Ricerc@Sapienza

We look at program synthesis where the aim is to automatically synthesize a controller that operates on data structures and from which a concrete program can be easily derived. We do not aim at a fully-automatic process or tool that produces a program meeting a given specification of the program’s behaviour. Rather, we aim at the design of a clear and well- founded approach for supporting programmers at the design and implementation phases. Concretely, we first show that a program synthesis task can be modeled as a generalized planning problem.

Nondeterministic strategies are strategies (or protocols, or plans) that, given a history in a game, assign a set of possible actions, all of which are winning. An important problem is that of refining such strategies. For instance, given a nondeterministic strategy that allows only safe executions, refine it to, additionally, eventually reach a desired state of affairs. We show that strategic problems involving strategy refinement can be solved elegantly in the framework of Strategy Logic (SL), a very expressive logic to reason about strategic abilities.

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.

Goal reasoning has been attracting much attention in AI recently. Here, we consider how an agent changes its goals as a result of interaction with humans and peers. In particular, we draw upon a model developed in Behavioral Science, the Elementary Pragmatic Model (EPM). We show how the EPM principles can be incorporated into a sophisticated theory of goal change based on the Situation Calculus. The resulting logical theory supports agents with a wide variety of relational styles, including some that we may consider irrational or creative.

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.

Most programming languages only support tests that refer exclusively to the current state. This applies even to high-level programming languages based on the situation calculus such as Golog. The result is that additional variables/fluents/data structures must be introduced to track conditions that the pro- gram uses in tests to make decisions.

In synthesis, assumption are constraints on the environments that rule out certain environment behaviors. A key observation is that even if we consider system with LTLf goals on finite traces, assumptions need to be expressed considering infinite traces, using LTL on infinite traces, since the decision to stop the trace is controlled by the agent. To solve synthesis of LTLf goals under LTL assumptions, we could reduce the problem to LTL synthesis.

By their very design, many robot control programs are non-terminating. This paper describes a situation calculus approach to expressing and proving properties of non-terminating programs expressed in Golog, a high level logic programming language for modeling and implementing dynamical systems. Because in this approach actions and programs are represented in classical (second-order) logic, it is natural to express and prove properties of Golog programs, including non-terminating ones, in the very same logic.