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

Pure-Past Linear Temporal and Dynamic Logic on Finite Traces

LTLf and LDLf are well-known logics on finite traces. We review PLTLf and PLDLf, their pure- past versions. These are interpreted backward from the end of the trace towards the beginning. Because of this, we can exploit a foundational result on reverse languages to get an exponential improvement, wrt LTLf /LDLf, in computing the corresponding DFA. This exponential improvement is reflected in several forms sequential decision making involving temporal specifications, such as planning and decision problems in non-deterministic and non-Markovian domains. Interestingly, PLTLf (resp. PLDLf ) has the same expressive power as LTLf (resp. LDLf ), but transforming a PLTLf (resp. PLDLf ) formula into its equivalent in LTLf (resp. LDLf ) is quite expensive. Hence, to take advantage of the exponential improvement, properties of interest must be directly expressed in PLTLf /PLTLf

Synthesizing strategies under expected and exceptional environment behaviors

We consider an agent that operates with two models of the environment: one that captures expected behaviors and one that captures additional exceptional behaviors. We study the problem of synthesizing agent strategies that enforce a goal against environments operating as expected while also making a best effort against exceptional environment behaviors. We formalize these concepts in the context of linear-temporal logic, and give an algorithm for solving this problem. We also show that there is no trade-off between enforcing the goal under the expected environment specification and making a best-effort for it under the exceptional one

Generalized planning: Non-deterministic abstractions and trajectory constraints

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 nondeterministic planning

FOND planning for pure-past linear temporal logic goals

Recently, Pure-Past Temporal Logic (PPLTL) has proven highly effective in specifying temporally extended goals in deterministic planning domains. In this paper, we show its effectiveness also for fully observable nondeterministic (FOND) planning, both for strong and strong-cyclic plans. We present a notably simple encoding of FOND planning for PPLTL goals into standard FOND planning for final-state goals. The encoding only introduces few fluents (at most linear in the PPLTL goal) without adding any spurious action and allows planners to lazily build the relevant part of the deterministic automaton for the goal formula on-the-fly during the search. We formally prove its correctness, implement it in a tool called Plan4Past, and experimentally show its practical effectiveness

Abstraction of nondeterministic situation calculus action theories

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 exist a refinement of it that is a (strong FOND) plan/strategy to achieve the refinement of the goal/task at the concrete level

Multi-agent verification and control with probabilistic model checking

Probabilistic model checking is a technique for formal automated reasoning about software or hardware systems that operate in the context of uncertainty or stochasticity. It builds upon ideas and techniques from a diverse range of fields, from logic, automata and graph theory, to optimisation, numerical methods and control. In recent years, probabilistic model checking has also been extended to integrate ideas from game theory, notably using models such as stochastic games and solution concepts such as equilibria, to formally verify the interaction of multiple rational agents with distinct objectives. This provides a means to reason flexibly about agents acting in either an adversarial or a collaborative fashion, and opens up opportunities to tackle new problems within, for example, artificial intelligence, robotics and autonomous systems. In this paper, we summarise some of the advances in this area, and highlight applications for which they have already been used. We discuss how the strengths of probabilistic model checking apply, or have the potential to apply, to the multi-agent setting and outline some of the key challenges required to make further progress in this field

Progressing intention progression: a call for a Goal-Plan Tree contest

User-supplied domain control knowledge in the form of hierarchically structured Goal-Plan Trees (GPTs) is at the heart of a number of approaches to reasoning about action. Reasoning with GPTs connects the AAMAS community with other communities such as automated planning, and forms the foundation for important reasoning capabilities, especially intention progression in Belief-Desire-Intention (BDI) agents. Research on GPTs has a long history but suffers from fragmentation and lack of common terminology, data formats, and enabling tools. One way to address this fragmentation is through a competition. Competitions are increasingly being used as a means to foster research and challenge the state of the art. For example, the AAMAS conference has a number of associated competitions, such as the Trading Agent Competition, while agent research is showcased at competitions such as RoboCup. We therefore issue a call for a Goal-Plan Tree Contest, with the ambition of drawing together a community and incentivizing research in intention progression