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Hybrid Reasoning About Relative Position and Orientation of Objects and Navigating Agents Using Answer Set Programming
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Proposes HOPA, a hybrid calculus extending OPRA with qualitative distance and quantitative constraints, and an Answer Set Programming framework for consistency checking, inconsistency explanation, inference and layout generation over discretized 2D space.
Problem
Reasoning about relative position, orientation and distance of point objects and navigating agents in 2D space, where OPRA is NP-hard/∃R-complete and existing tools (composition, path-consistency) are incomplete and cannot check consistency or generate configurations.
Approach
Augments OPRA with qualitative interval distance and quantitative location/heading/distance constraints, defines semantics over a discrete grid, and encodes consistency checking, disjunctive constraints, inference, inconsistency explanation (weak-constraint dropping) and presumed information as ASP rules solved by Clingo.
Key results
- Consistency checking for basic HOPA constraints with up to 120 objects and 150 constraints on 50x50 grids runs with mean times of a few seconds (e.g., 100 objects, 150 constraints: mean 15.2 s consistent).
- Disjunctive HOPA constraints (up to 24 disjunctive constraints with 8 disjuncts) add only modest overhead, with mean times typically under 20 s.
- On the cognitive robotics example, the ASP framework rejects that B2 is behind C, which composition-based path-consistency reasoning could not reject.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase the number of objects, constraints, or grid size | ASP HOPA consistency checking · Basic HOPA constraints | computation time | Hurt |
| Use inconsistent rather than consistent instances | ASP HOPA consistency checking · Basic HOPA constraints | computation time | Helped |
| Add disjunctive constraints | ASP HOPA consistency checking · Disjunctive HOPA constraints | computation time | Hurt |
| Increase the number of objects, constraints, granularity, or grid size | ASP OPRA consistency checking · Basic OPRA constraints | computation time | Hurt |
| Use inconsistent rather than consistent instances | ASP OPRA consistency checking · Basic OPRA constraints | maximum computation time | Mixed |
Surprising findings
- Inconsistent instances can show greater maximum solving time and timeouts than consistent ones for OPRA constraints, since the solver must search many combinations to refute consistency.
- Path-consistency (composition and inversion) reasoning is insufficient for OPRA, failing to reject an invalid relation that the ASP approach rejects.
Limitations
- Consistency problem is NP-complete over discretized space; scalability limited, motivating future constraint programming methods.
- Soundness and completeness hold only when grid resolution is at least sensor precision; coarser grids may yield no answer set despite satisfiable constraints.
Experimental setup
Datasets: randomly generated synthetic consistent and inconsistent constraint instances
Benchmarks: randomly generated HOPA and OPRA consistency instances
Metrics: grounding time mean solving time max solving time std of solving time
Baselines: path-consistency / composition-based OPRA reasoning
Builds on: OPRA Answer Set Programming qualitative interval-based distance relations
Closest papers by meaning
- Geometrically-Constrained Agent for Spatial Reasoning (CVPR 2026 · similarity 0.84)
- SpatialClaw: Rethinking Action Interface for Agentic Spatial Reasoning (NeurIPS 2026 · similarity 0.83)
- JRDB-Reasoning: A Difficulty-Graded Benchmark for Visual Reasoning in Robotics (AAAI 2026 · similarity 0.83)
- ClevrSkills: Compositional Language And Visual Reasoning in Robotics (NeurIPS 2024 · similarity 0.83)
- Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning (CVPR 2026 · similarity 0.83)
- Pursuing Minimal Sufficiency in Spatial Reasoning (ICLR 2026 · similarity 0.83)
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