Logic Programming

In this paper, we develop a novel logic-based approach to detecting high-level temporally extended events from timestamped data and background knowledge. Our framework employs logical rules to capture existence and termination conditions for simple temporal events and to combine these into meta-events. In the medical domain, for example, disease episodes and therapies are inferred from timestamped clinical observations, such as diagnoses and drug administrations stored in patient records, and can be further combined into higher-level disease events. As some incorrect events might be inferred, we use constraints to identify incompatible combinations of events and propose a repair mechanism to select preferred consistent sets of events. While reasoning in the full framework is intractable, we identify relevant restrictions that ensure polynomial-time data complexity. Our prototype system implements core components of the approach using answer set programming. An evaluation on a lung cancer use case supports the interest of the approach, both in terms of computational feasibility and positive alignment of our results with medical expert opinions. While strongly motivated by the needs of the healthcare domain, our framework is purposely generic, enabling its reuse in other areas.

Streamliner constraints reduce the search space of combinatorial problems by ruling out portions of the solution space. We adapt the StreamLLM approach, which uses Large Language Models (LLMs) to generate streamliners for Constraint Programming, to Answer Set Programming (ASP). Given an ASP encoding and a few small training instances, we prompt multiple LLMs to propose candidate constraints. Candidates that cause syntax errors, render satisfiable instances unsatisfiable, or degrade performance on all training instances are discarded. The surviving streamliners are evaluated together with the original encoding, and we report results for a virtual best encoding (VBE) that, for each instance, selects the fastest among the original encoding and its streamlined variants. On three ASP Competition benchmarks (Partner Units Problem, Sokoban, Towers of Hanoi), the VBE achieves speedups of up to 4--5x over the original encoding. Different LLMs produce semantically diverse constraints, not mere syntactic variations, indicating that the approach captures genuine problem structure.

This paper introduces PYTHEN, a novel Python-based framework for defeasible legal reasoning. PYTHEN is designed to model the inherently defeasible nature of legal argumentation, providing a flexible and intuitive syntax for representing legal rules, conditions, and exceptions. Inspired by PROLEG (PROlog-based LEGal reasoning support system) and guided by the philosophy of The Zen of Python, PYTHEN leverages Python's built-in any() and all() functions to offer enhanced flexibility by natively supporting both conjunctive (ALL) and disjunctive (ANY) conditions within a single rule, as well as a more expressive exception-handling mechanism. This paper details the architecture of PYTHEN, provides a comparative analysis with PROLEG, and discusses its potential applications in autoformalization and the development of next-generation legal AI systems. By bridging the gap between symbolic reasoning and the accessibility of Python, PYTHEN aims to democratize formal legal reasoning for young researchers, legal tech developers, and professionals without extensive logic programming expertise. We position PYTHEN as a practical bridge between the powerful symbolic reasoning capabilities of logic programming and the rich, ubiquitous ecosystem of Python, making formal legal reasoning accessible to a broader range of developers and legal professionals.

Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its paired reader, and may contain additional readers and/or writers. This enables the concise expression of rich multidirectional communication modalities. The language was introduced together with concurrent (cGLP) and multiagent (maGLP) operational semantics. Here, we derive from these (1) dGLP, a deterministic counterpart of cGLP, and (2) madGLP, a counterpart of maGLP in which deterministic agents communicate solely by asynchronous message passing, and prove them correct against their abstract counterparts. maGLP shared variable pairs spanning agents can be implemented by two local variable pairs joined by a global link, with correctness following from disjoint substitution commutativity (a consequence of GLP's single-occurrence invariant). We further prove that madGLP is grassroots. Both dGLP and madGLP serve as formal specifications for an AI-driven implementation discipline (math $\to$ informal spec $\to$ Dart) employed and described here: from dGLP, AI (Claude) developed a workstation-based GLP implementation in Dart, and from madGLP it is developing a smartphone-based multiagent one.

A grassroots platform is a multiagent distributed system in which multiple independent instances can form and operate independently of each other and of any global resource, yet may coalesce into ever larger instances, possibly resulting in a single global instance. Grassroots platforms aim to offer an egalitarian/democratic alternative to centralised/autocratic and decentralised/plutocratic global platforms. Here, we present Grassroots Logic Programs (GLP), a multiagent concurrent logic programming language designed for the implementation of grassroots platforms: we recall the standard operational semantics of logic programs; introduce the concurrent operational semantics of GLP as its restriction; recall multiagent atomic transactions; use them to introduce a multiagent operational semantics of GLP; and prove multiagent GLP to be grassroots. The grassroots social graph -- the foundational grassroots platform on which all others are based -- serves as a GLP programming example. These mathematical foundations are being used by AI to implement GLP as well as to program in GLP: a workstation-based implementation of concurrent GLP in Dart was derived from the concurrent operational semantics of GLP; a multiagent smartphone-based implementation of GLP in Dart/Flutter is being developed based on the multiagent operational semantics of GLP; a moded type system for GLP was designed (and implemented by AI in Dart) to facilitate collaborative human-AI development of GLP programs, where AI derives working GLP programs from human-approved type definitions and declarations; GLP implementations of grassroots platforms for the social graph, social networks, currencies and bonds, and more, have been derived by AI from mathematical specifications written as volitional multiagent atomic transactions.

DatalogMTL is a powerful rule-based language for temporal reasoning. Due to its high expressive power and flexible modeling capabilities, it is suitable for a wide range of applications, including tasks from industrial and financial sectors. However, due to its high computational complexity, practical reasoning in DatalogMTL is highly challenging. To address this difficulty, we introduce a new reasoning method for DatalogMTL which exploits the magic sets technique -- a rewriting approach developed for (non-temporal) Datalog to simulate top-down evaluation with bottom-up reasoning. We have implemented this approach and evaluated it on publicly available benchmarks, showing that the proposed approach significantly and consistently outperformed state-of-the-art reasoning techniques.