We investigate the problem of synthesizing strategies that guarantee the successful execution of a high-level nondeterministic agent program in Golog within a nondeterministic first-order basic action theory, considering the environment as adversarial. Our approach constructs a symbolic program graph that captures the control flow independently of the domain, enabling strategy synthesis through the cross product of the program graph with the domain model. We formally relate graph-based transitions to standard Golog semantics and provide a synthesis procedure that is sound though incomplete (in general, the problem is undecidable, given that we have a first-order representation of the state). We also extend the framework to handle the case where the environment's possible behaviors are specified by a Golog program.

Golog programs over Situation Calculus action theories were introduced as a specification of desired agent behavior, very much like temporally extended goals in planning, but with a focus on procedural aspects typical of programs. In the words of the original paper: "Golog allows the programmer to strike a compromise between the often computationally infeasible classical planning task, in which a plan must be deduced entirely from scratch, and detailed programming, in which every little step must be specified." In this paper, we study temporal synthesis with Golog programs as specifications over nondeterministic propositional action theories. We show that Golog has the same expressive power as linear dynamic logics on finite traces (LDLf), namely that of regular languages or monadic second-order logic (MSO) over finite traces, while exhibiting a markedly lower synthesis complexity: synthesis can be performed by constructing a polynomial-size program graph and taking its cross-product with the domain, whereas LDLf synthesis requires building a deterministic automaton of worst-case doubly exponential size. This advantage is confirmed experimentally.

This paper addresses the problem of suffix prediction in Business Process Management (BPM) by proposing a Neuro-Symbolic Predictive Process Monitoring (PPM) approach that integrates data-driven learning with temporal logic-based prior knowledge. While recent approaches leverage deep learning models for suffix prediction, they often fail to satisfy even basic logical constraints due to the absence of explicit integration of domain knowledge during training. We propose a novel method to incorporate Linear Temporal Logic over finite traces (LTLf) into the training process of autoregressive sequence predictors. Our approach introduces a differentiable logical loss function, defined using a soft approximation of LTLf semantics and the Gumbel-Softmax trick, which can be combined with standard predictive losses. This ensures the model learns to generate suffixes that are both accurate and logically consistent. Experimental evaluation on three real-world datasets shows that our method improves suffix prediction accuracy and compliance with temporal constraints. We also introduce two variants of the logic loss (local and global) and demonstrate their effectiveness under noisy and realistic settings. While developed in the context of BPM, our framework is applicable to any symbolic sequence generation task and contributes toward advancing Neuro-Symbolic AI.

We present a new formal framework for generalized planning (GP) based on the situation calculus extended with LTL constraints. The GP problem is specified by a first-order basic action theory whose models are the problem instances. This low-level theory is then abstracted into a high-level propositional nondeterministic basic action theory with a single model. A refinement mapping relates the two theories. LTL formulas are used to specify the temporally extended goals as well as assumed trace constraints. If all LTL trace constraints hold at the low level and the high-level model can simulate all the low-level models with respect to the mapping, we say that we have a temporally lifted abstraction. We prove that if we have such an abstraction and the agent has a strategy to achieve a LTL goal under some trace constraints at the abstract level, then there exists a refinement of the strategy to achieve the refinement of the goal at the concrete level. We use LTL synthesis to generate the strategy at the abstract level. We illustrate our approach by synthesizing a program that solves a data structure manipulation problem.