Probabilistic Event Calculus (PEC) is a logical framework for reasoning about actions and their effects in uncertain environments, which enables the representation of probabilistic narratives and computation of temporal projections. The PEC formalism offers significant advantages in interpretability and expressiveness for narrative reasoning. However, it lacks mechanisms for goal-directed reasoning. Our work bridges this gap by developing a formal translation of PEC domains into Markov Decision Processes (MDPs), introducing the concept of "action-taking situations" to preserve PEC’s flexible action semantics. The resulting PEC-MDP formalism enables the extensive collection of algorithms and theoretical tools developed for MDPs to be applied to PEC’s interpretable narrative domains. We demonstrate how the translation supports both temporal reasoning tasks and objective-driven planning, with methods for mapping learned policies back into human-readable PEC representations, maintaining interpretability while extending PEC’s capabilities.

Abstract In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications. Derivability in TPTND is interpreted as the process of extracting $n$ samples of possibly complex outputs with a certain frequency from a given categorical distribution. We formalize trust for such outputs as a form of hypothesis testing on the distance between such frequency and the intended probability. The main advantage of the calculus is to render such notion of trustworthiness checkable. We present a computational semantics for the terms over which we reason and then the semantics of TPTND, where logical operators as well as a Trust operator are defined through introduction and elimination rules. We illustrate structural and metatheoretical properties, with particular focus on the ability to establish under which term evaluations and logical rules applications the notion of trustworthiness can be preserved.

We describe a general procedure for translating Epistemic Probabilistic Event Calculus (EPEC) action language domains into Answer Set Programs (ASP), and show how the Python-driven features of the ASP solver Clingo can be used to provide efficient computation in this probabilistic setting. EPEC supports probabilistic, epistemic reasoning in domains containing narratives that include both an agent's own action executions and environmentally triggered events. Some of the agent's actions may be belief-conditioned, and some may be imperfect sensing actions that alter the strengths of previously held beliefs. We show that our ASP implementation can be used to provide query answers that fully correspond to EPEC's own declarative, Bayesian-inspired semantics.

Abstract We present and discuss a runtime architecture that integrates sensorial data and classifiers with a logic-based decision-making system in the context of an e-Health system for the rehabilitation of children with neuromotor disorders. In this application, children perform a rehabilitation task in the form of games. The main aim of the system is to derive a set of parameters the child’s current level of cognitive and behavioral performance (e.g., engagement, attention, task accuracy) from the available sensors and classifiers (e.g., eye trackers, motion sensors, emotion recognition techniques) and take decisions accordingly. These decisions are typically aimed at improving the child’s performance by triggering appropriate re-engagement stimuli when their attention is low, by changing the game or making it more difficult when the child is losing interest in the task as it is too easy. Alongside state-of-the-art techniques for emotion recognition and head pose estimation, we use a runtime variant of a probabilistic and epistemic logic programming dialect of the Event Calculus, known as the Epistemic Probabilistic Event Calculus. In particular, the probabilistic component of this symbolic framework allows for a natural interface with the machine learning techniques. We overview the architecture and its components, and show some of its characteristics through a discussion of a running example and experiments.

Depth-Bounded Boolean Logics (DBBL for short) are well-understood frameworks to model rational agents equipped with limited deductive capabilities. These Logics use a parameter k>=0 to limit the amount of virtual information, i.e., the information that the agent may temporarily assume throughout the deductive process. This restriction brings several advantageous properties over classical Propositional Logic, including polynomial decision procedures for deducibility and refutability. Inspired by DBBL, we propose a limited-depth version of the popular ASP system \clingo, tentatively dubbed k-lingo after the bound k on virtual information. We illustrate the connection between DBBL and ASP through examples involving both proof-theoretical and implementative aspects. The paper concludes with some comments on future work, which include a computational complexity characterization of the system, applications to multi-agent systems and feasible approximations of probability functions.

In this paper we advocate the use of Inductive Logic Programming as a device for explaining black-box models, e.g. Support Vector Machines (SVMs), when they are used to learn user preferences. We present a case study where we use the ILP system ILASP to explain the output of SVM classifiers trained on preference datasets. Explanations are produced in terms of weak constraints, which can be easily understood by humans. We use ILASP both as a global and a local approximator for SVMs, score its fidelity, and discuss how its output can prove useful e.g. for interactive learning tasks and for identifying unwanted biases when the original dataset is not available. Finally, we highlight directions for further work and discuss relevant application areas.