Shawn Bowers

Evgeny Skvortsov, Yilin Xia, Ojaswa Garg et al.

Logica is an open-source logic programming language that compiles to SQL and runs on DuckDB, SQLite, PostgreSQL, and BigQuery. Unlike classic Datalog, it freely combines recursion and aggregation, concisely expressing algorithms from shortest paths to PageRank. This expressiveness raises semantic challenges: aggregates update by replacement rather than accumulation, evaluation depends on rule scheduling, and programs may converge to meaningful results without reaching a fixpoint, placing them outside traditional fixpoint semantics. We address this with Defendant-Opponent (DO) semantics, a stabilization-based framework for nonmonotonic logic programs. Evaluation is modeled as a rewrite system over derivation states, and a ground atom is true if, from every reachable state, some continuation makes the atom persist in all further derivations. This admits two equivalent characterizations: game-theoretically, truth is what a Defendant can defend against any Opponent in a three-turn game; and modally, truth corresponds to []<>[]t in the derivation graph viewed as a Kripke structure, placing nonmonotonic reasoning within S4. DO semantics coincides with least fixpoint semantics for positive Datalog and is compatible with both Well-Founded and Stable Model Semantics. For programs that converge without a fixpoint, ω-limit interpretations give rigorous meaning to iterative computations such as PageRank.

Yilin Xia, Heng Zheng, Shawn Bowers et al.

Argumentation frameworks (AFs) provide formal approaches for legal reasoning, but identifying sources of ambiguity and explaining argument acceptance remains challenging for non-experts. We present AF-XRAY, an open-source toolkit for exploring, analyzing, and visualizing abstract AFs in legal reasoning. AF-XRAY introduces: (i) layered visualizations based on game-theoretic argument length revealing well-founded derivation structures; (ii) classification of attack edges by semantic roles (primary, secondary, blunders); (iii) overlay visualizations of alternative 2-valued solutions on ambiguous 3-valued grounded semantics; and (iv) identification of critical attack sets whose suspension resolves undecided arguments. Through systematic generation of critical attack sets, AF-XRAY transforms ambiguous scenarios into grounded solutions, enabling users to pinpoint specific causes of ambiguity and explore alternative resolutions. We use real-world legal cases (e.g., Wild Animals as modeled by Bench-Capon) to show that our tool supports teleological legal reasoning by revealing how different assumptions lead to different justified conclusions.

Evgeny Skvortsov, Yilin Xia, Ojaswa Garg et al.

We present Logical Robots, an interactive multi-agent simulation platform where autonomous robot behavior is specified declaratively in the logic programming language Logica. Robot behavior is defined by logical predicates that map observations from simulated radar arrays and shared memory to desired motor outputs. This approach allows low-level reactive control and high-level planning to coexist within a single programming environment, providing a coherent framework for exploring multi-agent robot behavior.

Bertram Ludäscher, Yilin Xia, Shawn Bowers

The rule $\mathrm{Defeated}(x) \leftarrow \mathrm{Attacks}(y,x),\, \neg \, \mathrm{Defeated}(y)$, evaluated under the well-founded semantics (WFS), yields a unique 3-valued (skeptical) solution of an abstract argumentation framework (AF). An argument $x$ is defeated ($\mathrm{OUT}$) if there exists an undefeated argument $y$ that attacks it. For 2-valued (stable) solutions, this is the case iff $y$ is accepted ($\mathrm{IN}$), i.e., if all of $y$'s attackers are defeated. Under WFS, arguments that are neither accepted nor defeated are undecided ($\mathrm{UNDEC}$). As shown in prior work, well-founded solutions (a.k.a. grounded labelings) "explain themselves": The provenance of arguments is given by subgraphs (definable via regular path queries) rooted at the node of interest. This provenance is closely related to winning strategies of a two-player argumentation game. We present a novel approach for extending this provenance to stable AF solutions. Unlike grounded solutions, which can be constructed via a bottom-up alternating fixpoint procedure, stable models often involve non-deterministic choice as part of the search for models. Thus, the provenance of stable solutions is of a different nature, and reflects a more expressive generate & test paradigm. Our approach identifies minimal sets of critical attacks, pinpointing choices and assumptions made by a stable model. These critical attack edges provide additional insights into the provenance of an argument's status, combining well-founded derivation steps with choice steps. Our approach can be understood as a form of diagnosis that finds minimal "repairs" to an AF graph such that the well-founded solution of the repaired graph coincides with the desired stable model of the original AF graph.