SMTB: Fast Structure-Mapping with Tight Bounds

Neurosymbolic systems can satisfy logical constraints during learning without achieving the intended concept-label correspondence; this is a problem known as reasoning shortcuts. We formalize reasoning shortcuts as a constraint satisfaction problem and investigate under which conditions concept mappings are uniquely determined by the constraints. We prove that a discrimination property (requiring that no valid concept mapping can be transformed into another valid mapping by swapping two concept values) is necessary for shortcut-freeness under bijective mappings, but demonstrate via a counterexample that it is insufficient even when the constraint graph is connected. We develop an ASP-based algorithm that verifies whether a given constraint set uniquely determines the intended concept mapping, with proven soundness and completeness. When shortcuts are detected, a greedy repair algorithm eliminates them by augmenting the constraint set, converging in at most $k$ iterations, where $k$ is the number of alternative valid mappings. We further provide a complexity classification: deciding shortcut-freeness is coNP-complete, counting shortcuts is #P-complete, and finding minimal repairs is NP-hard. We also establish sample complexity bounds showing that logarithmically many label queries suffice for disambiguation in favorable cases, while querying all ambiguous positions suffices in the worst case. Experiments across eight benchmark domains validate our approach.

Structural generalization in semantic parsing requires systems to apply learned compositional rules to novel structural combinations. Existing approaches either rely on hand-written algebraic rules (AM-Parser) or fail to generalize structurally (Transformer-based models). We present an alternative requiring no hand-written compositional rules, based on a neural cellular automaton (NCA) with a discrete bottleneck: all compositional rules are learned from data through local iteration. On the SLOG benchmark, the system achieves an overall accuracy of $67.3 \pm 0.2\%$ across 10 seeds (AM-Parser: $70.8 \pm 4.3\%$), with 11 of 17 structural generalization categories at $100\%$ type-exact match, including three where AM-Parser scores $0$--$74\%$. Analysis reveals that all 5,539 failure instances reduce to exactly two mechanisms: novel combinations of wh-extraction context with reduced verb types, and modifiers appearing on the subject side of verbs. When we decompose results by CCG structural features, each sub-pattern either succeeds on all instances or fails on all. Intermediate scores (e.g., $41.4\%$) are mixtures of structurally distinct CCG patterns, not partial generalization. These results suggest that CCG directed types provide higher resolution than SLOG's phenomenon-level categories for characterizing structural generalization, and that the success/failure boundary is determined by the coverage of directed operations in the training data.

Constraint Answer Set Programming (CASP) is a hybrid reasoning paradigm that combines Answer Set Programming (ASP) with Constraint Processing and Satisfiability Modulo Theories (SMT), enabling powerful declarative encodings of complex combinatorial search problems. This paper presents the design and implementation of EZSMTV3, an extensible SMT-based CASP framework that advances the translational approach to CASP solving. Building upon the foundation of the EZSMT+ system, EZSMTV3 introduces a more expressive input language, supports optimization via weak constraints, and offers foundations for streamlined integration of new constraint types. Rather than implementing custom search procedures, EZSMTV3 leverages state-of-the-art SMT solvers, such as CVC5, YICES, and Z3 to perform reasoning. The paper provides benchmarking results comparing EZSMTV3 with its CASP peers such as CLINGCON, CLINGO[DL], and CLINGO[LP], while showcasing its ability to handle mixed-domain constraints involving both integers and reals. The system provides a robust platform for future extensions and theoretical exploration within the CASP domain.