingly important in agent programming, particularly as it relates to the Web. We propose to develop underspecified, task-specific agent programs, and to automatically personalize them to the preferences of individual users. To this end, we propose a framework for agent programming that integrates rich, non-Markovian, qualitative user preferences expressed in a linear temporal logic with quantitative Markovian reward functions. We begin with DTGOLOG, a first-order, decisiontheoretic agent programming language in the situation calculus. We present an algorithm that compiles qualitative preferences into GOLOG programs and prove it sound and complete with respect to the space of solutions. To integrate these preferences into DTGOLOG we introduce the notion of multiprogram synchronization and restate the semantics of the language as a transition semantics. We demonstrate the utility of this framework with an application to personalized travel planning over the Web. To the best of our knowledge this is the first work to combine qualitative and quantitative preferences for agent programming. Further, while the focus of this paper is on the integration of qualitative and quantitative preferences, a side effect of this work is realization of the simpler task of integrating qualitative preferences alone into agent programming as well as the generation of GOLOG programs from LTL formulae.

Reasoning about LTL Synthesis over finite and infinite games

In the last few years, research formal methods for the analysis and the verification of properties of systems has increased greatly. A meaningful contribution in this area has been given by algorithmic methods developed in the context of synthesis. The basic idea is simple and appealing: instead of developing a system and verifying that it satisfies its specification, we look for an automated procedure that, given the specification returns a system that is correct by construction. Synthesis of reactive systems is one of the most popular variants of this problem, in which we want to synthesize a system characterized by an ongoing interaction with the environment. In this setting, large effort has been devoted to analyze specifications given as formulas of linear temporal logic, i.e., LTL synthesis. Traditional approaches to LTL synthesis rely on transforming the LTL specification into parity deterministic automata, and then to parity games, for which a so-called winning region is computed. Computing such an automaton is, in the worst-case, double-exponential in the size of the LTL formula, and this becomes a computational bottleneck in using the synthesis process in practice. The first part of this thesis is devoted to improve the solution of parity games as they are used in solving LTL synthesis, trying to give efficient techniques, in terms of running time and space consumption, for solving parity games. We start with the study and the implementation of an automata-theoretic technique to solve parity games. More precisely, we consider an algorithm introduced by Kupferman and Vardi that solves a parity game by solving the emptiness problem of a corresponding alternating parity automaton. Our empirical evaluation demonstrates that this algorithm outperforms other algorithms when the game has a small number of priorities relative to the size of the game. In many concrete applications, we do indeed end up with parity games where the number of priorities is relatively small. This makes the new algorithm quite useful in practice. We then provide a broad investigation of the symbolic approach for solving parity games. Specifically, we implement in a fresh tool, called SPGSolver, four symbolic algorithms to solve parity games and compare their performances to the corresponding explicit versions for different classes of games. By means of benchmarks, we show that for random games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms. The situation changes, however, for structured games, where symbolic algorithms seem to have the advantage. This suggests that when evaluating algorithms for parity-game solving, it would be useful to have real benchmarks and not only random benchmarks, as the common practice has been. LTL synthesis has been largely investigated also in artificial intelligence, and specifically in automated planning. Indeed, LTL synthesis corresponds to fully observable nondeterministic planning in which the domain is given compactly and the goal is an LTL formula, that in turn is related to two-player games with LTL goals. Finding a strategy for these games means to synthesize a plan for the planning problem. The last part of this thesis is then dedicated to investigate LTL synthesis under this different view. In particular, we study a generalized form of planning under partial observability, in which we have multiple, possibly infinitely many, planning domains with the same actions and observations, and goals expressed over observations, which are possibly temporally extended. By building on work on two-player games with imperfect information in the Formal Methods literature, we devise a general technique, generalizing the belief-state construction, to remove partial observability. This reduces the planning problem to a game of perfect information with a tight correspondence between plans and strategies. Then we instantiate the technique and solve some generalized planning problems